Properties

Label 1110.2.o.a.253.1
Level $1110$
Weight $2$
Character 1110.253
Analytic conductor $8.863$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.o (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 253.1
Character \(\chi\) \(=\) 1110.253
Dual form 1110.2.o.a.487.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.23554 + 0.0484605i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-0.707107 + 0.707107i) q^{3} +1.00000 q^{4} +(-2.23554 + 0.0484605i) q^{5} +(0.707107 - 0.707107i) q^{6} +(2.77693 - 2.77693i) q^{7} -1.00000 q^{8} -1.00000i q^{9} +(2.23554 - 0.0484605i) q^{10} -2.74073i q^{11} +(-0.707107 + 0.707107i) q^{12} -2.09781 q^{13} +(-2.77693 + 2.77693i) q^{14} +(1.54650 - 1.61503i) q^{15} +1.00000 q^{16} +4.54367i q^{17} +1.00000i q^{18} +(-3.00837 - 3.00837i) q^{19} +(-2.23554 + 0.0484605i) q^{20} +3.92718i q^{21} +2.74073i q^{22} -1.09307 q^{23} +(0.707107 - 0.707107i) q^{24} +(4.99530 - 0.216671i) q^{25} +2.09781 q^{26} +(0.707107 + 0.707107i) q^{27} +(2.77693 - 2.77693i) q^{28} +(-3.41798 + 3.41798i) q^{29} +(-1.54650 + 1.61503i) q^{30} +(-0.444286 - 0.444286i) q^{31} -1.00000 q^{32} +(1.93799 + 1.93799i) q^{33} -4.54367i q^{34} +(-6.07338 + 6.34253i) q^{35} -1.00000i q^{36} +(3.14301 + 5.20783i) q^{37} +(3.00837 + 3.00837i) q^{38} +(1.48338 - 1.48338i) q^{39} +(2.23554 - 0.0484605i) q^{40} +3.49239i q^{41} -3.92718i q^{42} -2.64615 q^{43} -2.74073i q^{44} +(0.0484605 + 2.23554i) q^{45} +1.09307 q^{46} +(-4.28090 + 4.28090i) q^{47} +(-0.707107 + 0.707107i) q^{48} -8.42272i q^{49} +(-4.99530 + 0.216671i) q^{50} +(-3.21286 - 3.21286i) q^{51} -2.09781 q^{52} +(-4.10770 - 4.10770i) q^{53} +(-0.707107 - 0.707107i) q^{54} +(0.132817 + 6.12703i) q^{55} +(-2.77693 + 2.77693i) q^{56} +4.25447 q^{57} +(3.41798 - 3.41798i) q^{58} +(-10.1179 - 10.1179i) q^{59} +(1.54650 - 1.61503i) q^{60} +(-4.77382 - 4.77382i) q^{61} +(0.444286 + 0.444286i) q^{62} +(-2.77693 - 2.77693i) q^{63} +1.00000 q^{64} +(4.68975 - 0.101661i) q^{65} +(-1.93799 - 1.93799i) q^{66} +(-3.42538 - 3.42538i) q^{67} +4.54367i q^{68} +(0.772920 - 0.772920i) q^{69} +(6.07338 - 6.34253i) q^{70} +0.512824 q^{71} +1.00000i q^{72} +(-9.57090 + 9.57090i) q^{73} +(-3.14301 - 5.20783i) q^{74} +(-3.37900 + 3.68542i) q^{75} +(-3.00837 - 3.00837i) q^{76} +(-7.61083 - 7.61083i) q^{77} +(-1.48338 + 1.48338i) q^{78} +(-4.84570 - 4.84570i) q^{79} +(-2.23554 + 0.0484605i) q^{80} -1.00000 q^{81} -3.49239i q^{82} +(4.09292 + 4.09292i) q^{83} +3.92718i q^{84} +(-0.220188 - 10.1576i) q^{85} +2.64615 q^{86} -4.83375i q^{87} +2.74073i q^{88} +(-9.59900 + 9.59900i) q^{89} +(-0.0484605 - 2.23554i) q^{90} +(-5.82548 + 5.82548i) q^{91} -1.09307 q^{92} +0.628315 q^{93} +(4.28090 - 4.28090i) q^{94} +(6.87112 + 6.57954i) q^{95} +(0.707107 - 0.707107i) q^{96} +5.08514i q^{97} +8.42272i q^{98} -2.74073 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} + O(q^{10}) \) \( 36q - 36q^{2} + 36q^{4} + 4q^{5} + 4q^{7} - 36q^{8} - 4q^{10} - 8q^{13} - 4q^{14} + 36q^{16} - 4q^{19} + 4q^{20} + 4q^{25} + 8q^{26} + 4q^{28} - 36q^{29} - 4q^{31} - 36q^{32} + 4q^{33} + 28q^{35} + 28q^{37} + 4q^{38} - 4q^{39} - 4q^{40} - 32q^{43} + 16q^{47} - 4q^{50} - 8q^{52} - 8q^{53} - 8q^{55} - 4q^{56} - 8q^{57} + 36q^{58} + 4q^{59} - 4q^{61} + 4q^{62} - 4q^{63} + 36q^{64} - 52q^{65} - 4q^{66} - 16q^{67} + 8q^{69} - 28q^{70} - 8q^{71} + 4q^{73} - 28q^{74} + 16q^{75} - 4q^{76} - 8q^{77} + 4q^{78} + 12q^{79} + 4q^{80} - 36q^{81} + 8q^{83} - 8q^{85} + 32q^{86} + 24q^{89} + 56q^{91} - 8q^{93} - 16q^{94} + 20q^{95} + 8q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

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 −0.707107
\(3\) −0.707107 + 0.707107i −0.408248 + 0.408248i
\(4\) 1.00000 0.500000
\(5\) −2.23554 + 0.0484605i −0.999765 + 0.0216722i
\(6\) 0.707107 0.707107i 0.288675 0.288675i
\(7\) 2.77693 2.77693i 1.04958 1.04958i 0.0508772 0.998705i \(-0.483798\pi\)
0.998705 0.0508772i \(-0.0162017\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000i 0.333333i
\(10\) 2.23554 0.0484605i 0.706941 0.0153246i
\(11\) 2.74073i 0.826362i −0.910649 0.413181i \(-0.864418\pi\)
0.910649 0.413181i \(-0.135582\pi\)
\(12\) −0.707107 + 0.707107i −0.204124 + 0.204124i
\(13\) −2.09781 −0.581828 −0.290914 0.956749i \(-0.593959\pi\)
−0.290914 + 0.956749i \(0.593959\pi\)
\(14\) −2.77693 + 2.77693i −0.742167 + 0.742167i
\(15\) 1.54650 1.61503i 0.399305 0.417000i
\(16\) 1.00000 0.250000
\(17\) 4.54367i 1.10200i 0.834505 + 0.551001i \(0.185754\pi\)
−0.834505 + 0.551001i \(0.814246\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.00837 3.00837i −0.690166 0.690166i 0.272102 0.962268i \(-0.412281\pi\)
−0.962268 + 0.272102i \(0.912281\pi\)
\(20\) −2.23554 + 0.0484605i −0.499883 + 0.0108361i
\(21\) 3.92718i 0.856980i
\(22\) 2.74073i 0.584326i
\(23\) −1.09307 −0.227922 −0.113961 0.993485i \(-0.536354\pi\)
−0.113961 + 0.993485i \(0.536354\pi\)
\(24\) 0.707107 0.707107i 0.144338 0.144338i
\(25\) 4.99530 0.216671i 0.999061 0.0433342i
\(26\) 2.09781 0.411415
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) 2.77693 2.77693i 0.524791 0.524791i
\(29\) −3.41798 + 3.41798i −0.634703 + 0.634703i −0.949244 0.314541i \(-0.898149\pi\)
0.314541 + 0.949244i \(0.398149\pi\)
\(30\) −1.54650 + 1.61503i −0.282351 + 0.294864i
\(31\) −0.444286 0.444286i −0.0797961 0.0797961i 0.666082 0.745878i \(-0.267970\pi\)
−0.745878 + 0.666082i \(0.767970\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.93799 + 1.93799i 0.337361 + 0.337361i
\(34\) 4.54367i 0.779232i
\(35\) −6.07338 + 6.34253i −1.02659 + 1.07208i
\(36\) 1.00000i 0.166667i
\(37\) 3.14301 + 5.20783i 0.516708 + 0.856162i
\(38\) 3.00837 + 3.00837i 0.488021 + 0.488021i
\(39\) 1.48338 1.48338i 0.237530 0.237530i
\(40\) 2.23554 0.0484605i 0.353470 0.00766228i
\(41\) 3.49239i 0.545420i 0.962096 + 0.272710i \(0.0879200\pi\)
−0.962096 + 0.272710i \(0.912080\pi\)
\(42\) 3.92718i 0.605977i
\(43\) −2.64615 −0.403534 −0.201767 0.979434i \(-0.564668\pi\)
−0.201767 + 0.979434i \(0.564668\pi\)
\(44\) 2.74073i 0.413181i
\(45\) 0.0484605 + 2.23554i 0.00722407 + 0.333255i
\(46\) 1.09307 0.161165
\(47\) −4.28090 + 4.28090i −0.624434 + 0.624434i −0.946662 0.322228i \(-0.895568\pi\)
0.322228 + 0.946662i \(0.395568\pi\)
\(48\) −0.707107 + 0.707107i −0.102062 + 0.102062i
\(49\) 8.42272i 1.20325i
\(50\) −4.99530 + 0.216671i −0.706443 + 0.0306419i
\(51\) −3.21286 3.21286i −0.449890 0.449890i
\(52\) −2.09781 −0.290914
\(53\) −4.10770 4.10770i −0.564235 0.564235i 0.366272 0.930508i \(-0.380634\pi\)
−0.930508 + 0.366272i \(0.880634\pi\)
\(54\) −0.707107 0.707107i −0.0962250 0.0962250i
\(55\) 0.132817 + 6.12703i 0.0179091 + 0.826168i
\(56\) −2.77693 + 2.77693i −0.371083 + 0.371083i
\(57\) 4.25447 0.563519
\(58\) 3.41798 3.41798i 0.448803 0.448803i
\(59\) −10.1179 10.1179i −1.31724 1.31724i −0.915954 0.401282i \(-0.868565\pi\)
−0.401282 0.915954i \(-0.631435\pi\)
\(60\) 1.54650 1.61503i 0.199652 0.208500i
\(61\) −4.77382 4.77382i −0.611226 0.611226i 0.332040 0.943265i \(-0.392263\pi\)
−0.943265 + 0.332040i \(0.892263\pi\)
\(62\) 0.444286 + 0.444286i 0.0564243 + 0.0564243i
\(63\) −2.77693 2.77693i −0.349861 0.349861i
\(64\) 1.00000 0.125000
\(65\) 4.68975 0.101661i 0.581692 0.0126095i
\(66\) −1.93799 1.93799i −0.238550 0.238550i
\(67\) −3.42538 3.42538i −0.418476 0.418476i 0.466202 0.884678i \(-0.345622\pi\)
−0.884678 + 0.466202i \(0.845622\pi\)
\(68\) 4.54367i 0.551001i
\(69\) 0.772920 0.772920i 0.0930486 0.0930486i
\(70\) 6.07338 6.34253i 0.725908 0.758077i
\(71\) 0.512824 0.0608611 0.0304305 0.999537i \(-0.490312\pi\)
0.0304305 + 0.999537i \(0.490312\pi\)
\(72\) 1.00000i 0.117851i
\(73\) −9.57090 + 9.57090i −1.12019 + 1.12019i −0.128477 + 0.991713i \(0.541009\pi\)
−0.991713 + 0.128477i \(0.958991\pi\)
\(74\) −3.14301 5.20783i −0.365368 0.605398i
\(75\) −3.37900 + 3.68542i −0.390174 + 0.425556i
\(76\) −3.00837 3.00837i −0.345083 0.345083i
\(77\) −7.61083 7.61083i −0.867335 0.867335i
\(78\) −1.48338 + 1.48338i −0.167959 + 0.167959i
\(79\) −4.84570 4.84570i −0.545184 0.545184i 0.379860 0.925044i \(-0.375972\pi\)
−0.925044 + 0.379860i \(0.875972\pi\)
\(80\) −2.23554 + 0.0484605i −0.249941 + 0.00541805i
\(81\) −1.00000 −0.111111
\(82\) 3.49239i 0.385670i
\(83\) 4.09292 + 4.09292i 0.449256 + 0.449256i 0.895107 0.445851i \(-0.147099\pi\)
−0.445851 + 0.895107i \(0.647099\pi\)
\(84\) 3.92718i 0.428490i
\(85\) −0.220188 10.1576i −0.0238828 1.10174i
\(86\) 2.64615 0.285341
\(87\) 4.83375i 0.518233i
\(88\) 2.74073i 0.292163i
\(89\) −9.59900 + 9.59900i −1.01749 + 1.01749i −0.0176477 + 0.999844i \(0.505618\pi\)
−0.999844 + 0.0176477i \(0.994382\pi\)
\(90\) −0.0484605 2.23554i −0.00510819 0.235647i
\(91\) −5.82548 + 5.82548i −0.610677 + 0.610677i
\(92\) −1.09307 −0.113961
\(93\) 0.628315 0.0651532
\(94\) 4.28090 4.28090i 0.441541 0.441541i
\(95\) 6.87112 + 6.57954i 0.704962 + 0.675047i
\(96\) 0.707107 0.707107i 0.0721688 0.0721688i
\(97\) 5.08514i 0.516318i 0.966102 + 0.258159i \(0.0831158\pi\)
−0.966102 + 0.258159i \(0.916884\pi\)
\(98\) 8.42272i 0.850823i
\(99\) −2.74073 −0.275454
\(100\) 4.99530 0.216671i 0.499530 0.0216671i
\(101\) 14.3173i 1.42463i −0.701861 0.712314i \(-0.747647\pi\)
0.701861 0.712314i \(-0.252353\pi\)
\(102\) 3.21286 + 3.21286i 0.318120 + 0.318120i
\(103\) 8.41065i 0.828726i 0.910112 + 0.414363i \(0.135996\pi\)
−0.910112 + 0.414363i \(0.864004\pi\)
\(104\) 2.09781 0.205707
\(105\) −0.190313 8.77937i −0.0185726 0.856779i
\(106\) 4.10770 + 4.10770i 0.398975 + 0.398975i
\(107\) 4.88230 4.88230i 0.471990 0.471990i −0.430568 0.902558i \(-0.641687\pi\)
0.902558 + 0.430568i \(0.141687\pi\)
\(108\) 0.707107 + 0.707107i 0.0680414 + 0.0680414i
\(109\) −9.37338 9.37338i −0.897806 0.897806i 0.0974354 0.995242i \(-0.468936\pi\)
−0.995242 + 0.0974354i \(0.968936\pi\)
\(110\) −0.132817 6.12703i −0.0126636 0.584189i
\(111\) −5.90494 1.46004i −0.560472 0.138581i
\(112\) 2.77693 2.77693i 0.262396 0.262396i
\(113\) 4.08857i 0.384620i −0.981334 0.192310i \(-0.938402\pi\)
0.981334 0.192310i \(-0.0615979\pi\)
\(114\) −4.25447 −0.398468
\(115\) 2.44361 0.0529709i 0.227868 0.00493956i
\(116\) −3.41798 + 3.41798i −0.317352 + 0.317352i
\(117\) 2.09781i 0.193943i
\(118\) 10.1179 + 10.1179i 0.931427 + 0.931427i
\(119\) 12.6175 + 12.6175i 1.15664 + 1.15664i
\(120\) −1.54650 + 1.61503i −0.141176 + 0.147432i
\(121\) 3.48838 0.317126
\(122\) 4.77382 + 4.77382i 0.432202 + 0.432202i
\(123\) −2.46949 2.46949i −0.222667 0.222667i
\(124\) −0.444286 0.444286i −0.0398980 0.0398980i
\(125\) −11.1567 + 0.726452i −0.997887 + 0.0649759i
\(126\) 2.77693 + 2.77693i 0.247389 + 0.247389i
\(127\) −8.71272 + 8.71272i −0.773129 + 0.773129i −0.978652 0.205523i \(-0.934110\pi\)
0.205523 + 0.978652i \(0.434110\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.87111 1.87111i 0.164742 0.164742i
\(130\) −4.68975 + 0.101661i −0.411318 + 0.00891626i
\(131\) −15.0456 15.0456i −1.31454 1.31454i −0.918032 0.396507i \(-0.870222\pi\)
−0.396507 0.918032i \(-0.629778\pi\)
\(132\) 1.93799 + 1.93799i 0.168680 + 0.168680i
\(133\) −16.7081 −1.44877
\(134\) 3.42538 + 3.42538i 0.295908 + 0.295908i
\(135\) −1.61503 1.54650i −0.139000 0.133102i
\(136\) 4.54367i 0.389616i
\(137\) 7.51357 7.51357i 0.641928 0.641928i −0.309101 0.951029i \(-0.600028\pi\)
0.951029 + 0.309101i \(0.100028\pi\)
\(138\) −0.772920 + 0.772920i −0.0657953 + 0.0657953i
\(139\) 7.58286 0.643170 0.321585 0.946881i \(-0.395784\pi\)
0.321585 + 0.946881i \(0.395784\pi\)
\(140\) −6.07338 + 6.34253i −0.513294 + 0.536041i
\(141\) 6.05411i 0.509848i
\(142\) −0.512824 −0.0430353
\(143\) 5.74954i 0.480801i
\(144\) 1.00000i 0.0833333i
\(145\) 7.47541 7.80668i 0.620799 0.648309i
\(146\) 9.57090 9.57090i 0.792093 0.792093i
\(147\) 5.95576 + 5.95576i 0.491223 + 0.491223i
\(148\) 3.14301 + 5.20783i 0.258354 + 0.428081i
\(149\) 18.5418i 1.51901i 0.650503 + 0.759504i \(0.274558\pi\)
−0.650503 + 0.759504i \(0.725442\pi\)
\(150\) 3.37900 3.68542i 0.275894 0.300913i
\(151\) 4.53529i 0.369077i −0.982825 0.184538i \(-0.940921\pi\)
0.982825 0.184538i \(-0.0590790\pi\)
\(152\) 3.00837 + 3.00837i 0.244011 + 0.244011i
\(153\) 4.54367 0.367334
\(154\) 7.61083 + 7.61083i 0.613298 + 0.613298i
\(155\) 1.01475 + 0.971689i 0.0815067 + 0.0780480i
\(156\) 1.48338 1.48338i 0.118765 0.118765i
\(157\) −2.15926 + 2.15926i −0.172328 + 0.172328i −0.788001 0.615674i \(-0.788884\pi\)
0.615674 + 0.788001i \(0.288884\pi\)
\(158\) 4.84570 + 4.84570i 0.385503 + 0.385503i
\(159\) 5.80916 0.460696
\(160\) 2.23554 0.0484605i 0.176735 0.00383114i
\(161\) −3.03539 + 3.03539i −0.239222 + 0.239222i
\(162\) 1.00000 0.0785674
\(163\) 13.2270i 1.03602i 0.855374 + 0.518011i \(0.173327\pi\)
−0.855374 + 0.518011i \(0.826673\pi\)
\(164\) 3.49239i 0.272710i
\(165\) −4.42638 4.23855i −0.344593 0.329970i
\(166\) −4.09292 4.09292i −0.317672 0.317672i
\(167\) 2.15667i 0.166888i 0.996512 + 0.0834441i \(0.0265920\pi\)
−0.996512 + 0.0834441i \(0.973408\pi\)
\(168\) 3.92718i 0.302988i
\(169\) −8.59918 −0.661476
\(170\) 0.220188 + 10.1576i 0.0168877 + 0.779049i
\(171\) −3.00837 + 3.00837i −0.230055 + 0.230055i
\(172\) −2.64615 −0.201767
\(173\) −12.7830 + 12.7830i −0.971877 + 0.971877i −0.999615 0.0277386i \(-0.991169\pi\)
0.0277386 + 0.999615i \(0.491169\pi\)
\(174\) 4.83375i 0.366446i
\(175\) 13.2699 14.4733i 1.00311 1.09408i
\(176\) 2.74073i 0.206591i
\(177\) 14.3089 1.07552
\(178\) 9.59900 9.59900i 0.719475 0.719475i
\(179\) 8.92829 8.92829i 0.667332 0.667332i −0.289766 0.957098i \(-0.593577\pi\)
0.957098 + 0.289766i \(0.0935774\pi\)
\(180\) 0.0484605 + 2.23554i 0.00361203 + 0.166628i
\(181\) 8.76543 0.651530 0.325765 0.945451i \(-0.394378\pi\)
0.325765 + 0.945451i \(0.394378\pi\)
\(182\) 5.82548 5.82548i 0.431814 0.431814i
\(183\) 6.75121 0.499064
\(184\) 1.09307 0.0805825
\(185\) −7.27871 11.4900i −0.535142 0.844762i
\(186\) −0.628315 −0.0460703
\(187\) 12.4530 0.910652
\(188\) −4.28090 + 4.28090i −0.312217 + 0.312217i
\(189\) 3.92718 0.285660
\(190\) −6.87112 6.57954i −0.498483 0.477330i
\(191\) 3.29001 3.29001i 0.238057 0.238057i −0.577988 0.816045i \(-0.696162\pi\)
0.816045 + 0.577988i \(0.196162\pi\)
\(192\) −0.707107 + 0.707107i −0.0510310 + 0.0510310i
\(193\) −19.3985 −1.39634 −0.698168 0.715934i \(-0.746001\pi\)
−0.698168 + 0.715934i \(0.746001\pi\)
\(194\) 5.08514i 0.365092i
\(195\) −3.24427 + 3.38804i −0.232327 + 0.242622i
\(196\) 8.42272i 0.601623i
\(197\) −12.6528 + 12.6528i −0.901476 + 0.901476i −0.995564 0.0940878i \(-0.970007\pi\)
0.0940878 + 0.995564i \(0.470007\pi\)
\(198\) 2.74073 0.194775
\(199\) 3.25794 3.25794i 0.230949 0.230949i −0.582140 0.813089i \(-0.697784\pi\)
0.813089 + 0.582140i \(0.197784\pi\)
\(200\) −4.99530 + 0.216671i −0.353221 + 0.0153210i
\(201\) 4.84421 0.341685
\(202\) 14.3173i 1.00736i
\(203\) 18.9830i 1.33235i
\(204\) −3.21286 3.21286i −0.224945 0.224945i
\(205\) −0.169243 7.80739i −0.0118205 0.545292i
\(206\) 8.41065i 0.585998i
\(207\) 1.09307i 0.0759739i
\(208\) −2.09781 −0.145457
\(209\) −8.24513 + 8.24513i −0.570327 + 0.570327i
\(210\) 0.190313 + 8.77937i 0.0131328 + 0.605834i
\(211\) −1.48256 −0.102064 −0.0510319 0.998697i \(-0.516251\pi\)
−0.0510319 + 0.998697i \(0.516251\pi\)
\(212\) −4.10770 4.10770i −0.282118 0.282118i
\(213\) −0.362622 + 0.362622i −0.0248464 + 0.0248464i
\(214\) −4.88230 + 4.88230i −0.333747 + 0.333747i
\(215\) 5.91557 0.128234i 0.403439 0.00874546i
\(216\) −0.707107 0.707107i −0.0481125 0.0481125i
\(217\) −2.46750 −0.167505
\(218\) 9.37338 + 9.37338i 0.634845 + 0.634845i
\(219\) 13.5353i 0.914631i
\(220\) 0.132817 + 6.12703i 0.00895454 + 0.413084i
\(221\) 9.53176i 0.641175i
\(222\) 5.90494 + 1.46004i 0.396313 + 0.0979918i
\(223\) 6.90996 + 6.90996i 0.462725 + 0.462725i 0.899548 0.436822i \(-0.143896\pi\)
−0.436822 + 0.899548i \(0.643896\pi\)
\(224\) −2.77693 + 2.77693i −0.185542 + 0.185542i
\(225\) −0.216671 4.99530i −0.0144447 0.333020i
\(226\) 4.08857i 0.271967i
\(227\) 0.338896i 0.0224933i 0.999937 + 0.0112467i \(0.00358000\pi\)
−0.999937 + 0.0112467i \(0.996420\pi\)
\(228\) 4.25447 0.281759
\(229\) 6.86738i 0.453810i 0.973917 + 0.226905i \(0.0728606\pi\)
−0.973917 + 0.226905i \(0.927139\pi\)
\(230\) −2.44361 + 0.0529709i −0.161127 + 0.00349280i
\(231\) 10.7633 0.708176
\(232\) 3.41798 3.41798i 0.224401 0.224401i
\(233\) 11.8523 11.8523i 0.776470 0.776470i −0.202758 0.979229i \(-0.564991\pi\)
0.979229 + 0.202758i \(0.0649906\pi\)
\(234\) 2.09781i 0.137138i
\(235\) 9.36269 9.77759i 0.610754 0.637820i
\(236\) −10.1179 10.1179i −0.658618 0.658618i
\(237\) 6.85285 0.445141
\(238\) −12.6175 12.6175i −0.817868 0.817868i
\(239\) 11.8453 + 11.8453i 0.766207 + 0.766207i 0.977437 0.211229i \(-0.0677467\pi\)
−0.211229 + 0.977437i \(0.567747\pi\)
\(240\) 1.54650 1.61503i 0.0998262 0.104250i
\(241\) −1.06176 + 1.06176i −0.0683939 + 0.0683939i −0.740476 0.672082i \(-0.765400\pi\)
0.672082 + 0.740476i \(0.265400\pi\)
\(242\) −3.48838 −0.224242
\(243\) 0.707107 0.707107i 0.0453609 0.0453609i
\(244\) −4.77382 4.77382i −0.305613 0.305613i
\(245\) 0.408169 + 18.8293i 0.0260770 + 1.20296i
\(246\) 2.46949 + 2.46949i 0.157449 + 0.157449i
\(247\) 6.31099 + 6.31099i 0.401558 + 0.401558i
\(248\) 0.444286 + 0.444286i 0.0282122 + 0.0282122i
\(249\) −5.78826 −0.366816
\(250\) 11.1567 0.726452i 0.705613 0.0459449i
\(251\) 10.3290 + 10.3290i 0.651960 + 0.651960i 0.953465 0.301505i \(-0.0974890\pi\)
−0.301505 + 0.953465i \(0.597489\pi\)
\(252\) −2.77693 2.77693i −0.174930 0.174930i
\(253\) 2.99582i 0.188346i
\(254\) 8.71272 8.71272i 0.546685 0.546685i
\(255\) 7.33818 + 7.02678i 0.459534 + 0.440034i
\(256\) 1.00000 0.0625000
\(257\) 28.1460i 1.75570i −0.478939 0.877848i \(-0.658978\pi\)
0.478939 0.877848i \(-0.341022\pi\)
\(258\) −1.87111 + 1.87111i −0.116490 + 0.116490i
\(259\) 23.1897 + 5.73385i 1.44094 + 0.356284i
\(260\) 4.68975 0.101661i 0.290846 0.00630475i
\(261\) 3.41798 + 3.41798i 0.211568 + 0.211568i
\(262\) 15.0456 + 15.0456i 0.929519 + 0.929519i
\(263\) −1.14169 + 1.14169i −0.0703994 + 0.0703994i −0.741430 0.671030i \(-0.765852\pi\)
0.671030 + 0.741430i \(0.265852\pi\)
\(264\) −1.93799 1.93799i −0.119275 0.119275i
\(265\) 9.38199 + 8.98387i 0.576331 + 0.551875i
\(266\) 16.7081 1.02444
\(267\) 13.5750i 0.830779i
\(268\) −3.42538 3.42538i −0.209238 0.209238i
\(269\) 0.755375i 0.0460560i 0.999735 + 0.0230280i \(0.00733069\pi\)
−0.999735 + 0.0230280i \(0.992669\pi\)
\(270\) 1.61503 + 1.54650i 0.0982879 + 0.0941170i
\(271\) 13.0803 0.794573 0.397286 0.917695i \(-0.369952\pi\)
0.397286 + 0.917695i \(0.369952\pi\)
\(272\) 4.54367i 0.275500i
\(273\) 8.23848i 0.498615i
\(274\) −7.51357 + 7.51357i −0.453912 + 0.453912i
\(275\) −0.593838 13.6908i −0.0358097 0.825586i
\(276\) 0.772920 0.772920i 0.0465243 0.0465243i
\(277\) 27.8958 1.67610 0.838048 0.545597i \(-0.183697\pi\)
0.838048 + 0.545597i \(0.183697\pi\)
\(278\) −7.58286 −0.454790
\(279\) −0.444286 + 0.444286i −0.0265987 + 0.0265987i
\(280\) 6.07338 6.34253i 0.362954 0.379038i
\(281\) 3.25168 3.25168i 0.193979 0.193979i −0.603434 0.797413i \(-0.706201\pi\)
0.797413 + 0.603434i \(0.206201\pi\)
\(282\) 6.05411i 0.360517i
\(283\) 12.8597i 0.764431i −0.924073 0.382216i \(-0.875161\pi\)
0.924073 0.382216i \(-0.124839\pi\)
\(284\) 0.512824 0.0304305
\(285\) −9.51105 + 0.206174i −0.563386 + 0.0122127i
\(286\) 5.74954i 0.339978i
\(287\) 9.69814 + 9.69814i 0.572463 + 0.572463i
\(288\) 1.00000i 0.0589256i
\(289\) −3.64491 −0.214406
\(290\) −7.47541 + 7.80668i −0.438971 + 0.458424i
\(291\) −3.59574 3.59574i −0.210786 0.210786i
\(292\) −9.57090 + 9.57090i −0.560095 + 0.560095i
\(293\) −8.19264 8.19264i −0.478619 0.478619i 0.426071 0.904690i \(-0.359897\pi\)
−0.904690 + 0.426071i \(0.859897\pi\)
\(294\) −5.95576 5.95576i −0.347347 0.347347i
\(295\) 23.1093 + 22.1287i 1.34547 + 1.28838i
\(296\) −3.14301 5.20783i −0.182684 0.302699i
\(297\) 1.93799 1.93799i 0.112454 0.112454i
\(298\) 18.5418i 1.07410i
\(299\) 2.29306 0.132611
\(300\) −3.37900 + 3.68542i −0.195087 + 0.212778i
\(301\) −7.34817 + 7.34817i −0.423542 + 0.423542i
\(302\) 4.53529i 0.260977i
\(303\) 10.1239 + 10.1239i 0.581602 + 0.581602i
\(304\) −3.00837 3.00837i −0.172542 0.172542i
\(305\) 10.9034 + 10.4407i 0.624329 + 0.597835i
\(306\) −4.54367 −0.259744
\(307\) 1.93471 + 1.93471i 0.110420 + 0.110420i 0.760158 0.649738i \(-0.225121\pi\)
−0.649738 + 0.760158i \(0.725121\pi\)
\(308\) −7.61083 7.61083i −0.433667 0.433667i
\(309\) −5.94723 5.94723i −0.338326 0.338326i
\(310\) −1.01475 0.971689i −0.0576339 0.0551882i
\(311\) −24.0063 24.0063i −1.36127 1.36127i −0.872298 0.488974i \(-0.837371\pi\)
−0.488974 0.872298i \(-0.662629\pi\)
\(312\) −1.48338 + 1.48338i −0.0839797 + 0.0839797i
\(313\) 28.6636 1.62016 0.810080 0.586319i \(-0.199424\pi\)
0.810080 + 0.586319i \(0.199424\pi\)
\(314\) 2.15926 2.15926i 0.121854 0.121854i
\(315\) 6.34253 + 6.07338i 0.357361 + 0.342196i
\(316\) −4.84570 4.84570i −0.272592 0.272592i
\(317\) −14.0253 14.0253i −0.787739 0.787739i 0.193384 0.981123i \(-0.438054\pi\)
−0.981123 + 0.193384i \(0.938054\pi\)
\(318\) −5.80916 −0.325761
\(319\) 9.36777 + 9.36777i 0.524495 + 0.524495i
\(320\) −2.23554 + 0.0484605i −0.124971 + 0.00270902i
\(321\) 6.90462i 0.385378i
\(322\) 3.03539 3.03539i 0.169156 0.169156i
\(323\) 13.6690 13.6690i 0.760564 0.760564i
\(324\) −1.00000 −0.0555556
\(325\) −10.4792 + 0.454535i −0.581282 + 0.0252131i
\(326\) 13.2270i 0.732578i
\(327\) 13.2560 0.733056
\(328\) 3.49239i 0.192835i
\(329\) 23.7756i 1.31079i
\(330\) 4.42638 + 4.23855i 0.243664 + 0.233324i
\(331\) −5.28358 + 5.28358i −0.290412 + 0.290412i −0.837243 0.546831i \(-0.815834\pi\)
0.546831 + 0.837243i \(0.315834\pi\)
\(332\) 4.09292 + 4.09292i 0.224628 + 0.224628i
\(333\) 5.20783 3.14301i 0.285387 0.172236i
\(334\) 2.15667i 0.118008i
\(335\) 7.82357 + 7.49158i 0.427447 + 0.409309i
\(336\) 3.92718i 0.214245i
\(337\) −15.8649 15.8649i −0.864216 0.864216i 0.127609 0.991825i \(-0.459270\pi\)
−0.991825 + 0.127609i \(0.959270\pi\)
\(338\) 8.59918 0.467734
\(339\) 2.89105 + 2.89105i 0.157020 + 0.157020i
\(340\) −0.220188 10.1576i −0.0119414 0.550871i
\(341\) −1.21767 + 1.21767i −0.0659404 + 0.0659404i
\(342\) 3.00837 3.00837i 0.162674 0.162674i
\(343\) −3.95079 3.95079i −0.213323 0.213323i
\(344\) 2.64615 0.142671
\(345\) −1.69044 + 1.76535i −0.0910102 + 0.0950433i
\(346\) 12.7830 12.7830i 0.687221 0.687221i
\(347\) 20.2697 1.08814 0.544068 0.839041i \(-0.316884\pi\)
0.544068 + 0.839041i \(0.316884\pi\)
\(348\) 4.83375i 0.259116i
\(349\) 23.3133i 1.24793i 0.781452 + 0.623965i \(0.214479\pi\)
−0.781452 + 0.623965i \(0.785521\pi\)
\(350\) −13.2699 + 14.4733i −0.709308 + 0.773631i
\(351\) −1.48338 1.48338i −0.0791768 0.0791768i
\(352\) 2.74073i 0.146082i
\(353\) 35.1904i 1.87300i 0.350671 + 0.936499i \(0.385953\pi\)
−0.350671 + 0.936499i \(0.614047\pi\)
\(354\) −14.3089 −0.760507
\(355\) −1.14644 + 0.0248517i −0.0608468 + 0.00131899i
\(356\) −9.59900 + 9.59900i −0.508746 + 0.508746i
\(357\) −17.8438 −0.944393
\(358\) −8.92829 + 8.92829i −0.471875 + 0.471875i
\(359\) 34.3706i 1.81401i −0.421118 0.907006i \(-0.638362\pi\)
0.421118 0.907006i \(-0.361638\pi\)
\(360\) −0.0484605 2.23554i −0.00255409 0.117823i
\(361\) 0.899470i 0.0473405i
\(362\) −8.76543 −0.460701
\(363\) −2.46666 + 2.46666i −0.129466 + 0.129466i
\(364\) −5.82548 + 5.82548i −0.305338 + 0.305338i
\(365\) 20.9323 21.8600i 1.09565 1.14420i
\(366\) −6.75121 −0.352891
\(367\) −15.7170 + 15.7170i −0.820421 + 0.820421i −0.986168 0.165747i \(-0.946996\pi\)
0.165747 + 0.986168i \(0.446996\pi\)
\(368\) −1.09307 −0.0569804
\(369\) 3.49239 0.181807
\(370\) 7.27871 + 11.4900i 0.378402 + 0.597337i
\(371\) −22.8136 −1.18442
\(372\) 0.628315 0.0325766
\(373\) 5.59113 5.59113i 0.289498 0.289498i −0.547384 0.836882i \(-0.684376\pi\)
0.836882 + 0.547384i \(0.184376\pi\)
\(374\) −12.4530 −0.643928
\(375\) 7.37531 8.40267i 0.380859 0.433912i
\(376\) 4.28090 4.28090i 0.220771 0.220771i
\(377\) 7.17028 7.17028i 0.369288 0.369288i
\(378\) −3.92718 −0.201992
\(379\) 20.7595i 1.06634i 0.846007 + 0.533171i \(0.179000\pi\)
−0.846007 + 0.533171i \(0.821000\pi\)
\(380\) 6.87112 + 6.57954i 0.352481 + 0.337523i
\(381\) 12.3216i 0.631257i
\(382\) −3.29001 + 3.29001i −0.168331 + 0.168331i
\(383\) 19.9351 1.01863 0.509317 0.860579i \(-0.329898\pi\)
0.509317 + 0.860579i \(0.329898\pi\)
\(384\) 0.707107 0.707107i 0.0360844 0.0360844i
\(385\) 17.3832 + 16.6455i 0.885928 + 0.848334i
\(386\) 19.3985 0.987358
\(387\) 2.64615i 0.134511i
\(388\) 5.08514i 0.258159i
\(389\) 2.00735 + 2.00735i 0.101777 + 0.101777i 0.756162 0.654385i \(-0.227072\pi\)
−0.654385 + 0.756162i \(0.727072\pi\)
\(390\) 3.24427 3.38804i 0.164280 0.171560i
\(391\) 4.96656i 0.251170i
\(392\) 8.42272i 0.425412i
\(393\) 21.2777 1.07332
\(394\) 12.6528 12.6528i 0.637440 0.637440i
\(395\) 11.0676 + 10.5979i 0.556871 + 0.533240i
\(396\) −2.74073 −0.137727
\(397\) −21.4010 21.4010i −1.07408 1.07408i −0.997027 0.0770566i \(-0.975448\pi\)
−0.0770566 0.997027i \(-0.524552\pi\)
\(398\) −3.25794 + 3.25794i −0.163306 + 0.163306i
\(399\) 11.8144 11.8144i 0.591459 0.591459i
\(400\) 4.99530 0.216671i 0.249765 0.0108336i
\(401\) 18.1649 + 18.1649i 0.907111 + 0.907111i 0.996038 0.0889270i \(-0.0283438\pi\)
−0.0889270 + 0.996038i \(0.528344\pi\)
\(402\) −4.84421 −0.241607
\(403\) 0.932028 + 0.932028i 0.0464276 + 0.0464276i
\(404\) 14.3173i 0.712314i
\(405\) 2.23554 0.0484605i 0.111085 0.00240802i
\(406\) 18.9830i 0.942111i
\(407\) 14.2733 8.61416i 0.707499 0.426988i
\(408\) 3.21286 + 3.21286i 0.159060 + 0.159060i
\(409\) −20.7880 + 20.7880i −1.02790 + 1.02790i −0.0283030 + 0.999599i \(0.509010\pi\)
−0.999599 + 0.0283030i \(0.990990\pi\)
\(410\) 0.169243 + 7.80739i 0.00835832 + 0.385580i
\(411\) 10.6258i 0.524132i
\(412\) 8.41065i 0.414363i
\(413\) −56.1934 −2.76510
\(414\) 1.09307i 0.0537216i
\(415\) −9.34824 8.95155i −0.458887 0.439414i
\(416\) 2.09781 0.102854
\(417\) −5.36189 + 5.36189i −0.262573 + 0.262573i
\(418\) 8.24513 8.24513i 0.403282 0.403282i
\(419\) 6.01083i 0.293648i 0.989163 + 0.146824i \(0.0469051\pi\)
−0.989163 + 0.146824i \(0.953095\pi\)
\(420\) −0.190313 8.77937i −0.00928632 0.428389i
\(421\) −14.1798 14.1798i −0.691081 0.691081i 0.271389 0.962470i \(-0.412517\pi\)
−0.962470 + 0.271389i \(0.912517\pi\)
\(422\) 1.48256 0.0721700
\(423\) 4.28090 + 4.28090i 0.208145 + 0.208145i
\(424\) 4.10770 + 4.10770i 0.199487 + 0.199487i
\(425\) 0.984481 + 22.6970i 0.0477543 + 1.10097i
\(426\) 0.362622 0.362622i 0.0175691 0.0175691i
\(427\) −26.5132 −1.28306
\(428\) 4.88230 4.88230i 0.235995 0.235995i
\(429\) −4.06554 4.06554i −0.196286 0.196286i
\(430\) −5.91557 + 0.128234i −0.285274 + 0.00618397i
\(431\) 19.4897 + 19.4897i 0.938784 + 0.938784i 0.998231 0.0594472i \(-0.0189338\pi\)
−0.0594472 + 0.998231i \(0.518934\pi\)
\(432\) 0.707107 + 0.707107i 0.0340207 + 0.0340207i
\(433\) −27.2929 27.2929i −1.31161 1.31161i −0.920226 0.391387i \(-0.871995\pi\)
−0.391387 0.920226i \(-0.628005\pi\)
\(434\) 2.46750 0.118444
\(435\) 0.234246 + 10.8061i 0.0112312 + 0.518111i
\(436\) −9.37338 9.37338i −0.448903 0.448903i
\(437\) 3.28837 + 3.28837i 0.157304 + 0.157304i
\(438\) 13.5353i 0.646742i
\(439\) −27.9211 + 27.9211i −1.33260 + 1.33260i −0.429564 + 0.903036i \(0.641333\pi\)
−0.903036 + 0.429564i \(0.858667\pi\)
\(440\) −0.132817 6.12703i −0.00633182 0.292094i
\(441\) −8.42272 −0.401082
\(442\) 9.53176i 0.453380i
\(443\) 13.8772 13.8772i 0.659326 0.659326i −0.295894 0.955221i \(-0.595618\pi\)
0.955221 + 0.295894i \(0.0956176\pi\)
\(444\) −5.90494 1.46004i −0.280236 0.0692907i
\(445\) 20.9938 21.9241i 0.995202 1.03930i
\(446\) −6.90996 6.90996i −0.327196 0.327196i
\(447\) −13.1111 13.1111i −0.620132 0.620132i
\(448\) 2.77693 2.77693i 0.131198 0.131198i
\(449\) −4.29038 4.29038i −0.202475 0.202475i 0.598584 0.801060i \(-0.295730\pi\)
−0.801060 + 0.598584i \(0.795730\pi\)
\(450\) 0.216671 + 4.99530i 0.0102140 + 0.235481i
\(451\) 9.57172 0.450715
\(452\) 4.08857i 0.192310i
\(453\) 3.20694 + 3.20694i 0.150675 + 0.150675i
\(454\) 0.338896i 0.0159052i
\(455\) 12.7408 13.3054i 0.597299 0.623768i
\(456\) −4.25447 −0.199234
\(457\) 37.1873i 1.73955i −0.493449 0.869775i \(-0.664264\pi\)
0.493449 0.869775i \(-0.335736\pi\)
\(458\) 6.86738i 0.320892i
\(459\) −3.21286 + 3.21286i −0.149963 + 0.149963i
\(460\) 2.44361 0.0529709i 0.113934 0.00246978i
\(461\) −13.3683 + 13.3683i −0.622625 + 0.622625i −0.946202 0.323577i \(-0.895115\pi\)
0.323577 + 0.946202i \(0.395115\pi\)
\(462\) −10.7633 −0.500756
\(463\) −41.3804 −1.92311 −0.961554 0.274614i \(-0.911450\pi\)
−0.961554 + 0.274614i \(0.911450\pi\)
\(464\) −3.41798 + 3.41798i −0.158676 + 0.158676i
\(465\) −1.40462 + 0.0304485i −0.0651379 + 0.00141201i
\(466\) −11.8523 + 11.8523i −0.549047 + 0.549047i
\(467\) 32.7500i 1.51549i −0.652552 0.757744i \(-0.726302\pi\)
0.652552 0.757744i \(-0.273698\pi\)
\(468\) 2.09781i 0.0969714i
\(469\) −19.0241 −0.878451
\(470\) −9.36269 + 9.77759i −0.431868 + 0.451007i
\(471\) 3.05366i 0.140705i
\(472\) 10.1179 + 10.1179i 0.465713 + 0.465713i
\(473\) 7.25238i 0.333465i
\(474\) −6.85285 −0.314762
\(475\) −15.6795 14.3759i −0.719426 0.659610i
\(476\) 12.6175 + 12.6175i 0.578320 + 0.578320i
\(477\) −4.10770 + 4.10770i −0.188078 + 0.188078i
\(478\) −11.8453 11.8453i −0.541790 0.541790i
\(479\) 16.6994 + 16.6994i 0.763017 + 0.763017i 0.976867 0.213849i \(-0.0686002\pi\)
−0.213849 + 0.976867i \(0.568600\pi\)
\(480\) −1.54650 + 1.61503i −0.0705878 + 0.0737159i
\(481\) −6.59345 10.9250i −0.300635 0.498139i
\(482\) 1.06176 1.06176i 0.0483618 0.0483618i
\(483\) 4.29269i 0.195324i
\(484\) 3.48838 0.158563
\(485\) −0.246429 11.3681i −0.0111897 0.516197i
\(486\) −0.707107 + 0.707107i −0.0320750 + 0.0320750i
\(487\) 0.862986i 0.0391056i −0.999809 0.0195528i \(-0.993776\pi\)
0.999809 0.0195528i \(-0.00622425\pi\)
\(488\) 4.77382 + 4.77382i 0.216101 + 0.216101i
\(489\) −9.35293 9.35293i −0.422954 0.422954i
\(490\) −0.408169 18.8293i −0.0184392 0.850623i
\(491\) −27.6627 −1.24840 −0.624201 0.781264i \(-0.714575\pi\)
−0.624201 + 0.781264i \(0.714575\pi\)
\(492\) −2.46949 2.46949i −0.111333 0.111333i
\(493\) −15.5302 15.5302i −0.699443 0.699443i
\(494\) −6.31099 6.31099i −0.283945 0.283945i
\(495\) 6.12703 0.132817i 0.275389 0.00596969i
\(496\) −0.444286 0.444286i −0.0199490 0.0199490i
\(497\) 1.42408 1.42408i 0.0638787 0.0638787i
\(498\) 5.78826 0.259378
\(499\) 3.33614 3.33614i 0.149346 0.149346i −0.628480 0.777826i \(-0.716322\pi\)
0.777826 + 0.628480i \(0.216322\pi\)
\(500\) −11.1567 + 0.726452i −0.498943 + 0.0324879i
\(501\) −1.52500 1.52500i −0.0681318 0.0681318i
\(502\) −10.3290 10.3290i −0.461005 0.461005i
\(503\) −25.4113 −1.13303 −0.566516 0.824050i \(-0.691709\pi\)
−0.566516 + 0.824050i \(0.691709\pi\)
\(504\) 2.77693 + 2.77693i 0.123694 + 0.123694i
\(505\) 0.693825 + 32.0070i 0.0308748 + 1.42429i
\(506\) 2.99582i 0.133181i
\(507\) 6.08054 6.08054i 0.270046 0.270046i
\(508\) −8.71272 + 8.71272i −0.386565 + 0.386565i
\(509\) −15.9962 −0.709020 −0.354510 0.935052i \(-0.615352\pi\)
−0.354510 + 0.935052i \(0.615352\pi\)
\(510\) −7.33818 7.02678i −0.324940 0.311151i
\(511\) 53.1555i 2.35146i
\(512\) −1.00000 −0.0441942
\(513\) 4.25447i 0.187840i
\(514\) 28.1460i 1.24146i
\(515\) −0.407584 18.8024i −0.0179603 0.828531i
\(516\) 1.87111 1.87111i 0.0823709 0.0823709i
\(517\) 11.7328 + 11.7328i 0.516008 + 0.516008i
\(518\) −23.1897 5.73385i −1.01890 0.251931i
\(519\) 18.0779i 0.793534i
\(520\) −4.68975 + 0.101661i −0.205659 + 0.00445813i
\(521\) 41.9890i 1.83957i −0.392421 0.919786i \(-0.628362\pi\)
0.392421 0.919786i \(-0.371638\pi\)
\(522\) −3.41798 3.41798i −0.149601 0.149601i
\(523\) −16.7289 −0.731505 −0.365753 0.930712i \(-0.619188\pi\)
−0.365753 + 0.930712i \(0.619188\pi\)
\(524\) −15.0456 15.0456i −0.657269 0.657269i
\(525\) 0.850906 + 19.6174i 0.0371366 + 0.856175i
\(526\) 1.14169 1.14169i 0.0497799 0.0497799i
\(527\) 2.01869 2.01869i 0.0879353 0.0879353i
\(528\) 1.93799 + 1.93799i 0.0843402 + 0.0843402i
\(529\) −21.8052 −0.948052
\(530\) −9.38199 8.98387i −0.407528 0.390234i
\(531\) −10.1179 + 10.1179i −0.439079 + 0.439079i
\(532\) −16.7081 −0.724386
\(533\) 7.32638i 0.317341i
\(534\) 13.5750i 0.587449i
\(535\) −10.6780 + 11.1512i −0.461650 + 0.482108i
\(536\) 3.42538 + 3.42538i 0.147954 + 0.147954i
\(537\) 12.6265i 0.544874i
\(538\) 0.755375i 0.0325665i
\(539\) −23.0844 −0.994316
\(540\) −1.61503 1.54650i −0.0695000 0.0665508i
\(541\) 5.79651 5.79651i 0.249212 0.249212i −0.571435 0.820647i \(-0.693613\pi\)
0.820647 + 0.571435i \(0.193613\pi\)
\(542\) −13.0803 −0.561848
\(543\) −6.19810 + 6.19810i −0.265986 + 0.265986i
\(544\) 4.54367i 0.194808i
\(545\) 21.4088 + 20.5003i 0.917053 + 0.878138i
\(546\) 8.23848i 0.352574i
\(547\) 20.4569 0.874675 0.437337 0.899298i \(-0.355922\pi\)
0.437337 + 0.899298i \(0.355922\pi\)
\(548\) 7.51357 7.51357i 0.320964 0.320964i
\(549\) −4.77382 + 4.77382i −0.203742 + 0.203742i
\(550\) 0.593838 + 13.6908i 0.0253213 + 0.583777i
\(551\) 20.5651 0.876102
\(552\) −0.772920 + 0.772920i −0.0328977 + 0.0328977i
\(553\) −26.9124 −1.14443
\(554\) −27.8958 −1.18518
\(555\) 13.2715 + 2.97784i 0.563343 + 0.126402i
\(556\) 7.58286 0.321585
\(557\) 5.28270 0.223835 0.111918 0.993717i \(-0.464301\pi\)
0.111918 + 0.993717i \(0.464301\pi\)
\(558\) 0.444286 0.444286i 0.0188081 0.0188081i
\(559\) 5.55112 0.234787
\(560\) −6.07338 + 6.34253i −0.256647 + 0.268021i
\(561\) −8.80558 + 8.80558i −0.371772 + 0.371772i
\(562\) −3.25168 + 3.25168i −0.137164 + 0.137164i
\(563\) 21.9241 0.923990 0.461995 0.886882i \(-0.347134\pi\)
0.461995 + 0.886882i \(0.347134\pi\)
\(564\) 6.05411i 0.254924i
\(565\) 0.198134 + 9.14016i 0.00833556 + 0.384530i
\(566\) 12.8597i 0.540534i
\(567\) −2.77693 + 2.77693i −0.116620 + 0.116620i
\(568\) −0.512824 −0.0215176
\(569\) 13.2365 13.2365i 0.554904 0.554904i −0.372948 0.927852i \(-0.621653\pi\)
0.927852 + 0.372948i \(0.121653\pi\)
\(570\) 9.51105 0.206174i 0.398374 0.00863567i
\(571\) −7.69386 −0.321978 −0.160989 0.986956i \(-0.551468\pi\)
−0.160989 + 0.986956i \(0.551468\pi\)
\(572\) 5.74954i 0.240400i
\(573\) 4.65277i 0.194372i
\(574\) −9.69814 9.69814i −0.404793 0.404793i
\(575\) −5.46023 + 0.236837i −0.227708 + 0.00987680i
\(576\) 1.00000i 0.0416667i
\(577\) 6.45917i 0.268899i −0.990920 0.134449i \(-0.957073\pi\)
0.990920 0.134449i \(-0.0429265\pi\)
\(578\) 3.64491 0.151608
\(579\) 13.7168 13.7168i 0.570051 0.570051i
\(580\) 7.47541 7.80668i 0.310399 0.324155i
\(581\) 22.7315 0.943062
\(582\) 3.59574 + 3.59574i 0.149048 + 0.149048i
\(583\) −11.2581 + 11.2581i −0.466263 + 0.466263i
\(584\) 9.57090 9.57090i 0.396047 0.396047i
\(585\) −0.101661 4.68975i −0.00420317 0.193897i
\(586\) 8.19264 + 8.19264i 0.338435 + 0.338435i
\(587\) 30.4031 1.25487 0.627435 0.778669i \(-0.284105\pi\)
0.627435 + 0.778669i \(0.284105\pi\)
\(588\) 5.95576 + 5.95576i 0.245611 + 0.245611i
\(589\) 2.67315i 0.110145i
\(590\) −23.1093 22.1287i −0.951394 0.911022i
\(591\) 17.8938i 0.736052i
\(592\) 3.14301 + 5.20783i 0.129177 + 0.214040i
\(593\) 4.55951 + 4.55951i 0.187237 + 0.187237i 0.794500 0.607264i \(-0.207733\pi\)
−0.607264 + 0.794500i \(0.707733\pi\)
\(594\) −1.93799 + 1.93799i −0.0795167 + 0.0795167i
\(595\) −28.8183 27.5954i −1.18144 1.13130i
\(596\) 18.5418i 0.759504i
\(597\) 4.60742i 0.188569i
\(598\) −2.29306 −0.0937703
\(599\) 20.9262i 0.855023i −0.904010 0.427511i \(-0.859390\pi\)
0.904010 0.427511i \(-0.140610\pi\)
\(600\) 3.37900 3.68542i 0.137947 0.150457i
\(601\) 46.3008 1.88865 0.944325 0.329013i \(-0.106716\pi\)
0.944325 + 0.329013i \(0.106716\pi\)
\(602\) 7.34817 7.34817i 0.299489 0.299489i
\(603\) −3.42538 + 3.42538i −0.139492 + 0.139492i
\(604\) 4.53529i 0.184538i
\(605\) −7.79843 + 0.169049i −0.317051 + 0.00687281i
\(606\) −10.1239 10.1239i −0.411255 0.411255i
\(607\) −20.3014 −0.824007 −0.412004 0.911182i \(-0.635171\pi\)
−0.412004 + 0.911182i \(0.635171\pi\)
\(608\) 3.00837 + 3.00837i 0.122005 + 0.122005i
\(609\) −13.4230 13.4230i −0.543928 0.543928i
\(610\) −10.9034 10.4407i −0.441467 0.422734i
\(611\) 8.98053 8.98053i 0.363313 0.363313i
\(612\) 4.54367 0.183667
\(613\) 11.6147 11.6147i 0.469115 0.469115i −0.432513 0.901628i \(-0.642373\pi\)
0.901628 + 0.432513i \(0.142373\pi\)
\(614\) −1.93471 1.93471i −0.0780787 0.0780787i
\(615\) 5.64033 + 5.40099i 0.227440 + 0.217789i
\(616\) 7.61083 + 7.61083i 0.306649 + 0.306649i
\(617\) 5.70622 + 5.70622i 0.229724 + 0.229724i 0.812577 0.582853i \(-0.198064\pi\)
−0.582853 + 0.812577i \(0.698064\pi\)
\(618\) 5.94723 + 5.94723i 0.239233 + 0.239233i
\(619\) −10.0488 −0.403896 −0.201948 0.979396i \(-0.564727\pi\)
−0.201948 + 0.979396i \(0.564727\pi\)
\(620\) 1.01475 + 0.971689i 0.0407533 + 0.0390240i
\(621\) −0.772920 0.772920i −0.0310162 0.0310162i
\(622\) 24.0063 + 24.0063i 0.962565 + 0.962565i
\(623\) 53.3116i 2.13588i
\(624\) 1.48338 1.48338i 0.0593826 0.0593826i
\(625\) 24.9061 2.16468i 0.996244 0.0865870i
\(626\) −28.6636 −1.14563
\(627\) 11.6604i 0.465670i
\(628\) −2.15926 + 2.15926i −0.0861639 + 0.0861639i
\(629\) −23.6626 + 14.2808i −0.943491 + 0.569413i
\(630\) −6.34253 6.07338i −0.252692 0.241969i
\(631\) 14.4480 + 14.4480i 0.575166 + 0.575166i 0.933568 0.358402i \(-0.116678\pi\)
−0.358402 + 0.933568i \(0.616678\pi\)
\(632\) 4.84570 + 4.84570i 0.192752 + 0.192752i
\(633\) 1.04833 1.04833i 0.0416674 0.0416674i
\(634\) 14.0253 + 14.0253i 0.557016 + 0.557016i
\(635\) 19.0554 19.8999i 0.756192 0.789703i
\(636\) 5.80916 0.230348
\(637\) 17.6693i 0.700082i
\(638\) −9.36777 9.36777i −0.370874 0.370874i
\(639\) 0.512824i 0.0202870i
\(640\) 2.23554 0.0484605i 0.0883676 0.00191557i
\(641\) −37.9442 −1.49870 −0.749352 0.662171i \(-0.769635\pi\)
−0.749352 + 0.662171i \(0.769635\pi\)
\(642\) 6.90462i 0.272504i
\(643\) 27.7110i 1.09281i −0.837520 0.546407i \(-0.815995\pi\)
0.837520 0.546407i \(-0.184005\pi\)
\(644\) −3.03539 + 3.03539i −0.119611 + 0.119611i
\(645\) −4.09227 + 4.27362i −0.161133 + 0.168273i
\(646\) −13.6690 + 13.6690i −0.537800 + 0.537800i
\(647\) 13.3729 0.525745 0.262872 0.964831i \(-0.415330\pi\)
0.262872 + 0.964831i \(0.415330\pi\)
\(648\) 1.00000 0.0392837
\(649\) −27.7304 + 27.7304i −1.08851 + 1.08851i
\(650\) 10.4792 0.454535i 0.411028 0.0178283i
\(651\) 1.74479 1.74479i 0.0683837 0.0683837i
\(652\) 13.2270i 0.518011i
\(653\) 10.9215i 0.427391i −0.976900 0.213695i \(-0.931450\pi\)
0.976900 0.213695i \(-0.0685500\pi\)
\(654\) −13.2560 −0.518349
\(655\) 34.3642 + 32.9059i 1.34272 + 1.28574i
\(656\) 3.49239i 0.136355i
\(657\) 9.57090 + 9.57090i 0.373396 + 0.373396i
\(658\) 23.7756i 0.926868i
\(659\) 29.6060 1.15329 0.576644 0.816996i \(-0.304362\pi\)
0.576644 + 0.816996i \(0.304362\pi\)
\(660\) −4.42638 4.23855i −0.172297 0.164985i
\(661\) 31.8938 + 31.8938i 1.24053 + 1.24053i 0.959783 + 0.280744i \(0.0905812\pi\)
0.280744 + 0.959783i \(0.409419\pi\)
\(662\) 5.28358 5.28358i 0.205352 0.205352i
\(663\) 6.73997 + 6.73997i 0.261759 + 0.261759i
\(664\) −4.09292 4.09292i −0.158836 0.158836i
\(665\) 37.3516 0.809681i 1.44843 0.0313981i
\(666\) −5.20783 + 3.14301i −0.201799 + 0.121789i
\(667\) 3.73610 3.73610i 0.144663 0.144663i
\(668\) 2.15667i 0.0834441i
\(669\) −9.77217 −0.377814
\(670\) −7.82357 7.49158i −0.302251 0.289425i
\(671\) −13.0838 + 13.0838i −0.505094 + 0.505094i
\(672\) 3.92718i 0.151494i
\(673\) 20.0029 + 20.0029i 0.771053 + 0.771053i 0.978291 0.207237i \(-0.0664472\pi\)
−0.207237 + 0.978291i \(0.566447\pi\)
\(674\) 15.8649 + 15.8649i 0.611093 + 0.611093i
\(675\) 3.68542 + 3.37900i 0.141852 + 0.130058i
\(676\) −8.59918 −0.330738
\(677\) 4.10184 + 4.10184i 0.157646 + 0.157646i 0.781523 0.623876i \(-0.214443\pi\)
−0.623876 + 0.781523i \(0.714443\pi\)
\(678\) −2.89105 2.89105i −0.111030 0.111030i
\(679\) 14.1211 + 14.1211i 0.541918 + 0.541918i
\(680\) 0.220188 + 10.1576i 0.00844384 + 0.389525i
\(681\) −0.239636 0.239636i −0.00918287 0.00918287i
\(682\) 1.21767 1.21767i 0.0466269 0.0466269i
\(683\) 26.9295 1.03043 0.515215 0.857061i \(-0.327712\pi\)
0.515215 + 0.857061i \(0.327712\pi\)
\(684\) −3.00837 + 3.00837i −0.115028 + 0.115028i
\(685\) −16.4328 + 17.1610i −0.627865 + 0.655689i
\(686\) 3.95079 + 3.95079i 0.150842 + 0.150842i
\(687\) −4.85597 4.85597i −0.185267 0.185267i
\(688\) −2.64615 −0.100883
\(689\) 8.61717 + 8.61717i 0.328288 + 0.328288i
\(690\) 1.69044 1.76535i 0.0643539 0.0672058i
\(691\) 4.39008i 0.167007i −0.996508 0.0835033i \(-0.973389\pi\)
0.996508 0.0835033i \(-0.0266109\pi\)
\(692\) −12.7830 + 12.7830i −0.485938 + 0.485938i
\(693\) −7.61083 + 7.61083i −0.289112 + 0.289112i
\(694\) −20.2697 −0.769428
\(695\) −16.9518 + 0.367469i −0.643019 + 0.0139389i
\(696\) 4.83375i 0.183223i
\(697\) −15.8683 −0.601054
\(698\) 23.3133i 0.882420i
\(699\) 16.7617i 0.633985i
\(700\) 13.2699 14.4733i 0.501557 0.547040i
\(701\) 7.67375 7.67375i 0.289834 0.289834i −0.547181 0.837014i \(-0.684299\pi\)
0.837014 + 0.547181i \(0.184299\pi\)
\(702\) 1.48338 + 1.48338i 0.0559865 + 0.0559865i
\(703\) 6.21172 25.1224i 0.234279 0.947509i
\(704\) 2.74073i 0.103295i
\(705\) 0.293385 + 13.5342i 0.0110495 + 0.509728i
\(706\) 35.1904i 1.32441i
\(707\) −39.7583 39.7583i −1.49526 1.49526i
\(708\) 14.3089 0.537760
\(709\) 4.72562 + 4.72562i 0.177474 + 0.177474i 0.790254 0.612779i \(-0.209949\pi\)
−0.612779 + 0.790254i \(0.709949\pi\)
\(710\) 1.14644 0.0248517i 0.0430252 0.000932669i
\(711\) −4.84570 + 4.84570i −0.181728 + 0.181728i
\(712\) 9.59900 9.59900i 0.359738 0.359738i
\(713\) 0.485637 + 0.485637i 0.0181872 + 0.0181872i
\(714\) 17.8438 0.667787
\(715\) −0.278626 12.8533i −0.0104200 0.480688i
\(716\) 8.92829 8.92829i 0.333666 0.333666i
\(717\) −16.7517 −0.625606
\(718\) 34.3706i 1.28270i
\(719\) 48.1348i 1.79513i −0.440887 0.897563i \(-0.645336\pi\)
0.440887 0.897563i \(-0.354664\pi\)
\(720\) 0.0484605 + 2.23554i 0.00180602 + 0.0833138i
\(721\) 23.3558 + 23.3558i 0.869816 + 0.869816i
\(722\) 0.899470i 0.0334748i
\(723\) 1.50155i 0.0558433i
\(724\) 8.76543 0.325765
\(725\) −16.3333 + 17.8144i −0.606603 + 0.661611i
\(726\) 2.46666 2.46666i 0.0915463 0.0915463i
\(727\) −30.0659 −1.11508 −0.557541 0.830150i \(-0.688255\pi\)
−0.557541 + 0.830150i \(0.688255\pi\)
\(728\) 5.82548 5.82548i 0.215907 0.215907i
\(729\) 1.00000i 0.0370370i
\(730\) −20.9323 + 21.8600i −0.774741 + 0.809074i
\(731\) 12.0232i 0.444694i
\(732\) 6.75121 0.249532
\(733\) −0.507990 + 0.507990i −0.0187630 + 0.0187630i −0.716426 0.697663i \(-0.754223\pi\)
0.697663 + 0.716426i \(0.254223\pi\)
\(734\) 15.7170 15.7170i 0.580125 0.580125i
\(735\) −13.6030 13.0257i −0.501753 0.480462i
\(736\) 1.09307 0.0402912
\(737\) −9.38804 + 9.38804i −0.345813 + 0.345813i
\(738\) −3.49239 −0.128557
\(739\) 33.1591 1.21978 0.609889 0.792487i \(-0.291214\pi\)
0.609889 + 0.792487i \(0.291214\pi\)
\(740\) −7.27871 11.4900i −0.267571 0.422381i
\(741\) −8.92508 −0.327871
\(742\) 22.8136 0.837513
\(743\) 7.44969 7.44969i 0.273303 0.273303i −0.557126 0.830428i \(-0.688096\pi\)
0.830428 + 0.557126i \(0.188096\pi\)
\(744\) −0.628315 −0.0230351
\(745\) −0.898547 41.4511i −0.0329202 1.51865i
\(746\) −5.59113 + 5.59113i −0.204706 + 0.204706i
\(747\) 4.09292 4.09292i 0.149752 0.149752i
\(748\) 12.4530 0.455326
\(749\) 27.1157i 0.990785i
\(750\) −7.37531 + 8.40267i −0.269308 + 0.306822i
\(751\) 40.2247i 1.46782i −0.679246 0.733911i \(-0.737693\pi\)
0.679246 0.733911i \(-0.262307\pi\)
\(752\) −4.28090 + 4.28090i −0.156108 + 0.156108i
\(753\) −14.6074 −0.532323
\(754\) −7.17028 + 7.17028i −0.261126 + 0.261126i
\(755\) 0.219783 + 10.1388i 0.00799871 + 0.368990i
\(756\) 3.92718 0.142830
\(757\) 4.85976i 0.176631i −0.996093 0.0883156i \(-0.971852\pi\)
0.996093 0.0883156i \(-0.0281484\pi\)
\(758\) 20.7595i 0.754018i
\(759\) −2.11837 2.11837i −0.0768918 0.0768918i
\(760\) −6.87112 6.57954i −0.249242 0.238665i
\(761\) 10.4339i 0.378230i 0.981955 + 0.189115i \(0.0605618\pi\)
−0.981955 + 0.189115i \(0.939438\pi\)
\(762\) 12.3216i 0.446366i
\(763\) −52.0585 −1.88464
\(764\) 3.29001 3.29001i 0.119028 0.119028i
\(765\) −10.1576 + 0.220188i −0.367247 + 0.00796093i
\(766\) −19.9351 −0.720284
\(767\) 21.2254 + 21.2254i 0.766406 + 0.766406i
\(768\) −0.707107 + 0.707107i −0.0255155 + 0.0255155i
\(769\) 29.8513 29.8513i 1.07647 1.07647i 0.0796432 0.996823i \(-0.474622\pi\)
0.996823 0.0796432i \(-0.0253781\pi\)
\(770\) −17.3832 16.6455i −0.626446 0.599863i
\(771\) 19.9022 + 19.9022i 0.716760 + 0.716760i
\(772\) −19.3985 −0.698168
\(773\) −31.7498 31.7498i −1.14196 1.14196i −0.988091 0.153868i \(-0.950827\pi\)
−0.153868 0.988091i \(-0.549173\pi\)
\(774\) 2.64615i 0.0951138i
\(775\) −2.31561 2.12308i −0.0831790 0.0762632i
\(776\) 5.08514i 0.182546i
\(777\) −20.4521 + 12.3432i −0.733714 + 0.442809i
\(778\) −2.00735 2.00735i −0.0719671 0.0719671i
\(779\) 10.5064 10.5064i 0.376431 0.376431i