Properties

Label 690.3.k.b.277.7
Level $690$
Weight $3$
Character 690.277
Analytic conductor $18.801$
Analytic rank $0$
Dimension $48$
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: \(48\)
Relative dimension: \(24\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 277.7
Character \(\chi\) \(=\) 690.277
Dual form 690.3.k.b.553.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.29808 - 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 + 4.10164i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-1.22474 + 1.22474i) q^{3} +2.00000i q^{4} +(4.29808 - 2.55470i) q^{5} +2.44949 q^{6} +(4.10164 + 4.10164i) q^{7} +(2.00000 - 2.00000i) q^{8} -3.00000i q^{9} +(-6.85278 - 1.74338i) q^{10} -12.9366 q^{11} +(-2.44949 - 2.44949i) q^{12} +(-7.48881 + 7.48881i) q^{13} -8.20327i q^{14} +(-2.13519 + 8.39291i) q^{15} -4.00000 q^{16} +(-23.2692 - 23.2692i) q^{17} +(-3.00000 + 3.00000i) q^{18} +2.66503i q^{19} +(5.10941 + 8.59616i) q^{20} -10.0469 q^{21} +(12.9366 + 12.9366i) q^{22} +(-3.39116 + 3.39116i) q^{23} +4.89898i q^{24} +(11.9470 - 21.9606i) q^{25} +14.9776 q^{26} +(3.67423 + 3.67423i) q^{27} +(-8.20327 + 8.20327i) q^{28} -13.0859i q^{29} +(10.5281 - 6.25772i) q^{30} +21.6535 q^{31} +(4.00000 + 4.00000i) q^{32} +(15.8440 - 15.8440i) q^{33} +46.5384i q^{34} +(28.1076 + 7.15070i) q^{35} +6.00000 q^{36} +(-1.73017 - 1.73017i) q^{37} +(2.66503 - 2.66503i) q^{38} -18.3438i q^{39} +(3.48675 - 13.7056i) q^{40} -41.1577 q^{41} +(10.0469 + 10.0469i) q^{42} +(-2.10451 + 2.10451i) q^{43} -25.8731i q^{44} +(-7.66411 - 12.8942i) q^{45} +6.78233 q^{46} +(-2.10608 - 2.10608i) q^{47} +(4.89898 - 4.89898i) q^{48} -15.3532i q^{49} +(-33.9076 + 10.0137i) q^{50} +56.9977 q^{51} +(-14.9776 - 14.9776i) q^{52} +(-8.58604 + 8.58604i) q^{53} -7.34847i q^{54} +(-55.6024 + 33.0491i) q^{55} +16.4065 q^{56} +(-3.26398 - 3.26398i) q^{57} +(-13.0859 + 13.0859i) q^{58} -65.6109i q^{59} +(-16.7858 - 4.27038i) q^{60} -39.1540 q^{61} +(-21.6535 - 21.6535i) q^{62} +(12.3049 - 12.3049i) q^{63} -8.00000i q^{64} +(-13.0558 + 51.3192i) q^{65} -31.6880 q^{66} +(-42.4434 - 42.4434i) q^{67} +(46.5384 - 46.5384i) q^{68} -8.30662i q^{69} +(-20.9569 - 35.2583i) q^{70} -119.297 q^{71} +(-6.00000 - 6.00000i) q^{72} +(-86.2712 + 86.2712i) q^{73} +3.46035i q^{74} +(12.2642 + 41.5282i) q^{75} -5.33005 q^{76} +(-53.0611 - 53.0611i) q^{77} +(-18.3438 + 18.3438i) q^{78} -63.9660i q^{79} +(-17.1923 + 10.2188i) q^{80} -9.00000 q^{81} +(41.1577 + 41.1577i) q^{82} +(98.1743 - 98.1743i) q^{83} -20.0938i q^{84} +(-159.459 - 40.5670i) q^{85} +4.20901 q^{86} +(16.0268 + 16.0268i) q^{87} +(-25.8731 + 25.8731i) q^{88} -156.409i q^{89} +(-5.23013 + 20.5583i) q^{90} -61.4328 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-26.5200 + 26.5200i) q^{93} +4.21215i q^{94} +(6.80835 + 11.4545i) q^{95} -9.79796 q^{96} +(49.2914 + 49.2914i) q^{97} +(-15.3532 + 15.3532i) q^{98} +38.8097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + O(q^{10}) \) \( 48q - 48q^{2} - 8q^{5} - 8q^{7} + 96q^{8} + 8q^{10} - 32q^{11} - 24q^{13} + 24q^{15} - 192q^{16} + 72q^{17} - 144q^{18} + 32q^{22} + 24q^{25} + 48q^{26} + 16q^{28} - 24q^{30} + 24q^{31} + 192q^{32} - 24q^{33} + 288q^{36} - 128q^{37} - 16q^{38} - 16q^{40} - 40q^{41} + 48q^{43} - 136q^{47} - 80q^{50} - 48q^{52} + 144q^{53} - 144q^{55} - 32q^{56} + 96q^{57} + 8q^{58} + 128q^{61} - 24q^{62} - 24q^{63} + 184q^{65} + 48q^{66} - 144q^{68} + 40q^{70} - 40q^{71} - 288q^{72} + 40q^{73} - 72q^{75} + 32q^{76} - 104q^{77} + 96q^{78} + 32q^{80} - 432q^{81} + 40q^{82} - 88q^{85} - 96q^{86} + 120q^{87} - 64q^{88} + 24q^{90} + 144q^{91} - 96q^{93} + 312q^{95} + 480q^{97} + 584q^{98} + O(q^{100}) \)

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
\(5\) 4.29808 2.55470i 0.859616 0.510941i
\(6\) 2.44949 0.408248
\(7\) 4.10164 + 4.10164i 0.585948 + 0.585948i 0.936532 0.350583i \(-0.114017\pi\)
−0.350583 + 0.936532i \(0.614017\pi\)
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 3.00000i 0.333333i
\(10\) −6.85278 1.74338i −0.685278 0.174338i
\(11\) −12.9366 −1.17605 −0.588025 0.808842i \(-0.700095\pi\)
−0.588025 + 0.808842i \(0.700095\pi\)
\(12\) −2.44949 2.44949i −0.204124 0.204124i
\(13\) −7.48881 + 7.48881i −0.576062 + 0.576062i −0.933816 0.357754i \(-0.883543\pi\)
0.357754 + 0.933816i \(0.383543\pi\)
\(14\) 8.20327i 0.585948i
\(15\) −2.13519 + 8.39291i −0.142346 + 0.559527i
\(16\) −4.00000 −0.250000
\(17\) −23.2692 23.2692i −1.36878 1.36878i −0.862186 0.506591i \(-0.830905\pi\)
−0.506591 0.862186i \(-0.669095\pi\)
\(18\) −3.00000 + 3.00000i −0.166667 + 0.166667i
\(19\) 2.66503i 0.140265i 0.997538 + 0.0701323i \(0.0223421\pi\)
−0.997538 + 0.0701323i \(0.977658\pi\)
\(20\) 5.10941 + 8.59616i 0.255470 + 0.429808i
\(21\) −10.0469 −0.478425
\(22\) 12.9366 + 12.9366i 0.588025 + 0.588025i
\(23\) −3.39116 + 3.39116i −0.147442 + 0.147442i
\(24\) 4.89898i 0.204124i
\(25\) 11.9470 21.9606i 0.477879 0.878425i
\(26\) 14.9776 0.576062
\(27\) 3.67423 + 3.67423i 0.136083 + 0.136083i
\(28\) −8.20327 + 8.20327i −0.292974 + 0.292974i
\(29\) 13.0859i 0.451237i −0.974216 0.225618i \(-0.927560\pi\)
0.974216 0.225618i \(-0.0724402\pi\)
\(30\) 10.5281 6.25772i 0.350937 0.208591i
\(31\) 21.6535 0.698500 0.349250 0.937030i \(-0.386436\pi\)
0.349250 + 0.937030i \(0.386436\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 15.8440 15.8440i 0.480121 0.480121i
\(34\) 46.5384i 1.36878i
\(35\) 28.1076 + 7.15070i 0.803075 + 0.204306i
\(36\) 6.00000 0.166667
\(37\) −1.73017 1.73017i −0.0467614 0.0467614i 0.683339 0.730101i \(-0.260527\pi\)
−0.730101 + 0.683339i \(0.760527\pi\)
\(38\) 2.66503 2.66503i 0.0701323 0.0701323i
\(39\) 18.3438i 0.470353i
\(40\) 3.48675 13.7056i 0.0871689 0.342639i
\(41\) −41.1577 −1.00385 −0.501923 0.864912i \(-0.667374\pi\)
−0.501923 + 0.864912i \(0.667374\pi\)
\(42\) 10.0469 + 10.0469i 0.239212 + 0.239212i
\(43\) −2.10451 + 2.10451i −0.0489420 + 0.0489420i −0.731154 0.682212i \(-0.761018\pi\)
0.682212 + 0.731154i \(0.261018\pi\)
\(44\) 25.8731i 0.588025i
\(45\) −7.66411 12.8942i −0.170314 0.286539i
\(46\) 6.78233 0.147442
\(47\) −2.10608 2.10608i −0.0448101 0.0448101i 0.684347 0.729157i \(-0.260088\pi\)
−0.729157 + 0.684347i \(0.760088\pi\)
\(48\) 4.89898 4.89898i 0.102062 0.102062i
\(49\) 15.3532i 0.313330i
\(50\) −33.9076 + 10.0137i −0.678152 + 0.200273i
\(51\) 56.9977 1.11760
\(52\) −14.9776 14.9776i −0.288031 0.288031i
\(53\) −8.58604 + 8.58604i −0.162001 + 0.162001i −0.783452 0.621452i \(-0.786543\pi\)
0.621452 + 0.783452i \(0.286543\pi\)
\(54\) 7.34847i 0.136083i
\(55\) −55.6024 + 33.0491i −1.01095 + 0.600892i
\(56\) 16.4065 0.292974
\(57\) −3.26398 3.26398i −0.0572628 0.0572628i
\(58\) −13.0859 + 13.0859i −0.225618 + 0.225618i
\(59\) 65.6109i 1.11205i −0.831166 0.556025i \(-0.812326\pi\)
0.831166 0.556025i \(-0.187674\pi\)
\(60\) −16.7858 4.27038i −0.279764 0.0711731i
\(61\) −39.1540 −0.641869 −0.320935 0.947101i \(-0.603997\pi\)
−0.320935 + 0.947101i \(0.603997\pi\)
\(62\) −21.6535 21.6535i −0.349250 0.349250i
\(63\) 12.3049 12.3049i 0.195316 0.195316i
\(64\) 8.00000i 0.125000i
\(65\) −13.0558 + 51.3192i −0.200859 + 0.789526i
\(66\) −31.6880 −0.480121
\(67\) −42.4434 42.4434i −0.633483 0.633483i 0.315457 0.948940i \(-0.397842\pi\)
−0.948940 + 0.315457i \(0.897842\pi\)
\(68\) 46.5384 46.5384i 0.684389 0.684389i
\(69\) 8.30662i 0.120386i
\(70\) −20.9569 35.2583i −0.299385 0.503690i
\(71\) −119.297 −1.68023 −0.840117 0.542405i \(-0.817514\pi\)
−0.840117 + 0.542405i \(0.817514\pi\)
\(72\) −6.00000 6.00000i −0.0833333 0.0833333i
\(73\) −86.2712 + 86.2712i −1.18180 + 1.18180i −0.202519 + 0.979278i \(0.564913\pi\)
−0.979278 + 0.202519i \(0.935087\pi\)
\(74\) 3.46035i 0.0467614i
\(75\) 12.2642 + 41.5282i 0.163522 + 0.553709i
\(76\) −5.33005 −0.0701323
\(77\) −53.0611 53.0611i −0.689105 0.689105i
\(78\) −18.3438 + 18.3438i −0.235176 + 0.235176i
\(79\) 63.9660i 0.809697i −0.914384 0.404848i \(-0.867324\pi\)
0.914384 0.404848i \(-0.132676\pi\)
\(80\) −17.1923 + 10.2188i −0.214904 + 0.127735i
\(81\) −9.00000 −0.111111
\(82\) 41.1577 + 41.1577i 0.501923 + 0.501923i
\(83\) 98.1743 98.1743i 1.18282 1.18282i 0.203814 0.979010i \(-0.434666\pi\)
0.979010 0.203814i \(-0.0653337\pi\)
\(84\) 20.0938i 0.239212i
\(85\) −159.459 40.5670i −1.87599 0.477259i
\(86\) 4.20901 0.0489420
\(87\) 16.0268 + 16.0268i 0.184217 + 0.184217i
\(88\) −25.8731 + 25.8731i −0.294013 + 0.294013i
\(89\) 156.409i 1.75740i −0.477373 0.878701i \(-0.658411\pi\)
0.477373 0.878701i \(-0.341589\pi\)
\(90\) −5.23013 + 20.5583i −0.0581126 + 0.228426i
\(91\) −61.4328 −0.675085
\(92\) −6.78233 6.78233i −0.0737210 0.0737210i
\(93\) −26.5200 + 26.5200i −0.285161 + 0.285161i
\(94\) 4.21215i 0.0448101i
\(95\) 6.80835 + 11.4545i 0.0716669 + 0.120574i
\(96\) −9.79796 −0.102062
\(97\) 49.2914 + 49.2914i 0.508158 + 0.508158i 0.913961 0.405802i \(-0.133008\pi\)
−0.405802 + 0.913961i \(0.633008\pi\)
\(98\) −15.3532 + 15.3532i −0.156665 + 0.156665i
\(99\) 38.8097i 0.392017i
\(100\) 43.9213 + 23.8940i 0.439213 + 0.238940i
\(101\) −41.2318 −0.408236 −0.204118 0.978946i \(-0.565433\pi\)
−0.204118 + 0.978946i \(0.565433\pi\)
\(102\) −56.9977 56.9977i −0.558801 0.558801i
\(103\) −121.357 + 121.357i −1.17822 + 1.17822i −0.198028 + 0.980196i \(0.563454\pi\)
−0.980196 + 0.198028i \(0.936546\pi\)
\(104\) 29.9552i 0.288031i
\(105\) −43.1825 + 25.6669i −0.411261 + 0.244447i
\(106\) 17.1721 0.162001
\(107\) 79.5289 + 79.5289i 0.743261 + 0.743261i 0.973204 0.229943i \(-0.0738540\pi\)
−0.229943 + 0.973204i \(0.573854\pi\)
\(108\) −7.34847 + 7.34847i −0.0680414 + 0.0680414i
\(109\) 110.939i 1.01779i −0.860828 0.508896i \(-0.830054\pi\)
0.860828 0.508896i \(-0.169946\pi\)
\(110\) 88.6514 + 22.5533i 0.805922 + 0.205030i
\(111\) 4.23804 0.0381805
\(112\) −16.4065 16.4065i −0.146487 0.146487i
\(113\) −107.518 + 107.518i −0.951488 + 0.951488i −0.998877 0.0473884i \(-0.984910\pi\)
0.0473884 + 0.998877i \(0.484910\pi\)
\(114\) 6.52796i 0.0572628i
\(115\) −5.91208 + 23.2389i −0.0514094 + 0.202078i
\(116\) 26.1717 0.225618
\(117\) 22.4664 + 22.4664i 0.192021 + 0.192021i
\(118\) −65.6109 + 65.6109i −0.556025 + 0.556025i
\(119\) 190.884i 1.60407i
\(120\) 12.5154 + 21.0562i 0.104295 + 0.175468i
\(121\) 46.3546 0.383096
\(122\) 39.1540 + 39.1540i 0.320935 + 0.320935i
\(123\) 50.4077 50.4077i 0.409818 0.409818i
\(124\) 43.3070i 0.349250i
\(125\) −4.75380 124.910i −0.0380304 0.999277i
\(126\) −24.6098 −0.195316
\(127\) 78.0096 + 78.0096i 0.614249 + 0.614249i 0.944050 0.329801i \(-0.106982\pi\)
−0.329801 + 0.944050i \(0.606982\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 5.15497i 0.0399610i
\(130\) 64.3750 38.2634i 0.495192 0.294334i
\(131\) 133.553 1.01949 0.509744 0.860326i \(-0.329740\pi\)
0.509744 + 0.860326i \(0.329740\pi\)
\(132\) 31.6880 + 31.6880i 0.240060 + 0.240060i
\(133\) −10.9310 + 10.9310i −0.0821878 + 0.0821878i
\(134\) 84.8868i 0.633483i
\(135\) 25.1787 + 6.40558i 0.186509 + 0.0474487i
\(136\) −93.0769 −0.684389
\(137\) 72.6388 + 72.6388i 0.530210 + 0.530210i 0.920635 0.390425i \(-0.127672\pi\)
−0.390425 + 0.920635i \(0.627672\pi\)
\(138\) −8.30662 + 8.30662i −0.0601929 + 0.0601929i
\(139\) 194.073i 1.39621i −0.715997 0.698103i \(-0.754028\pi\)
0.715997 0.698103i \(-0.245972\pi\)
\(140\) −14.3014 + 56.2153i −0.102153 + 0.401538i
\(141\) 5.15881 0.0365873
\(142\) 119.297 + 119.297i 0.840117 + 0.840117i
\(143\) 96.8794 96.8794i 0.677479 0.677479i
\(144\) 12.0000i 0.0833333i
\(145\) −33.4305 56.2441i −0.230555 0.387890i
\(146\) 172.542 1.18180
\(147\) 18.8037 + 18.8037i 0.127916 + 0.127916i
\(148\) 3.46035 3.46035i 0.0233807 0.0233807i
\(149\) 118.977i 0.798506i 0.916841 + 0.399253i \(0.130730\pi\)
−0.916841 + 0.399253i \(0.869270\pi\)
\(150\) 29.2640 53.7924i 0.195093 0.358616i
\(151\) −211.993 −1.40392 −0.701962 0.712214i \(-0.747692\pi\)
−0.701962 + 0.712214i \(0.747692\pi\)
\(152\) 5.33005 + 5.33005i 0.0350661 + 0.0350661i
\(153\) −69.8077 + 69.8077i −0.456259 + 0.456259i
\(154\) 106.122i 0.689105i
\(155\) 93.0685 55.3183i 0.600442 0.356892i
\(156\) 36.6875 0.235176
\(157\) −161.138 161.138i −1.02636 1.02636i −0.999643 0.0267147i \(-0.991495\pi\)
−0.0267147 0.999643i \(-0.508505\pi\)
\(158\) −63.9660 + 63.9660i −0.404848 + 0.404848i
\(159\) 21.0314i 0.132273i
\(160\) 27.4111 + 6.97351i 0.171320 + 0.0435844i
\(161\) −27.8187 −0.172787
\(162\) 9.00000 + 9.00000i 0.0555556 + 0.0555556i
\(163\) −171.976 + 171.976i −1.05507 + 1.05507i −0.0566742 + 0.998393i \(0.518050\pi\)
−0.998393 + 0.0566742i \(0.981950\pi\)
\(164\) 82.3154i 0.501923i
\(165\) 27.6220 108.575i 0.167406 0.658033i
\(166\) −196.349 −1.18282
\(167\) 145.411 + 145.411i 0.870724 + 0.870724i 0.992551 0.121828i \(-0.0388755\pi\)
−0.121828 + 0.992551i \(0.538876\pi\)
\(168\) −20.0938 + 20.0938i −0.119606 + 0.119606i
\(169\) 56.8354i 0.336304i
\(170\) 118.892 + 200.026i 0.699364 + 1.17662i
\(171\) 7.99508 0.0467549
\(172\) −4.20901 4.20901i −0.0244710 0.0244710i
\(173\) −98.5498 + 98.5498i −0.569652 + 0.569652i −0.932031 0.362379i \(-0.881965\pi\)
0.362379 + 0.932031i \(0.381965\pi\)
\(174\) 32.0537i 0.184217i
\(175\) 139.077 41.0724i 0.794724 0.234699i
\(176\) 51.7462 0.294013
\(177\) 80.3567 + 80.3567i 0.453992 + 0.453992i
\(178\) −156.409 + 156.409i −0.878701 + 0.878701i
\(179\) 150.914i 0.843097i −0.906806 0.421549i \(-0.861487\pi\)
0.906806 0.421549i \(-0.138513\pi\)
\(180\) 25.7885 15.3282i 0.143269 0.0851568i
\(181\) −113.802 −0.628740 −0.314370 0.949301i \(-0.601793\pi\)
−0.314370 + 0.949301i \(0.601793\pi\)
\(182\) 61.4328 + 61.4328i 0.337543 + 0.337543i
\(183\) 47.9537 47.9537i 0.262042 0.262042i
\(184\) 13.5647i 0.0737210i
\(185\) −11.8565 3.01634i −0.0640892 0.0163046i
\(186\) 53.0400 0.285161
\(187\) 301.024 + 301.024i 1.60975 + 1.60975i
\(188\) 4.21215 4.21215i 0.0224051 0.0224051i
\(189\) 30.1408i 0.159475i
\(190\) 4.64615 18.2629i 0.0244534 0.0961203i
\(191\) −5.60105 −0.0293249 −0.0146624 0.999893i \(-0.504667\pi\)
−0.0146624 + 0.999893i \(0.504667\pi\)
\(192\) 9.79796 + 9.79796i 0.0510310 + 0.0510310i
\(193\) 179.654 179.654i 0.930848 0.930848i −0.0669105 0.997759i \(-0.521314\pi\)
0.997759 + 0.0669105i \(0.0213142\pi\)
\(194\) 98.5827i 0.508158i
\(195\) −46.8629 78.8430i −0.240322 0.404323i
\(196\) 30.7063 0.156665
\(197\) −107.119 107.119i −0.543749 0.543749i 0.380876 0.924626i \(-0.375622\pi\)
−0.924626 + 0.380876i \(0.875622\pi\)
\(198\) 38.8097 38.8097i 0.196008 0.196008i
\(199\) 108.814i 0.546805i 0.961900 + 0.273403i \(0.0881491\pi\)
−0.961900 + 0.273403i \(0.911851\pi\)
\(200\) −20.0273 67.8152i −0.100137 0.339076i
\(201\) 103.965 0.517237
\(202\) 41.2318 + 41.2318i 0.204118 + 0.204118i
\(203\) 53.6734 53.6734i 0.264401 0.264401i
\(204\) 113.995i 0.558801i
\(205\) −176.899 + 105.146i −0.862922 + 0.512906i
\(206\) 242.714 1.17822
\(207\) 10.1735 + 10.1735i 0.0491473 + 0.0491473i
\(208\) 29.9552 29.9552i 0.144016 0.144016i
\(209\) 34.4763i 0.164958i
\(210\) 68.8493 + 17.5156i 0.327854 + 0.0834075i
\(211\) 208.930 0.990192 0.495096 0.868838i \(-0.335133\pi\)
0.495096 + 0.868838i \(0.335133\pi\)
\(212\) −17.1721 17.1721i −0.0810003 0.0810003i
\(213\) 146.108 146.108i 0.685953 0.685953i
\(214\) 159.058i 0.743261i
\(215\) −3.66895 + 14.4217i −0.0170649 + 0.0670778i
\(216\) 14.6969 0.0680414
\(217\) 88.8148 + 88.8148i 0.409285 + 0.409285i
\(218\) −110.939 + 110.939i −0.508896 + 0.508896i
\(219\) 211.320i 0.964934i
\(220\) −66.0981 111.205i −0.300446 0.505476i
\(221\) 348.518 1.57700
\(222\) −4.23804 4.23804i −0.0190903 0.0190903i
\(223\) −68.2548 + 68.2548i −0.306075 + 0.306075i −0.843385 0.537310i \(-0.819441\pi\)
0.537310 + 0.843385i \(0.319441\pi\)
\(224\) 32.8131i 0.146487i
\(225\) −65.8819 35.8410i −0.292808 0.159293i
\(226\) 215.036 0.951488
\(227\) −6.98511 6.98511i −0.0307714 0.0307714i 0.691554 0.722325i \(-0.256927\pi\)
−0.722325 + 0.691554i \(0.756927\pi\)
\(228\) 6.52796 6.52796i 0.0286314 0.0286314i
\(229\) 95.6049i 0.417488i −0.977970 0.208744i \(-0.933062\pi\)
0.977970 0.208744i \(-0.0669376\pi\)
\(230\) 29.1510 17.3268i 0.126743 0.0753341i
\(231\) 129.973 0.562652
\(232\) −26.1717 26.1717i −0.112809 0.112809i
\(233\) 221.116 221.116i 0.948996 0.948996i −0.0497647 0.998761i \(-0.515847\pi\)
0.998761 + 0.0497647i \(0.0158471\pi\)
\(234\) 44.9329i 0.192021i
\(235\) −14.4325 3.67168i −0.0614148 0.0156242i
\(236\) 131.222 0.556025
\(237\) 78.3421 + 78.3421i 0.330557 + 0.330557i
\(238\) −190.884 + 190.884i −0.802033 + 0.802033i
\(239\) 210.437i 0.880491i −0.897877 0.440246i \(-0.854891\pi\)
0.897877 0.440246i \(-0.145109\pi\)
\(240\) 8.54077 33.5716i 0.0355865 0.139882i
\(241\) 300.706 1.24774 0.623872 0.781527i \(-0.285559\pi\)
0.623872 + 0.781527i \(0.285559\pi\)
\(242\) −46.3546 46.3546i −0.191548 0.191548i
\(243\) 11.0227 11.0227i 0.0453609 0.0453609i
\(244\) 78.3080i 0.320935i
\(245\) −39.2227 65.9891i −0.160093 0.269343i
\(246\) −100.815 −0.409818
\(247\) −19.9579 19.9579i −0.0808011 0.0808011i
\(248\) 43.3070 43.3070i 0.174625 0.174625i
\(249\) 240.477i 0.965771i
\(250\) −120.156 + 129.663i −0.480623 + 0.518653i
\(251\) −301.201 −1.20000 −0.600002 0.799999i \(-0.704833\pi\)
−0.600002 + 0.799999i \(0.704833\pi\)
\(252\) 24.6098 + 24.6098i 0.0976580 + 0.0976580i
\(253\) 43.8700 43.8700i 0.173399 0.173399i
\(254\) 156.019i 0.614249i
\(255\) 244.981 145.612i 0.960709 0.571028i
\(256\) 16.0000 0.0625000
\(257\) −81.1010 81.1010i −0.315568 0.315568i 0.531494 0.847062i \(-0.321631\pi\)
−0.847062 + 0.531494i \(0.821631\pi\)
\(258\) −5.15497 + 5.15497i −0.0199805 + 0.0199805i
\(259\) 14.1931i 0.0547995i
\(260\) −102.638 26.1116i −0.394763 0.100429i
\(261\) −39.2576 −0.150412
\(262\) −133.553 133.553i −0.509744 0.509744i
\(263\) 203.519 203.519i 0.773838 0.773838i −0.204937 0.978775i \(-0.565699\pi\)
0.978775 + 0.204937i \(0.0656990\pi\)
\(264\) 63.3759i 0.240060i
\(265\) −14.9687 + 58.8382i −0.0564857 + 0.222031i
\(266\) 21.8619 0.0821878
\(267\) 191.561 + 191.561i 0.717456 + 0.717456i
\(268\) 84.8868 84.8868i 0.316742 0.316742i
\(269\) 382.826i 1.42315i 0.702612 + 0.711573i \(0.252017\pi\)
−0.702612 + 0.711573i \(0.747983\pi\)
\(270\) −18.7732 31.5843i −0.0695302 0.116979i
\(271\) 261.659 0.965532 0.482766 0.875749i \(-0.339632\pi\)
0.482766 + 0.875749i \(0.339632\pi\)
\(272\) 93.0769 + 93.0769i 0.342194 + 0.342194i
\(273\) 75.2395 75.2395i 0.275602 0.275602i
\(274\) 145.278i 0.530210i
\(275\) −154.553 + 284.095i −0.562011 + 1.03307i
\(276\) 16.6132 0.0601929
\(277\) −221.694 221.694i −0.800340 0.800340i 0.182809 0.983149i \(-0.441481\pi\)
−0.983149 + 0.182809i \(0.941481\pi\)
\(278\) −194.073 + 194.073i −0.698103 + 0.698103i
\(279\) 64.9605i 0.232833i
\(280\) 70.5167 41.9139i 0.251845 0.149692i
\(281\) −4.44209 −0.0158081 −0.00790407 0.999969i \(-0.502516\pi\)
−0.00790407 + 0.999969i \(0.502516\pi\)
\(282\) −5.15881 5.15881i −0.0182937 0.0182937i
\(283\) 154.746 154.746i 0.546804 0.546804i −0.378711 0.925515i \(-0.623633\pi\)
0.925515 + 0.378711i \(0.123633\pi\)
\(284\) 238.593i 0.840117i
\(285\) −22.3673 5.69034i −0.0784819 0.0199661i
\(286\) −193.759 −0.677479
\(287\) −168.814 168.814i −0.588202 0.588202i
\(288\) 12.0000 12.0000i 0.0416667 0.0416667i
\(289\) 793.913i 2.74710i
\(290\) −22.8136 + 89.6746i −0.0786675 + 0.309223i
\(291\) −120.739 −0.414910
\(292\) −172.542 172.542i −0.590899 0.590899i
\(293\) −194.221 + 194.221i −0.662871 + 0.662871i −0.956056 0.293185i \(-0.905285\pi\)
0.293185 + 0.956056i \(0.405285\pi\)
\(294\) 37.6074i 0.127916i
\(295\) −167.616 282.001i −0.568191 0.955936i
\(296\) −6.92069 −0.0233807
\(297\) −47.5320 47.5320i −0.160040 0.160040i
\(298\) 118.977 118.977i 0.399253 0.399253i
\(299\) 50.7916i 0.169872i
\(300\) −83.0564 + 24.5283i −0.276855 + 0.0817611i
\(301\) −17.2638 −0.0573550
\(302\) 211.993 + 211.993i 0.701962 + 0.701962i
\(303\) 50.4985 50.4985i 0.166662 0.166662i
\(304\) 10.6601i 0.0350661i
\(305\) −168.287 + 100.027i −0.551761 + 0.327957i
\(306\) 139.615 0.456259
\(307\) 342.709 + 342.709i 1.11632 + 1.11632i 0.992277 + 0.124040i \(0.0395851\pi\)
0.124040 + 0.992277i \(0.460415\pi\)
\(308\) 106.122 106.122i 0.344552 0.344552i
\(309\) 297.263i 0.962016i
\(310\) −148.387 37.7502i −0.478667 0.121775i
\(311\) 44.3383 0.142567 0.0712834 0.997456i \(-0.477291\pi\)
0.0712834 + 0.997456i \(0.477291\pi\)
\(312\) −36.6875 36.6875i −0.117588 0.117588i
\(313\) −3.37158 + 3.37158i −0.0107718 + 0.0107718i −0.712472 0.701700i \(-0.752425\pi\)
0.701700 + 0.712472i \(0.252425\pi\)
\(314\) 322.276i 1.02636i
\(315\) 21.4521 84.3229i 0.0681019 0.267692i
\(316\) 127.932 0.404848
\(317\) 65.0482 + 65.0482i 0.205199 + 0.205199i 0.802223 0.597024i \(-0.203650\pi\)
−0.597024 + 0.802223i \(0.703650\pi\)
\(318\) −21.0314 + 21.0314i −0.0661365 + 0.0661365i
\(319\) 169.286i 0.530677i
\(320\) −20.4376 34.3846i −0.0638676 0.107452i
\(321\) −194.805 −0.606870
\(322\) 27.8187 + 27.8187i 0.0863933 + 0.0863933i
\(323\) 62.0131 62.0131i 0.191991 0.191991i
\(324\) 18.0000i 0.0555556i
\(325\) 74.9903 + 253.928i 0.230739 + 0.781316i
\(326\) 343.952 1.05507
\(327\) 135.872 + 135.872i 0.415512 + 0.415512i
\(328\) −82.3154 + 82.3154i −0.250962 + 0.250962i
\(329\) 17.2767i 0.0525128i
\(330\) −136.197 + 80.9534i −0.412720 + 0.245313i
\(331\) −50.7044 −0.153186 −0.0765928 0.997062i \(-0.524404\pi\)
−0.0765928 + 0.997062i \(0.524404\pi\)
\(332\) 196.349 + 196.349i 0.591412 + 0.591412i
\(333\) −5.19052 + 5.19052i −0.0155871 + 0.0155871i
\(334\) 290.822i 0.870724i
\(335\) −290.855 73.9948i −0.868225 0.220880i
\(336\) 40.1877 0.119606
\(337\) 80.1441 + 80.1441i 0.237816 + 0.237816i 0.815945 0.578129i \(-0.196217\pi\)
−0.578129 + 0.815945i \(0.696217\pi\)
\(338\) 56.8354 56.8354i 0.168152 0.168152i
\(339\) 263.365i 0.776887i
\(340\) 81.1341 318.918i 0.238630 0.937994i
\(341\) −280.122 −0.821472
\(342\) −7.99508 7.99508i −0.0233774 0.0233774i
\(343\) 263.953 263.953i 0.769543 0.769543i
\(344\) 8.41803i 0.0244710i
\(345\) −21.2210 35.7025i −0.0615100 0.103486i
\(346\) 197.100 0.569652
\(347\) 312.785 + 312.785i 0.901398 + 0.901398i 0.995557 0.0941595i \(-0.0300164\pi\)
−0.0941595 + 0.995557i \(0.530016\pi\)
\(348\) −32.0537 + 32.0537i −0.0921083 + 0.0921083i
\(349\) 12.2678i 0.0351514i −0.999846 0.0175757i \(-0.994405\pi\)
0.999846 0.0175757i \(-0.00559481\pi\)
\(350\) −180.149 98.0044i −0.514712 0.280013i
\(351\) −55.0313 −0.156784
\(352\) −51.7462 51.7462i −0.147006 0.147006i
\(353\) −394.880 + 394.880i −1.11864 + 1.11864i −0.126699 + 0.991941i \(0.540438\pi\)
−0.991941 + 0.126699i \(0.959562\pi\)
\(354\) 160.713i 0.453992i
\(355\) −512.746 + 304.767i −1.44436 + 0.858500i
\(356\) 312.817 0.878701
\(357\) 233.784 + 233.784i 0.654857 + 0.654857i
\(358\) −150.914 + 150.914i −0.421549 + 0.421549i
\(359\) 405.015i 1.12818i 0.825715 + 0.564088i \(0.190772\pi\)
−0.825715 + 0.564088i \(0.809228\pi\)
\(360\) −41.1167 10.4603i −0.114213 0.0290563i
\(361\) 353.898 0.980326
\(362\) 113.802 + 113.802i 0.314370 + 0.314370i
\(363\) −56.7725 + 56.7725i −0.156398 + 0.156398i
\(364\) 122.866i 0.337543i
\(365\) −150.403 + 591.198i −0.412064 + 1.61972i
\(366\) −95.9074 −0.262042
\(367\) 17.0463 + 17.0463i 0.0464477 + 0.0464477i 0.729949 0.683501i \(-0.239544\pi\)
−0.683501 + 0.729949i \(0.739544\pi\)
\(368\) 13.5647 13.5647i 0.0368605 0.0368605i
\(369\) 123.473i 0.334615i
\(370\) 8.84016 + 14.8728i 0.0238923 + 0.0401969i
\(371\) −70.4336 −0.189848
\(372\) −53.0400 53.0400i −0.142581 0.142581i
\(373\) −330.618 + 330.618i −0.886375 + 0.886375i −0.994173 0.107798i \(-0.965620\pi\)
0.107798 + 0.994173i \(0.465620\pi\)
\(374\) 602.047i 1.60975i
\(375\) 158.805 + 147.160i 0.423479 + 0.392427i
\(376\) −8.42430 −0.0224051
\(377\) 97.9975 + 97.9975i 0.259940 + 0.259940i
\(378\) 30.1408 30.1408i 0.0797374 0.0797374i
\(379\) 169.928i 0.448358i 0.974548 + 0.224179i \(0.0719700\pi\)
−0.974548 + 0.224179i \(0.928030\pi\)
\(380\) −22.9090 + 13.6167i −0.0602868 + 0.0358334i
\(381\) −191.084 −0.501532
\(382\) 5.60105 + 5.60105i 0.0146624 + 0.0146624i
\(383\) −159.003 + 159.003i −0.415151 + 0.415151i −0.883528 0.468377i \(-0.844839\pi\)
0.468377 + 0.883528i \(0.344839\pi\)
\(384\) 19.5959i 0.0510310i
\(385\) −363.616 92.5055i −0.944457 0.240274i
\(386\) −359.308 −0.930848
\(387\) 6.31352 + 6.31352i 0.0163140 + 0.0163140i
\(388\) −98.5827 + 98.5827i −0.254079 + 0.254079i
\(389\) 494.731i 1.27180i −0.771770 0.635901i \(-0.780629\pi\)
0.771770 0.635901i \(-0.219371\pi\)
\(390\) −31.9801 + 125.706i −0.0820003 + 0.322323i
\(391\) 157.820 0.403631
\(392\) −30.7063 30.7063i −0.0783324 0.0783324i
\(393\) −163.568 + 163.568i −0.416204 + 0.416204i
\(394\) 214.237i 0.543749i
\(395\) −163.414 274.931i −0.413707 0.696028i
\(396\) −77.6194 −0.196008
\(397\) 61.8230 + 61.8230i 0.155725 + 0.155725i 0.780669 0.624944i \(-0.214878\pi\)
−0.624944 + 0.780669i \(0.714878\pi\)
\(398\) 108.814 108.814i 0.273403 0.273403i
\(399\) 26.7753i 0.0671060i
\(400\) −47.7879 + 87.8425i −0.119470 + 0.219606i
\(401\) −301.250 −0.751248 −0.375624 0.926772i \(-0.622572\pi\)
−0.375624 + 0.926772i \(0.622572\pi\)
\(402\) −103.965 103.965i −0.258619 0.258619i
\(403\) −162.159 + 162.159i −0.402380 + 0.402380i
\(404\) 82.4637i 0.204118i
\(405\) −38.6827 + 22.9923i −0.0955129 + 0.0567712i
\(406\) −107.347 −0.264401
\(407\) 22.3825 + 22.3825i 0.0549938 + 0.0549938i
\(408\) 113.995 113.995i 0.279401 0.279401i
\(409\) 425.582i 1.04054i −0.854001 0.520271i \(-0.825831\pi\)
0.854001 0.520271i \(-0.174169\pi\)
\(410\) 282.045 + 71.7534i 0.687914 + 0.175008i
\(411\) −177.928 −0.432915
\(412\) −242.714 242.714i −0.589112 0.589112i
\(413\) 269.112 269.112i 0.651604 0.651604i
\(414\) 20.3470i 0.0491473i
\(415\) 171.155 672.767i 0.412421 1.62113i
\(416\) −59.9105 −0.144016
\(417\) 237.689 + 237.689i 0.569999 + 0.569999i
\(418\) −34.4763 + 34.4763i −0.0824791 + 0.0824791i
\(419\) 253.765i 0.605645i −0.953047 0.302822i \(-0.902071\pi\)
0.953047 0.302822i \(-0.0979289\pi\)
\(420\) −51.3338 86.3649i −0.122223 0.205631i
\(421\) 239.342 0.568508 0.284254 0.958749i \(-0.408254\pi\)
0.284254 + 0.958749i \(0.408254\pi\)
\(422\) −208.930 208.930i −0.495096 0.495096i
\(423\) −6.31823 + 6.31823i −0.0149367 + 0.0149367i
\(424\) 34.3441i 0.0810003i
\(425\) −789.004 + 233.010i −1.85648 + 0.548258i
\(426\) −292.216 −0.685953
\(427\) −160.596 160.596i −0.376102 0.376102i
\(428\) −159.058 + 159.058i −0.371630 + 0.371630i
\(429\) 237.305i 0.553159i
\(430\) 18.0907 10.7528i 0.0420714 0.0250065i
\(431\) 515.995 1.19720 0.598602 0.801047i \(-0.295723\pi\)
0.598602 + 0.801047i \(0.295723\pi\)
\(432\) −14.6969 14.6969i −0.0340207 0.0340207i
\(433\) −123.940 + 123.940i −0.286237 + 0.286237i −0.835590 0.549353i \(-0.814874\pi\)
0.549353 + 0.835590i \(0.314874\pi\)
\(434\) 177.630i 0.409285i
\(435\) 109.828 + 27.9408i 0.252479 + 0.0642318i
\(436\) 221.879 0.508896
\(437\) −9.03755 9.03755i −0.0206809 0.0206809i
\(438\) −211.320 + 211.320i −0.482467 + 0.482467i
\(439\) 177.022i 0.403238i −0.979464 0.201619i \(-0.935380\pi\)
0.979464 0.201619i \(-0.0646203\pi\)
\(440\) −45.1066 + 177.303i −0.102515 + 0.402961i
\(441\) −46.0595 −0.104443
\(442\) −348.518 348.518i −0.788501 0.788501i
\(443\) 172.073 172.073i 0.388428 0.388428i −0.485699 0.874126i \(-0.661435\pi\)
0.874126 + 0.485699i \(0.161435\pi\)
\(444\) 8.47608i 0.0190903i
\(445\) −399.578 672.257i −0.897928 1.51069i
\(446\) 136.510 0.306075
\(447\) −145.717 145.717i −0.325989 0.325989i
\(448\) 32.8131 32.8131i 0.0732435 0.0732435i
\(449\) 661.173i 1.47254i 0.676685 + 0.736272i \(0.263416\pi\)
−0.676685 + 0.736272i \(0.736584\pi\)
\(450\) 30.0410 + 101.723i 0.0667577 + 0.226051i
\(451\) 532.439 1.18057
\(452\) −215.036 215.036i −0.475744 0.475744i
\(453\) 259.637 259.637i 0.573150 0.573150i
\(454\) 13.9702i 0.0307714i
\(455\) −264.043 + 156.942i −0.580314 + 0.344928i
\(456\) −13.0559 −0.0286314
\(457\) 397.994 + 397.994i 0.870885 + 0.870885i 0.992569 0.121684i \(-0.0388295\pi\)
−0.121684 + 0.992569i \(0.538829\pi\)
\(458\) −95.6049 + 95.6049i −0.208744 + 0.208744i
\(459\) 170.993i 0.372534i
\(460\) −46.4778 11.8242i −0.101039 0.0257047i
\(461\) 23.4186 0.0507996 0.0253998 0.999677i \(-0.491914\pi\)
0.0253998 + 0.999677i \(0.491914\pi\)
\(462\) −129.973 129.973i −0.281326 0.281326i
\(463\) 109.823 109.823i 0.237199 0.237199i −0.578490 0.815689i \(-0.696358\pi\)
0.815689 + 0.578490i \(0.196358\pi\)
\(464\) 52.3434i 0.112809i
\(465\) −46.2344 + 181.736i −0.0994288 + 0.390830i
\(466\) −442.232 −0.948996
\(467\) −585.760 585.760i −1.25430 1.25430i −0.953771 0.300534i \(-0.902835\pi\)
−0.300534 0.953771i \(-0.597165\pi\)
\(468\) −44.9329 + 44.9329i −0.0960104 + 0.0960104i
\(469\) 348.175i 0.742377i
\(470\) 10.7608 + 18.1042i 0.0228953 + 0.0385195i
\(471\) 394.706 0.838018
\(472\) −131.222 131.222i −0.278012 0.278012i
\(473\) 27.2251 27.2251i 0.0575583 0.0575583i
\(474\) 156.684i 0.330557i
\(475\) 58.5257 + 31.8390i 0.123212 + 0.0670296i
\(476\) 381.768 0.802033
\(477\) 25.7581 + 25.7581i 0.0540002 + 0.0540002i
\(478\) −210.437 + 210.437i −0.440246 + 0.440246i
\(479\) 654.854i 1.36713i 0.729891 + 0.683564i \(0.239571\pi\)
−0.729891 + 0.683564i \(0.760429\pi\)
\(480\) −42.1124 + 25.0309i −0.0877342 + 0.0521477i
\(481\) 25.9139 0.0538750
\(482\) −300.706 300.706i −0.623872 0.623872i
\(483\) 34.0708 34.0708i 0.0705399 0.0705399i
\(484\) 92.7092i 0.191548i
\(485\) 337.783 + 85.9334i 0.696460 + 0.177182i
\(486\) −22.0454 −0.0453609
\(487\) 168.359 + 168.359i 0.345706 + 0.345706i 0.858507 0.512801i \(-0.171392\pi\)
−0.512801 + 0.858507i \(0.671392\pi\)
\(488\) −78.3080 + 78.3080i −0.160467 + 0.160467i
\(489\) 421.253i 0.861459i
\(490\) −26.7663 + 105.212i −0.0546252 + 0.214718i
\(491\) −705.190 −1.43623 −0.718117 0.695923i \(-0.754996\pi\)
−0.718117 + 0.695923i \(0.754996\pi\)
\(492\) 100.815 + 100.815i 0.204909 + 0.204909i
\(493\) −304.498 + 304.498i −0.617642 + 0.617642i
\(494\) 39.9158i 0.0808011i
\(495\) 99.1472 + 166.807i 0.200297 + 0.336984i
\(496\) −86.6140 −0.174625
\(497\) −489.311 489.311i −0.984530 0.984530i
\(498\) 240.477 240.477i 0.482886 0.482886i
\(499\) 199.214i 0.399227i −0.979875 0.199614i \(-0.936031\pi\)
0.979875 0.199614i \(-0.0639687\pi\)
\(500\) 249.819 9.50760i 0.499638 0.0190152i
\(501\) −356.182 −0.710943
\(502\) 301.201 + 301.201i 0.600002 + 0.600002i
\(503\) 10.4047 10.4047i 0.0206852 0.0206852i −0.696689 0.717374i \(-0.745344\pi\)
0.717374 + 0.696689i \(0.245344\pi\)
\(504\) 49.2196i 0.0976580i
\(505\) −177.218 + 105.335i −0.350926 + 0.208584i
\(506\) −87.7400 −0.173399
\(507\) −69.6089 69.6089i −0.137296 0.137296i
\(508\) −156.019 + 156.019i −0.307124 + 0.307124i
\(509\) 691.773i 1.35908i −0.733637 0.679541i \(-0.762179\pi\)
0.733637 0.679541i \(-0.237821\pi\)
\(510\) −390.593 99.3685i −0.765869 0.194840i
\(511\) −707.706 −1.38494
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −9.79193 + 9.79193i −0.0190876 + 0.0190876i
\(514\) 162.202i 0.315568i
\(515\) −211.571 + 831.634i −0.410818 + 1.61482i
\(516\) 10.3099 0.0199805
\(517\) 27.2454 + 27.2454i 0.0526990 + 0.0526990i
\(518\) −14.1931 + 14.1931i −0.0273998 + 0.0273998i
\(519\) 241.397i 0.465119i
\(520\) 76.5267 + 128.750i 0.147167 + 0.247596i
\(521\) 928.776 1.78268 0.891340 0.453336i \(-0.149766\pi\)
0.891340 + 0.453336i \(0.149766\pi\)
\(522\) 39.2576 + 39.2576i 0.0752061 + 0.0752061i
\(523\) 167.034 167.034i 0.319377 0.319377i −0.529151 0.848528i \(-0.677490\pi\)
0.848528 + 0.529151i \(0.177490\pi\)
\(524\) 267.106i 0.509744i
\(525\) −120.030 + 220.637i −0.228629 + 0.420260i
\(526\) −407.039 −0.773838
\(527\) −503.860 503.860i −0.956091 0.956091i
\(528\) −63.3759 + 63.3759i −0.120030 + 0.120030i
\(529\) 23.0000i 0.0434783i
\(530\) 73.8069 43.8695i 0.139258 0.0827727i
\(531\) −196.833 −0.370683
\(532\) −21.8619 21.8619i −0.0410939 0.0410939i
\(533\) 308.222 308.222i 0.578278 0.578278i
\(534\) 383.122i 0.717456i
\(535\) 544.994 + 138.649i 1.01868 + 0.259157i
\(536\) −169.774 −0.316742
\(537\) 184.832 + 184.832i 0.344193 + 0.344193i
\(538\) 382.826 382.826i 0.711573 0.711573i
\(539\) 198.617i 0.368492i
\(540\) −12.8112 + 50.3575i −0.0237244 + 0.0932546i
\(541\) −233.251 −0.431148 −0.215574 0.976488i \(-0.569162\pi\)
−0.215574 + 0.976488i \(0.569162\pi\)
\(542\) −261.659 261.659i −0.482766 0.482766i
\(543\) 139.378 139.378i 0.256682 0.256682i
\(544\) 186.154i 0.342194i
\(545\) −283.417 476.826i −0.520031 0.874911i
\(546\) −150.479 −0.275602
\(547\) −65.6316 65.6316i −0.119985 0.119985i 0.644565 0.764550i \(-0.277039\pi\)
−0.764550 + 0.644565i \(0.777039\pi\)
\(548\) −145.278 + 145.278i −0.265105 + 0.265105i
\(549\) 117.462i 0.213956i
\(550\) 438.648 129.542i 0.797542 0.235531i
\(551\) 34.8742 0.0632925
\(552\) −16.6132 16.6132i −0.0300965 0.0300965i
\(553\) 262.365 262.365i 0.474440 0.474440i
\(554\) 443.388i 0.800340i
\(555\) 18.2154 10.8269i 0.0328206 0.0195080i
\(556\) 388.145 0.698103
\(557\) −41.4036 41.4036i −0.0743332 0.0743332i 0.668963 0.743296i \(-0.266739\pi\)
−0.743296 + 0.668963i \(0.766739\pi\)
\(558\) −64.9605 + 64.9605i −0.116417 + 0.116417i
\(559\) 31.5205i 0.0563873i
\(560\) −112.431 28.6028i −0.200769 0.0510764i
\(561\) −737.354 −1.31436
\(562\) 4.44209 + 4.44209i 0.00790407 + 0.00790407i
\(563\) −715.121 + 715.121i −1.27020 + 1.27020i −0.324213 + 0.945984i \(0.605099\pi\)
−0.945984 + 0.324213i \(0.894901\pi\)
\(564\) 10.3176i 0.0182937i
\(565\) −187.445 + 736.799i −0.331761 + 1.30407i
\(566\) −309.491 −0.546804
\(567\) −36.9147 36.9147i −0.0651053 0.0651053i
\(568\) −238.593 + 238.593i −0.420059 + 0.420059i
\(569\) 332.987i 0.585215i −0.956233 0.292608i \(-0.905477\pi\)
0.956233 0.292608i \(-0.0945229\pi\)
\(570\) 16.6770 + 28.0577i 0.0292579 + 0.0492240i
\(571\) −42.8085 −0.0749712 −0.0374856 0.999297i \(-0.511935\pi\)
−0.0374856 + 0.999297i \(0.511935\pi\)
\(572\) 193.759 + 193.759i 0.338739 + 0.338739i
\(573\) 6.85986 6.85986i 0.0119718 0.0119718i
\(574\) 337.628i 0.588202i
\(575\) 33.9579 + 114.986i 0.0590573 + 0.199976i
\(576\) −24.0000 −0.0416667
\(577\) 186.404 + 186.404i 0.323057 + 0.323057i 0.849939 0.526882i \(-0.176639\pi\)
−0.526882 + 0.849939i \(0.676639\pi\)
\(578\) 793.913 793.913i 1.37355 1.37355i
\(579\) 440.060i 0.760035i
\(580\) 112.488 66.8610i 0.193945 0.115278i
\(581\) 805.351 1.38615
\(582\) 120.739 + 120.739i 0.207455 + 0.207455i
\(583\) 111.074 111.074i 0.190521 0.190521i
\(584\) 345.085i 0.590899i
\(585\) 153.958 + 39.1675i 0.263175 + 0.0669529i
\(586\) 388.443 0.662871
\(587\) 692.061 + 692.061i 1.17898 + 1.17898i 0.980004 + 0.198976i \(0.0637616\pi\)
0.198976 + 0.980004i \(0.436238\pi\)
\(588\) −37.6074 + 37.6074i −0.0639581 + 0.0639581i
\(589\) 57.7072i 0.0979748i
\(590\) −114.385 + 449.618i −0.193872 + 0.762064i
\(591\) 262.386 0.443970
\(592\) 6.92069 + 6.92069i 0.0116904 + 0.0116904i
\(593\) 453.459 453.459i 0.764686 0.764686i −0.212480 0.977165i \(-0.568154\pi\)
0.977165 + 0.212480i \(0.0681539\pi\)
\(594\) 95.0639i 0.160040i
\(595\) −487.651 820.434i −0.819582 1.37888i
\(596\) −237.955 −0.399253
\(597\) −133.270 133.270i −0.223232 0.223232i
\(598\) −50.7916 + 50.7916i −0.0849358 + 0.0849358i
\(599\) 644.669i 1.07624i 0.842868 + 0.538121i \(0.180866\pi\)
−0.842868 + 0.538121i \(0.819134\pi\)
\(600\) 107.585 + 58.5280i 0.179308 + 0.0975467i
\(601\) −147.557 −0.245519 −0.122760 0.992436i \(-0.539174\pi\)
−0.122760 + 0.992436i \(0.539174\pi\)
\(602\) 17.2638 + 17.2638i 0.0286775 + 0.0286775i
\(603\) −127.330 + 127.330i −0.211161 + 0.211161i
\(604\) 423.985i 0.701962i
\(605\) 199.236 118.422i 0.329315 0.195739i
\(606\) −100.997 −0.166662
\(607\) 280.715 + 280.715i 0.462462 + 0.462462i 0.899462 0.436999i \(-0.143959\pi\)
−0.436999 + 0.899462i \(0.643959\pi\)
\(608\) −10.6601 + 10.6601i −0.0175331 + 0.0175331i
\(609\) 131.473i 0.215883i
\(610\) 268.314 + 68.2602i 0.439859 + 0.111902i
\(611\) 31.5440 0.0516268
\(612\) −139.615 139.615i −0.228130 0.228130i
\(613\) 534.330 534.330i 0.871665 0.871665i −0.120989 0.992654i \(-0.538607\pi\)
0.992654 + 0.120989i \(0.0386066\pi\)
\(614\) 685.419i 1.11632i
\(615\) 87.8796 345.433i 0.142894 0.561679i
\(616\) −212.244 −0.344552
\(617\) −747.441 747.441i −1.21141 1.21141i −0.970563 0.240848i \(-0.922574\pi\)
−0.240848 0.970563i \(-0.577426\pi\)
\(618\) −297.263 + 297.263i −0.481008 + 0.481008i
\(619\) 627.150i 1.01317i −0.862191 0.506583i \(-0.830908\pi\)
0.862191 0.506583i \(-0.169092\pi\)
\(620\) 110.637 + 186.137i 0.178446 + 0.300221i
\(621\) −24.9199 −0.0401286
\(622\) −44.3383 44.3383i −0.0712834 0.0712834i
\(623\) 641.532 641.532i 1.02975 1.02975i
\(624\) 73.3751i 0.117588i
\(625\) −339.539 524.727i −0.543263 0.839563i
\(626\) 6.74316 0.0107718
\(627\) 42.2246 + 42.2246i 0.0673439 + 0.0673439i
\(628\) 322.276 322.276i 0.513179 0.513179i
\(629\) 80.5195i 0.128012i
\(630\) −105.775 + 62.8708i −0.167897 + 0.0997949i
\(631\) 23.8992 0.0378750 0.0189375 0.999821i \(-0.493972\pi\)
0.0189375 + 0.999821i \(0.493972\pi\)
\(632\) −127.932 127.932i −0.202424 0.202424i
\(633\) −255.887 + 255.887i −0.404244 + 0.404244i
\(634\) 130.096i 0.205199i
\(635\) 534.583 + 136.000i 0.841863 + 0.214173i
\(636\) 42.0628 0.0661365
\(637\) 114.977 + 114.977i 0.180497 + 0.180497i
\(638\) 169.286 169.286i 0.265339 0.265339i
\(639\) 357.890i 0.560078i
\(640\) −13.9470 + 54.8223i −0.0217922 + 0.0856598i
\(641\) −406.130 −0.633588 −0.316794 0.948494i \(-0.602606\pi\)
−0.316794 + 0.948494i \(0.602606\pi\)
\(642\) 194.805 + 194.805i 0.303435 + 0.303435i
\(643\) −37.4307 + 37.4307i −0.0582126 + 0.0582126i −0.735614 0.677401i \(-0.763106\pi\)
0.677401 + 0.735614i \(0.263106\pi\)
\(644\) 55.6373i 0.0863933i
\(645\) −13.1694 22.1565i −0.0204177 0.0343511i
\(646\) −124.026 −0.191991
\(647\) 361.519 + 361.519i 0.558762 + 0.558762i 0.928955 0.370193i \(-0.120708\pi\)
−0.370193 + 0.928955i \(0.620708\pi\)
\(648\) −18.0000 + 18.0000i −0.0277778 + 0.0277778i
\(649\) 848.780i 1.30783i
\(650\) 178.937 328.918i 0.275288 0.506028i
\(651\) −217.551 −0.334180
\(652\) −343.952 343.952i −0.527533 0.527533i
\(653\) −613.695 + 613.695i −0.939809 + 0.939809i −0.998289 0.0584794i \(-0.981375\pi\)
0.0584794 + 0.998289i \(0.481375\pi\)
\(654\) 271.745i 0.415512i
\(655\) 574.021 341.188i 0.876368 0.520897i
\(656\) 164.631 0.250962
\(657\) 258.814 + 258.814i 0.393933 + 0.393933i
\(658\) −17.2767 + 17.2767i −0.0262564 + 0.0262564i
\(659\) 43.1767i 0.0655185i −0.999463 0.0327592i \(-0.989571\pi\)
0.999463 0.0327592i \(-0.0104295\pi\)
\(660\) 217.151 + 55.2441i 0.329016 + 0.0837032i
\(661\) 121.963 0.184513 0.0922564 0.995735i \(-0.470592\pi\)
0.0922564 + 0.995735i \(0.470592\pi\)
\(662\) 50.7044 + 50.7044i 0.0765928 + 0.0765928i
\(663\) −426.845 + 426.845i −0.643809 + 0.643809i
\(664\) 392.697i 0.591412i
\(665\) −19.0568 + 74.9076i −0.0286569 + 0.112643i
\(666\) 10.3810 0.0155871
\(667\) 44.3763 + 44.3763i 0.0665312 + 0.0665312i
\(668\) −290.822 + 290.822i −0.435362 + 0.435362i
\(669\) 167.189i 0.249909i
\(670\) 216.860 + 364.850i 0.323672 + 0.544552i
\(671\) 506.518 0.754871
\(672\) −40.1877 40.1877i −0.0598031 0.0598031i
\(673\) 320.935 320.935i 0.476873 0.476873i −0.427257 0.904130i \(-0.640520\pi\)
0.904130 + 0.427257i \(0.140520\pi\)
\(674\) 160.288i 0.237816i
\(675\) 124.585 36.7925i 0.184570 0.0545074i
\(676\) −113.671 −0.168152
\(677\) −827.103 827.103i −1.22172 1.22172i −0.967021 0.254696i \(-0.918024\pi\)
−0.254696 0.967021i \(-0.581976\pi\)
\(678\) −263.365 + 263.365i −0.388443 + 0.388443i
\(679\) 404.351i 0.595509i
\(680\) −400.052 + 237.784i −0.588312 + 0.349682i
\(681\) 17.1100 0.0251248
\(682\) 280.122 + 280.122i 0.410736 + 0.410736i
\(683\) 400.994 400.994i 0.587107 0.587107i −0.349740 0.936847i \(-0.613730\pi\)
0.936847 + 0.349740i \(0.113730\pi\)
\(684\) 15.9902i 0.0233774i
\(685\) 497.778 + 126.637i 0.726683 + 0.184871i
\(686\) −527.907 −0.769543
\(687\) 117.092 + 117.092i 0.170439 + 0.170439i
\(688\) 8.41803 8.41803i 0.0122355 0.0122355i
\(689\) 128.598i 0.186645i
\(690\) −14.4816 + 56.9235i −0.0209878 + 0.0824978i
\(691\) 802.239 1.16098 0.580491 0.814267i \(-0.302861\pi\)
0.580491 + 0.814267i \(0.302861\pi\)
\(692\) −197.100 197.100i −0.284826 0.284826i
\(693\) −159.183 + 159.183i −0.229702 + 0.229702i
\(694\) 625.570i 0.901398i
\(695\) −495.798 834.140i −0.713378 1.20020i
\(696\) 64.1074 0.0921083
\(697\) 957.707 + 957.707i 1.37404 + 1.37404i
\(698\) −12.2678 + 12.2678i −0.0175757 + 0.0175757i
\(699\) 541.622i 0.774852i
\(700\) 82.1447 + 278.153i 0.117350 + 0.397362i
\(701\) 896.380 1.27872 0.639358 0.768909i \(-0.279200\pi\)
0.639358 + 0.768909i \(0.279200\pi\)
\(702\) 55.0313 + 55.0313i 0.0783922 + 0.0783922i
\(703\) 4.61096 4.61096i 0.00655897 0.00655897i
\(704\) 103.492i 0.147006i
\(705\) 22.1730 13.1792i 0.0314510 0.0186939i
\(706\) 789.760 1.11864
\(707\) −169.118 169.118i −0.239205 0.239205i
\(708\) −160.713 + 160.713i −0.226996 + 0.226996i
\(709\) 266.000i 0.375176i 0.982248 + 0.187588i \(0.0600670\pi\)
−0.982248 + 0.187588i \(0.939933\pi\)
\(710\) 817.514 + 207.979i 1.15143 + 0.292928i
\(711\) −191.898 −0.269899
\(712\) −312.817 312.817i −0.439350 0.439350i
\(713\) −73.4306 + 73.4306i −0.102988 + 0.102988i
\(714\) 467.568i 0.654857i
\(715\) 168.897 663.894i 0.236220 0.928523i
\(716\) 301.829 0.421549
\(717\) 257.732 + 257.732i 0.359459 + 0.359459i
\(718\) 405.015 405.015i 0.564088 0.564088i
\(719\) 1262.51i 1.75592i 0.478734 + 0.877960i \(0.341096\pi\)
−0.478734 + 0.877960i \(0.658904\pi\)
\(720\) 30.6564 + 51.5770i 0.0425784 + 0.0716347i
\(721\) −995.525 −1.38076
\(722\) −353.898 353.898i −0.490163 0.490163i
\(723\) −368.288 + 368.288i −0.509389 + 0.509389i
\(724\) 227.604i 0.314370i
\(725\) −287.374 156.337i −0.396378 0.215637i
\(726\) 113.545 0.156398
\(727\) −530.129 530.129i −0.729201 0.729201i 0.241259 0.970461i \(-0.422440\pi\)
−0.970461 + 0.241259i \(0.922440\pi\)
\(728\) −122.866 + 122.866i −0.168771 + 0.168771i
\(729\) 27.0000i 0.0370370i
\(730\) 741.601 440.795i 1.01589 0.603828i
\(731\) 97.9405 0.133982
\(732\) 95.9074 + 95.9074i 0.131021 + 0.131021i
\(733\) −468.474 + 468.474i −0.639119 + 0.639119i −0.950338 0.311220i \(-0.899263\pi\)
0.311220 + 0.950338i \(0.399263\pi\)
\(734\) 34.0926i 0.0464477i
\(735\) 128.858 + 32.7819i 0.175317 + 0.0446013i
\(736\) −27.1293 −0.0368605
\(737\) 549.071 + 549.071i 0.745009 + 0.745009i
\(738\) 123.473 123.473i 0.167308 0.167308i
\(739\) 1042.62i 1.41085i −0.708785 0.705424i \(-0.750757\pi\)
0.708785 0.705424i \(-0.249243\pi\)
\(740\) 6.03269 23.7130i 0.00815228 0.0320446i
\(741\) 48.8866 0.0659739
\(742\) 70.4336 + 70.4336i 0.0949240 + 0.0949240i
\(743\) 1013.36 1013.36i 1.36387 1.36387i 0.494948 0.868923i \(-0.335187\pi\)
0.868923 0.494948i \(-0.164813\pi\)
\(744\) 106.080i 0.142581i
\(745\) 303.952 + 511.374i 0.407989 + 0.686408i
\(746\) 661.235 0.886375
\(747\) −294.523 294.523i −0.394274 0.394274i
\(748\) −602.047 + 602.047i −0.804876 + 0.804876i
\(749\) 652.398i 0.871025i
\(750\) −11.6444 305.965i −0.0155259 0.407953i
\(751\) −639.972 −0.852160 −0.426080 0.904686i \(-0.640106\pi\)
−0.426080 + 0.904686i \(0.640106\pi\)
\(752\) 8.42430 + 8.42430i 0.0112025 + 0.0112025i
\(753\) 368.894 368.894i 0.489899 0.489899i
\(754\) 195.995i 0.259940i
\(755\) −911.161 + 541.578i −1.20684 + 0.717322i
\(756\) −60.2815 −0.0797374
\(757\) 53.7428 + 53.7428i 0.0709945 + 0.0709945i 0.741712 0.670718i \(-0.234014\pi\)
−0.670718 + 0.741712i \(0.734014\pi\)
\(758\) 169.928 169.928i 0.224179 0.224179i
\(759\) 107.459i 0.141580i
\(760\) 36.5257 + 9.29229i 0.0480601 + 0.0122267i
\(761\) −595.415 −0.782411 −0.391205 0.920303i \(-0.627942\pi\)
−0.391205 + 0.920303i \(0.627942\pi\)
\(762\) 191.084 + 191.084i 0.250766 + 0.250766i
\(763\) 455.033 455.033i 0.596373 0.596373i
\(764\) 11.2021i 0.0146624i
\(765\) −121.701 + 478.377i −0.159086 + 0.625329i
\(766\) 318.006 0.415151
\(767\) 491.348 + 491.348i 0.640610 + 0.640610i
\(768\) −19.5959 + 19.5959i −0.0255155 + 0.0255155i
\(769\) 825.742i 1.07379i −0.843650 0.536893i \(-0.819598\pi\)
0.843650 0.536893i \(-0.180402\pi\)
\(770\) 271.111 + 456.121i 0.352092 + 0.592366i
\(771\) 198.656 0.257660
\(772\) 359.308 + 359.308i 0.465424 + 0.465424i
\(773\) 248.538 248.538i 0.321523 0.321523i −0.527828 0.849351i \(-0.676993\pi\)
0.849351 + 0.527828i \(0.176993\pi\)
\(774\) 12.6270i 0.0163140i
\(775\) 258.694 475.525i 0.333799 0.613580i
\(776\) 197.165 0.254079
\(777\) 17.3829 + 17.3829i 0.0223718 + 0.0223718i
\(778\) −494.731 + 494.731i −0.635901 + 0.635901i