Properties

Label 441.2.h.f.373.1
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(1.19343 + 2.06709i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.f.214.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.38687 q^{2} +(1.61557 + 0.624446i) q^{3} +3.69714 q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 - 1.49047i) q^{6} -4.05086 q^{8} +(2.22013 + 2.01767i) q^{9} +O(q^{10})\) \(q-2.38687 q^{2} +(1.61557 + 0.624446i) q^{3} +3.69714 q^{4} +(-1.46043 - 2.52954i) q^{5} +(-3.85615 - 1.49047i) q^{6} -4.05086 q^{8} +(2.22013 + 2.01767i) q^{9} +(3.48586 + 6.03769i) q^{10} +(0.676857 - 1.17235i) q^{11} +(5.97299 + 2.30867i) q^{12} +(0.733001 - 1.26960i) q^{13} +(-0.779867 - 4.99862i) q^{15} +2.27458 q^{16} +(-1.65514 - 2.86678i) q^{17} +(-5.29917 - 4.81592i) q^{18} +(1.10329 - 1.91096i) q^{19} +(-5.39943 - 9.35209i) q^{20} +(-1.61557 + 2.79825i) q^{22} +(-1.31415 - 2.27617i) q^{23} +(-6.54444 - 2.52954i) q^{24} +(-1.76573 + 3.05833i) q^{25} +(-1.74958 + 3.03036i) q^{26} +(2.32685 + 4.64605i) q^{27} +(0.521720 + 0.903646i) q^{29} +(1.86144 + 11.9310i) q^{30} -3.27458 q^{31} +2.67259 q^{32} +(1.82558 - 1.47135i) q^{33} +(3.95060 + 6.84263i) q^{34} +(8.20815 + 7.45963i) q^{36} +(5.43773 - 9.41842i) q^{37} +(-2.63342 + 4.56121i) q^{38} +(1.97701 - 1.59340i) q^{39} +(5.91601 + 10.2468i) q^{40} +(0.904289 - 1.56627i) q^{41} +(-2.17129 - 3.76078i) q^{43} +(2.50244 - 4.33435i) q^{44} +(1.86144 - 8.56260i) q^{45} +(3.13670 + 5.43292i) q^{46} -3.97914 q^{47} +(3.67474 + 1.42035i) q^{48} +(4.21456 - 7.29984i) q^{50} +(-0.883838 - 5.66503i) q^{51} +(2.71001 - 4.69388i) q^{52} +(-3.22743 - 5.59008i) q^{53} +(-5.55389 - 11.0895i) q^{54} -3.95402 q^{55} +(2.97574 - 2.39834i) q^{57} +(-1.24528 - 2.15688i) q^{58} +12.2140 q^{59} +(-2.88328 - 18.4806i) q^{60} -0.559734 q^{61} +7.81600 q^{62} -10.9283 q^{64} -4.28200 q^{65} +(-4.35742 + 3.51193i) q^{66} +12.8118 q^{67} +(-6.11928 - 10.5989i) q^{68} +(-0.701751 - 4.49793i) q^{69} +12.9177 q^{71} +(-8.99344 - 8.17331i) q^{72} +(-5.22772 - 9.05467i) q^{73} +(-12.9791 + 22.4805i) q^{74} +(-4.76242 + 3.83835i) q^{75} +(4.07903 - 7.06509i) q^{76} +(-4.71886 + 3.80324i) q^{78} +0.767677 q^{79} +(-3.32187 - 5.75365i) q^{80} +(0.857983 + 8.95901i) q^{81} +(-2.15842 + 3.73849i) q^{82} +(0.983707 + 1.70383i) q^{83} +(-4.83443 + 8.37348i) q^{85} +(5.18258 + 8.97649i) q^{86} +(0.278597 + 1.78569i) q^{87} +(-2.74185 + 4.74903i) q^{88} +(-3.20356 + 5.54872i) q^{89} +(-4.44301 + 20.4378i) q^{90} +(-4.85859 - 8.41533i) q^{92} +(-5.29031 - 2.04480i) q^{93} +9.49769 q^{94} -6.44514 q^{95} +(4.31776 + 1.66889i) q^{96} +(4.14143 + 7.17316i) q^{97} +(3.86814 - 1.23710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + O(q^{10}) \) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + 7q^{10} + 4q^{11} + 20q^{12} + 8q^{13} - 19q^{15} - 4q^{16} - 12q^{17} + 4q^{18} - q^{19} - 5q^{20} - q^{22} + 3q^{23} - 6q^{24} - q^{25} - 11q^{26} + 7q^{27} + 7q^{29} + 16q^{30} - 6q^{31} + 4q^{32} - 14q^{33} - 3q^{34} + 34q^{36} - 20q^{38} + 2q^{39} + 3q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + 16q^{45} + 3q^{46} + 54q^{47} + 5q^{48} + 19q^{50} - 9q^{51} + 10q^{52} - 21q^{53} - q^{54} - 4q^{55} - 4q^{57} - 10q^{58} + 60q^{59} + 10q^{60} - 28q^{61} + 12q^{62} - 50q^{64} + 22q^{65} - 19q^{66} + 4q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 36q^{72} - 15q^{73} - 36q^{74} + 14q^{75} - 5q^{76} - 20q^{78} + 8q^{79} - 20q^{80} + 23q^{81} + 5q^{82} - 9q^{83} - 6q^{85} - 8q^{86} - 2q^{87} - 18q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 6q^{93} - 6q^{94} + 28q^{95} - 59q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.38687 −1.68777 −0.843886 0.536523i \(-0.819737\pi\)
−0.843886 + 0.536523i \(0.819737\pi\)
\(3\) 1.61557 + 0.624446i 0.932750 + 0.360524i
\(4\) 3.69714 1.84857
\(5\) −1.46043 2.52954i −0.653125 1.13125i −0.982360 0.186998i \(-0.940124\pi\)
0.329235 0.944248i \(-0.393209\pi\)
\(6\) −3.85615 1.49047i −1.57427 0.608483i
\(7\) 0 0
\(8\) −4.05086 −1.43219
\(9\) 2.22013 + 2.01767i 0.740044 + 0.672558i
\(10\) 3.48586 + 6.03769i 1.10233 + 1.90929i
\(11\) 0.676857 1.17235i 0.204080 0.353477i −0.745759 0.666216i \(-0.767913\pi\)
0.949839 + 0.312738i \(0.101246\pi\)
\(12\) 5.97299 + 2.30867i 1.72425 + 0.666455i
\(13\) 0.733001 1.26960i 0.203298 0.352123i −0.746291 0.665620i \(-0.768167\pi\)
0.949589 + 0.313497i \(0.101501\pi\)
\(14\) 0 0
\(15\) −0.779867 4.99862i −0.201361 1.29064i
\(16\) 2.27458 0.568645
\(17\) −1.65514 2.86678i −0.401430 0.695297i 0.592469 0.805593i \(-0.298153\pi\)
−0.993899 + 0.110297i \(0.964820\pi\)
\(18\) −5.29917 4.81592i −1.24903 1.13512i
\(19\) 1.10329 1.91096i 0.253113 0.438404i −0.711268 0.702921i \(-0.751879\pi\)
0.964381 + 0.264516i \(0.0852123\pi\)
\(20\) −5.39943 9.35209i −1.20735 2.09119i
\(21\) 0 0
\(22\) −1.61557 + 2.79825i −0.344441 + 0.596589i
\(23\) −1.31415 2.27617i −0.274019 0.474614i 0.695868 0.718169i \(-0.255020\pi\)
−0.969887 + 0.243555i \(0.921686\pi\)
\(24\) −6.54444 2.52954i −1.33588 0.516341i
\(25\) −1.76573 + 3.05833i −0.353146 + 0.611666i
\(26\) −1.74958 + 3.03036i −0.343121 + 0.594302i
\(27\) 2.32685 + 4.64605i 0.447803 + 0.894132i
\(28\) 0 0
\(29\) 0.521720 + 0.903646i 0.0968810 + 0.167803i 0.910392 0.413747i \(-0.135780\pi\)
−0.813511 + 0.581549i \(0.802447\pi\)
\(30\) 1.86144 + 11.9310i 0.339851 + 2.17830i
\(31\) −3.27458 −0.588132 −0.294066 0.955785i \(-0.595009\pi\)
−0.294066 + 0.955785i \(0.595009\pi\)
\(32\) 2.67259 0.472452
\(33\) 1.82558 1.47135i 0.317793 0.256130i
\(34\) 3.95060 + 6.84263i 0.677521 + 1.17350i
\(35\) 0 0
\(36\) 8.20815 + 7.45963i 1.36803 + 1.24327i
\(37\) 5.43773 9.41842i 0.893957 1.54838i 0.0588664 0.998266i \(-0.481251\pi\)
0.835090 0.550113i \(-0.185415\pi\)
\(38\) −2.63342 + 4.56121i −0.427197 + 0.739926i
\(39\) 1.97701 1.59340i 0.316575 0.255148i
\(40\) 5.91601 + 10.2468i 0.935403 + 1.62017i
\(41\) 0.904289 1.56627i 0.141226 0.244611i −0.786732 0.617294i \(-0.788229\pi\)
0.927959 + 0.372683i \(0.121562\pi\)
\(42\) 0 0
\(43\) −2.17129 3.76078i −0.331118 0.573514i 0.651613 0.758551i \(-0.274093\pi\)
−0.982731 + 0.185038i \(0.940759\pi\)
\(44\) 2.50244 4.33435i 0.377257 0.653428i
\(45\) 1.86144 8.56260i 0.277487 1.27644i
\(46\) 3.13670 + 5.43292i 0.462481 + 0.801041i
\(47\) −3.97914 −0.580417 −0.290209 0.956963i \(-0.593725\pi\)
−0.290209 + 0.956963i \(0.593725\pi\)
\(48\) 3.67474 + 1.42035i 0.530404 + 0.205010i
\(49\) 0 0
\(50\) 4.21456 7.29984i 0.596029 1.03235i
\(51\) −0.883838 5.66503i −0.123762 0.793263i
\(52\) 2.71001 4.69388i 0.375811 0.650924i
\(53\) −3.22743 5.59008i −0.443322 0.767856i 0.554612 0.832109i \(-0.312867\pi\)
−0.997934 + 0.0642533i \(0.979533\pi\)
\(54\) −5.55389 11.0895i −0.755789 1.50909i
\(55\) −3.95402 −0.533160
\(56\) 0 0
\(57\) 2.97574 2.39834i 0.394146 0.317668i
\(58\) −1.24528 2.15688i −0.163513 0.283213i
\(59\) 12.2140 1.59013 0.795064 0.606526i \(-0.207437\pi\)
0.795064 + 0.606526i \(0.207437\pi\)
\(60\) −2.88328 18.4806i −0.372230 2.38584i
\(61\) −0.559734 −0.0716666 −0.0358333 0.999358i \(-0.511409\pi\)
−0.0358333 + 0.999358i \(0.511409\pi\)
\(62\) 7.81600 0.992632
\(63\) 0 0
\(64\) −10.9283 −1.36604
\(65\) −4.28200 −0.531117
\(66\) −4.35742 + 3.51193i −0.536362 + 0.432289i
\(67\) 12.8118 1.56521 0.782603 0.622521i \(-0.213891\pi\)
0.782603 + 0.622521i \(0.213891\pi\)
\(68\) −6.11928 10.5989i −0.742072 1.28531i
\(69\) −0.701751 4.49793i −0.0844809 0.541487i
\(70\) 0 0
\(71\) 12.9177 1.53305 0.766525 0.642214i \(-0.221984\pi\)
0.766525 + 0.642214i \(0.221984\pi\)
\(72\) −8.99344 8.17331i −1.05989 0.963234i
\(73\) −5.22772 9.05467i −0.611858 1.05977i −0.990927 0.134401i \(-0.957089\pi\)
0.379069 0.925368i \(-0.376244\pi\)
\(74\) −12.9791 + 22.4805i −1.50879 + 2.61331i
\(75\) −4.76242 + 3.83835i −0.549917 + 0.443214i
\(76\) 4.07903 7.06509i 0.467897 0.810422i
\(77\) 0 0
\(78\) −4.71886 + 3.80324i −0.534306 + 0.430632i
\(79\) 0.767677 0.0863704 0.0431852 0.999067i \(-0.486249\pi\)
0.0431852 + 0.999067i \(0.486249\pi\)
\(80\) −3.32187 5.75365i −0.371397 0.643278i
\(81\) 0.857983 + 8.95901i 0.0953314 + 0.995446i
\(82\) −2.15842 + 3.73849i −0.238358 + 0.412847i
\(83\) 0.983707 + 1.70383i 0.107976 + 0.187020i 0.914950 0.403567i \(-0.132230\pi\)
−0.806974 + 0.590587i \(0.798896\pi\)
\(84\) 0 0
\(85\) −4.83443 + 8.37348i −0.524368 + 0.908232i
\(86\) 5.18258 + 8.97649i 0.558852 + 0.967960i
\(87\) 0.278597 + 1.78569i 0.0298687 + 0.191446i
\(88\) −2.74185 + 4.74903i −0.292283 + 0.506248i
\(89\) −3.20356 + 5.54872i −0.339576 + 0.588163i −0.984353 0.176208i \(-0.943617\pi\)
0.644777 + 0.764371i \(0.276950\pi\)
\(90\) −4.44301 + 20.4378i −0.468335 + 2.15433i
\(91\) 0 0
\(92\) −4.85859 8.41533i −0.506543 0.877359i
\(93\) −5.29031 2.04480i −0.548580 0.212036i
\(94\) 9.49769 0.979612
\(95\) −6.44514 −0.661258
\(96\) 4.31776 + 1.66889i 0.440679 + 0.170330i
\(97\) 4.14143 + 7.17316i 0.420498 + 0.728324i 0.995988 0.0894847i \(-0.0285220\pi\)
−0.575490 + 0.817809i \(0.695189\pi\)
\(98\) 0 0
\(99\) 3.86814 1.23710i 0.388762 0.124333i
\(100\) −6.52815 + 11.3071i −0.652815 + 1.13071i
\(101\) −8.11331 + 14.0527i −0.807305 + 1.39829i 0.107419 + 0.994214i \(0.465741\pi\)
−0.914724 + 0.404079i \(0.867592\pi\)
\(102\) 2.10961 + 13.5217i 0.208882 + 1.33885i
\(103\) −1.11342 1.92849i −0.109708 0.190020i 0.805944 0.591992i \(-0.201658\pi\)
−0.915652 + 0.401972i \(0.868325\pi\)
\(104\) −2.96929 + 5.14295i −0.291162 + 0.504308i
\(105\) 0 0
\(106\) 7.70346 + 13.3428i 0.748226 + 1.29597i
\(107\) −8.75403 + 15.1624i −0.846284 + 1.46581i 0.0382175 + 0.999269i \(0.487832\pi\)
−0.884501 + 0.466537i \(0.845501\pi\)
\(108\) 8.60270 + 17.1771i 0.827795 + 1.65287i
\(109\) −7.79917 13.5086i −0.747025 1.29388i −0.949243 0.314544i \(-0.898148\pi\)
0.202218 0.979341i \(-0.435185\pi\)
\(110\) 9.43773 0.899852
\(111\) 14.6663 11.8205i 1.39207 1.12196i
\(112\) 0 0
\(113\) −0.844555 + 1.46281i −0.0794491 + 0.137610i −0.903012 0.429615i \(-0.858649\pi\)
0.823563 + 0.567224i \(0.191983\pi\)
\(114\) −7.10270 + 5.72453i −0.665229 + 0.536151i
\(115\) −3.83845 + 6.64839i −0.357937 + 0.619966i
\(116\) 1.92887 + 3.34091i 0.179092 + 0.310196i
\(117\) 4.18899 1.33971i 0.387272 0.123857i
\(118\) −29.1532 −2.68377
\(119\) 0 0
\(120\) 3.15913 + 20.2487i 0.288388 + 1.84844i
\(121\) 4.58373 + 7.93925i 0.416703 + 0.721750i
\(122\) 1.33601 0.120957
\(123\) 2.43900 1.96575i 0.219917 0.177245i
\(124\) −12.1066 −1.08720
\(125\) −4.28942 −0.383657
\(126\) 0 0
\(127\) −3.96918 −0.352208 −0.176104 0.984372i \(-0.556350\pi\)
−0.176104 + 0.984372i \(0.556350\pi\)
\(128\) 20.7392 1.83310
\(129\) −1.15946 7.43166i −0.102085 0.654321i
\(130\) 10.2206 0.896403
\(131\) 2.66432 + 4.61473i 0.232782 + 0.403191i 0.958626 0.284669i \(-0.0918837\pi\)
−0.725844 + 0.687860i \(0.758550\pi\)
\(132\) 6.74944 5.43981i 0.587463 0.473475i
\(133\) 0 0
\(134\) −30.5800 −2.64171
\(135\) 8.35417 12.6711i 0.719013 1.09056i
\(136\) 6.70473 + 11.6129i 0.574925 + 0.995800i
\(137\) 3.74772 6.49124i 0.320189 0.554584i −0.660338 0.750969i \(-0.729587\pi\)
0.980527 + 0.196385i \(0.0629202\pi\)
\(138\) 1.67499 + 10.7360i 0.142584 + 0.913906i
\(139\) −7.03285 + 12.1812i −0.596518 + 1.03320i 0.396812 + 0.917900i \(0.370116\pi\)
−0.993331 + 0.115300i \(0.963217\pi\)
\(140\) 0 0
\(141\) −6.42858 2.48476i −0.541384 0.209255i
\(142\) −30.8329 −2.58744
\(143\) −0.992275 1.71867i −0.0829782 0.143722i
\(144\) 5.04987 + 4.58936i 0.420823 + 0.382447i
\(145\) 1.52388 2.63943i 0.126551 0.219193i
\(146\) 12.4779 + 21.6123i 1.03268 + 1.78865i
\(147\) 0 0
\(148\) 20.1041 34.8212i 1.65254 2.86229i
\(149\) −1.08986 1.88769i −0.0892846 0.154645i 0.817924 0.575326i \(-0.195125\pi\)
−0.907209 + 0.420680i \(0.861791\pi\)
\(150\) 11.3673 9.16163i 0.928135 0.748044i
\(151\) −7.01387 + 12.1484i −0.570781 + 0.988621i 0.425705 + 0.904862i \(0.360026\pi\)
−0.996486 + 0.0837595i \(0.973307\pi\)
\(152\) −4.46929 + 7.74103i −0.362507 + 0.627880i
\(153\) 2.10961 9.70416i 0.170552 0.784535i
\(154\) 0 0
\(155\) 4.78231 + 8.28320i 0.384124 + 0.665322i
\(156\) 7.30929 5.89103i 0.585211 0.471660i
\(157\) −2.96623 −0.236731 −0.118365 0.992970i \(-0.537765\pi\)
−0.118365 + 0.992970i \(0.537765\pi\)
\(158\) −1.83234 −0.145773
\(159\) −1.72344 11.0465i −0.136678 0.876046i
\(160\) −3.90314 6.76043i −0.308570 0.534459i
\(161\) 0 0
\(162\) −2.04789 21.3840i −0.160898 1.68008i
\(163\) −0.194278 + 0.336499i −0.0152170 + 0.0263566i −0.873534 0.486764i \(-0.838177\pi\)
0.858317 + 0.513120i \(0.171511\pi\)
\(164\) 3.34329 5.79074i 0.261067 0.452181i
\(165\) −6.38800 2.46907i −0.497305 0.192217i
\(166\) −2.34798 4.06682i −0.182239 0.315646i
\(167\) −3.64889 + 6.32006i −0.282360 + 0.489061i −0.971965 0.235124i \(-0.924450\pi\)
0.689606 + 0.724185i \(0.257784\pi\)
\(168\) 0 0
\(169\) 5.42542 + 9.39710i 0.417340 + 0.722854i
\(170\) 11.5392 19.9864i 0.885013 1.53289i
\(171\) 6.30515 2.01650i 0.482167 0.154206i
\(172\) −8.02756 13.9041i −0.612096 1.06018i
\(173\) 4.05508 0.308302 0.154151 0.988047i \(-0.450736\pi\)
0.154151 + 0.988047i \(0.450736\pi\)
\(174\) −0.664975 4.26221i −0.0504116 0.323117i
\(175\) 0 0
\(176\) 1.53957 2.66661i 0.116049 0.201003i
\(177\) 19.7326 + 7.62699i 1.48319 + 0.573280i
\(178\) 7.64647 13.2441i 0.573127 0.992685i
\(179\) 5.29243 + 9.16675i 0.395575 + 0.685155i 0.993174 0.116639i \(-0.0372121\pi\)
−0.597600 + 0.801795i \(0.703879\pi\)
\(180\) 6.88201 31.6572i 0.512955 2.35959i
\(181\) 19.6312 1.45917 0.729586 0.683889i \(-0.239713\pi\)
0.729586 + 0.683889i \(0.239713\pi\)
\(182\) 0 0
\(183\) −0.904289 0.349524i −0.0668470 0.0258375i
\(184\) 5.32343 + 9.22045i 0.392448 + 0.679740i
\(185\) −31.7657 −2.33546
\(186\) 12.6273 + 4.88067i 0.925878 + 0.357868i
\(187\) −4.48117 −0.327695
\(188\) −14.7115 −1.07294
\(189\) 0 0
\(190\) 15.3837 1.11605
\(191\) 8.28714 0.599637 0.299818 0.953996i \(-0.403074\pi\)
0.299818 + 0.953996i \(0.403074\pi\)
\(192\) −17.6554 6.82413i −1.27417 0.492489i
\(193\) −18.7848 −1.35216 −0.676082 0.736827i \(-0.736323\pi\)
−0.676082 + 0.736827i \(0.736323\pi\)
\(194\) −9.88504 17.1214i −0.709705 1.22924i
\(195\) −6.91787 2.67388i −0.495399 0.191480i
\(196\) 0 0
\(197\) 5.99634 0.427222 0.213611 0.976919i \(-0.431478\pi\)
0.213611 + 0.976919i \(0.431478\pi\)
\(198\) −9.23274 + 2.95279i −0.656142 + 0.209846i
\(199\) −7.20434 12.4783i −0.510702 0.884562i −0.999923 0.0124022i \(-0.996052\pi\)
0.489221 0.872160i \(-0.337281\pi\)
\(200\) 7.15272 12.3889i 0.505773 0.876025i
\(201\) 20.6983 + 8.00026i 1.45995 + 0.564295i
\(202\) 19.3654 33.5419i 1.36255 2.36000i
\(203\) 0 0
\(204\) −3.26768 20.9444i −0.228783 1.46640i
\(205\) −5.28261 −0.368954
\(206\) 2.65758 + 4.60306i 0.185162 + 0.320710i
\(207\) 1.67499 7.70492i 0.116420 0.535529i
\(208\) 1.66727 2.88780i 0.115604 0.200233i
\(209\) −1.49354 2.58690i −0.103311 0.178939i
\(210\) 0 0
\(211\) −6.92418 + 11.9930i −0.476680 + 0.825634i −0.999643 0.0267212i \(-0.991493\pi\)
0.522963 + 0.852356i \(0.324827\pi\)
\(212\) −11.9323 20.6673i −0.819512 1.41944i
\(213\) 20.8695 + 8.06642i 1.42995 + 0.552702i
\(214\) 20.8947 36.1907i 1.42833 2.47395i
\(215\) −6.34204 + 10.9847i −0.432523 + 0.749153i
\(216\) −9.42574 18.8205i −0.641341 1.28057i
\(217\) 0 0
\(218\) 18.6156 + 32.2431i 1.26081 + 2.18378i
\(219\) −2.79158 17.8929i −0.188638 1.20909i
\(220\) −14.6186 −0.985584
\(221\) −4.85287 −0.326439
\(222\) −35.0066 + 28.2141i −2.34949 + 1.89361i
\(223\) −2.33756 4.04878i −0.156535 0.271126i 0.777082 0.629399i \(-0.216699\pi\)
−0.933617 + 0.358273i \(0.883366\pi\)
\(224\) 0 0
\(225\) −10.0909 + 3.22724i −0.672725 + 0.215149i
\(226\) 2.01584 3.49154i 0.134092 0.232254i
\(227\) 9.85631 17.0716i 0.654187 1.13308i −0.327910 0.944709i \(-0.606344\pi\)
0.982097 0.188376i \(-0.0603222\pi\)
\(228\) 11.0017 8.86702i 0.728608 0.587232i
\(229\) 14.0364 + 24.3118i 0.927552 + 1.60657i 0.787404 + 0.616437i \(0.211425\pi\)
0.140148 + 0.990131i \(0.455242\pi\)
\(230\) 9.16188 15.8688i 0.604116 1.04636i
\(231\) 0 0
\(232\) −2.11342 3.66054i −0.138753 0.240326i
\(233\) −6.90113 + 11.9531i −0.452108 + 0.783074i −0.998517 0.0544448i \(-0.982661\pi\)
0.546409 + 0.837518i \(0.315994\pi\)
\(234\) −9.99857 + 3.19772i −0.653627 + 0.209042i
\(235\) 5.81127 + 10.0654i 0.379085 + 0.656595i
\(236\) 45.1569 2.93947
\(237\) 1.24024 + 0.479373i 0.0805619 + 0.0311386i
\(238\) 0 0
\(239\) 5.53069 9.57944i 0.357751 0.619642i −0.629834 0.776730i \(-0.716877\pi\)
0.987585 + 0.157087i \(0.0502104\pi\)
\(240\) −1.77387 11.3698i −0.114503 0.733915i
\(241\) −11.5849 + 20.0656i −0.746247 + 1.29254i 0.203362 + 0.979104i \(0.434813\pi\)
−0.949610 + 0.313435i \(0.898520\pi\)
\(242\) −10.9408 18.9499i −0.703299 1.21815i
\(243\) −4.20829 + 15.0097i −0.269962 + 0.962871i
\(244\) −2.06942 −0.132481
\(245\) 0 0
\(246\) −5.82157 + 4.69198i −0.371169 + 0.299150i
\(247\) −1.61743 2.80147i −0.102915 0.178253i
\(248\) 13.2649 0.842320
\(249\) 0.525297 + 3.36693i 0.0332893 + 0.213371i
\(250\) 10.2383 0.647525
\(251\) 7.78402 0.491323 0.245662 0.969356i \(-0.420995\pi\)
0.245662 + 0.969356i \(0.420995\pi\)
\(252\) 0 0
\(253\) −3.55796 −0.223687
\(254\) 9.47392 0.594447
\(255\) −13.0392 + 10.5091i −0.816544 + 0.658106i
\(256\) −27.6452 −1.72782
\(257\) 5.18798 + 8.98585i 0.323618 + 0.560522i 0.981232 0.192833i \(-0.0617676\pi\)
−0.657614 + 0.753355i \(0.728434\pi\)
\(258\) 2.76748 + 17.7384i 0.172296 + 1.10434i
\(259\) 0 0
\(260\) −15.8312 −0.981807
\(261\) −0.664975 + 3.05888i −0.0411609 + 0.189340i
\(262\) −6.35937 11.0148i −0.392883 0.680494i
\(263\) 9.56654 16.5697i 0.589898 1.02173i −0.404347 0.914605i \(-0.632501\pi\)
0.994245 0.107128i \(-0.0341653\pi\)
\(264\) −7.39517 + 5.96025i −0.455141 + 0.366828i
\(265\) −9.42689 + 16.3279i −0.579090 + 1.00301i
\(266\) 0 0
\(267\) −8.64045 + 6.96390i −0.528787 + 0.426184i
\(268\) 47.3669 2.89340
\(269\) 4.41840 + 7.65290i 0.269395 + 0.466605i 0.968706 0.248212i \(-0.0798430\pi\)
−0.699311 + 0.714818i \(0.746510\pi\)
\(270\) −19.9403 + 30.2443i −1.21353 + 1.84061i
\(271\) 9.16955 15.8821i 0.557010 0.964770i −0.440734 0.897638i \(-0.645282\pi\)
0.997744 0.0671321i \(-0.0213849\pi\)
\(272\) −3.76474 6.52073i −0.228271 0.395377i
\(273\) 0 0
\(274\) −8.94531 + 15.4937i −0.540406 + 0.936010i
\(275\) 2.39029 + 4.14011i 0.144140 + 0.249658i
\(276\) −2.59447 16.6295i −0.156169 1.00098i
\(277\) −2.55241 + 4.42091i −0.153360 + 0.265627i −0.932460 0.361272i \(-0.882343\pi\)
0.779101 + 0.626899i \(0.215676\pi\)
\(278\) 16.7865 29.0750i 1.00679 1.74381i
\(279\) −7.27001 6.60704i −0.435244 0.395553i
\(280\) 0 0
\(281\) −0.853180 1.47775i −0.0508964 0.0881552i 0.839455 0.543430i \(-0.182875\pi\)
−0.890351 + 0.455274i \(0.849541\pi\)
\(282\) 15.3442 + 5.93080i 0.913733 + 0.353174i
\(283\) 12.4883 0.742352 0.371176 0.928562i \(-0.378955\pi\)
0.371176 + 0.928562i \(0.378955\pi\)
\(284\) 47.7586 2.83395
\(285\) −10.4126 4.02465i −0.616788 0.238400i
\(286\) 2.36843 + 4.10224i 0.140048 + 0.242571i
\(287\) 0 0
\(288\) 5.93351 + 5.39242i 0.349635 + 0.317751i
\(289\) 3.02104 5.23260i 0.177708 0.307800i
\(290\) −3.63729 + 6.29997i −0.213589 + 0.369947i
\(291\) 2.21151 + 14.1748i 0.129641 + 0.830944i
\(292\) −19.3276 33.4764i −1.13106 1.95906i
\(293\) 2.60202 4.50684i 0.152012 0.263292i −0.779955 0.625835i \(-0.784758\pi\)
0.931967 + 0.362543i \(0.118091\pi\)
\(294\) 0 0
\(295\) −17.8377 30.8959i −1.03855 1.79883i
\(296\) −22.0275 + 38.1527i −1.28032 + 2.21758i
\(297\) 7.02175 + 0.416825i 0.407443 + 0.0241866i
\(298\) 2.60135 + 4.50566i 0.150692 + 0.261006i
\(299\) −3.85309 −0.222830
\(300\) −17.6074 + 14.1909i −1.01656 + 0.819313i
\(301\) 0 0
\(302\) 16.7412 28.9966i 0.963347 1.66857i
\(303\) −21.8828 + 17.6367i −1.25713 + 1.01320i
\(304\) 2.50953 4.34663i 0.143931 0.249297i
\(305\) 0.817453 + 1.41587i 0.0468072 + 0.0810725i
\(306\) −5.03535 + 23.1626i −0.287852 + 1.32412i
\(307\) −5.00136 −0.285442 −0.142721 0.989763i \(-0.545585\pi\)
−0.142721 + 0.989763i \(0.545585\pi\)
\(308\) 0 0
\(309\) −0.594560 3.81088i −0.0338234 0.216793i
\(310\) −11.4147 19.7709i −0.648313 1.12291i
\(311\) 32.3968 1.83706 0.918528 0.395355i \(-0.129379\pi\)
0.918528 + 0.395355i \(0.129379\pi\)
\(312\) −8.00859 + 6.45464i −0.453397 + 0.365422i
\(313\) −1.51907 −0.0858629 −0.0429315 0.999078i \(-0.513670\pi\)
−0.0429315 + 0.999078i \(0.513670\pi\)
\(314\) 7.08000 0.399548
\(315\) 0 0
\(316\) 2.83821 0.159662
\(317\) −21.5089 −1.20806 −0.604029 0.796962i \(-0.706439\pi\)
−0.604029 + 0.796962i \(0.706439\pi\)
\(318\) 4.11362 + 26.3666i 0.230680 + 1.47856i
\(319\) 1.41252 0.0790860
\(320\) 15.9600 + 27.6436i 0.892193 + 1.54532i
\(321\) −23.6109 + 19.0295i −1.31783 + 1.06213i
\(322\) 0 0
\(323\) −7.30441 −0.406428
\(324\) 3.17208 + 33.1227i 0.176227 + 1.84015i
\(325\) 2.58856 + 4.48352i 0.143588 + 0.248701i
\(326\) 0.463715 0.803178i 0.0256828 0.0444839i
\(327\) −4.16473 26.6942i −0.230310 1.47619i
\(328\) −3.66315 + 6.34476i −0.202263 + 0.350330i
\(329\) 0 0
\(330\) 15.2473 + 5.89336i 0.839337 + 0.324419i
\(331\) 19.4780 1.07061 0.535305 0.844659i \(-0.320197\pi\)
0.535305 + 0.844659i \(0.320197\pi\)
\(332\) 3.63691 + 6.29931i 0.199601 + 0.345719i
\(333\) 31.0758 9.93858i 1.70294 0.544631i
\(334\) 8.70942 15.0852i 0.476558 0.825423i
\(335\) −18.7107 32.4079i −1.02228 1.77063i
\(336\) 0 0
\(337\) 4.84742 8.39598i 0.264056 0.457358i −0.703260 0.710933i \(-0.748273\pi\)
0.967316 + 0.253575i \(0.0816063\pi\)
\(338\) −12.9498 22.4296i −0.704374 1.22001i
\(339\) −2.27789 + 1.83590i −0.123718 + 0.0997122i
\(340\) −17.8736 + 30.9580i −0.969332 + 1.67893i
\(341\) −2.21642 + 3.83896i −0.120026 + 0.207891i
\(342\) −15.0496 + 4.81312i −0.813788 + 0.260264i
\(343\) 0 0
\(344\) 8.79558 + 15.2344i 0.474226 + 0.821383i
\(345\) −10.3528 + 8.34403i −0.557379 + 0.449228i
\(346\) −9.67895 −0.520344
\(347\) 2.02604 0.108763 0.0543817 0.998520i \(-0.482681\pi\)
0.0543817 + 0.998520i \(0.482681\pi\)
\(348\) 1.03001 + 6.60195i 0.0552145 + 0.353902i
\(349\) −8.14577 14.1089i −0.436033 0.755231i 0.561346 0.827581i \(-0.310284\pi\)
−0.997379 + 0.0723497i \(0.976950\pi\)
\(350\) 0 0
\(351\) 7.60419 + 0.451400i 0.405882 + 0.0240939i
\(352\) 1.80896 3.13321i 0.0964180 0.167001i
\(353\) 8.53072 14.7756i 0.454045 0.786428i −0.544588 0.838704i \(-0.683314\pi\)
0.998633 + 0.0522753i \(0.0166473\pi\)
\(354\) −47.0991 18.2046i −2.50329 0.967565i
\(355\) −18.8655 32.6759i −1.00127 1.73426i
\(356\) −11.8440 + 20.5144i −0.627731 + 1.08726i
\(357\) 0 0
\(358\) −12.6323 21.8798i −0.667639 1.15639i
\(359\) 1.48363 2.56972i 0.0783030 0.135625i −0.824215 0.566277i \(-0.808383\pi\)
0.902518 + 0.430652i \(0.141717\pi\)
\(360\) −7.54043 + 34.6859i −0.397415 + 1.82811i
\(361\) 7.06549 + 12.2378i 0.371868 + 0.644094i
\(362\) −46.8570 −2.46275
\(363\) 2.44770 + 15.6887i 0.128471 + 0.823444i
\(364\) 0 0
\(365\) −15.2695 + 26.4475i −0.799240 + 1.38432i
\(366\) 2.15842 + 0.834267i 0.112822 + 0.0436078i
\(367\) −5.07874 + 8.79664i −0.265108 + 0.459181i −0.967592 0.252519i \(-0.918741\pi\)
0.702484 + 0.711700i \(0.252074\pi\)
\(368\) −2.98914 5.17733i −0.155819 0.269887i
\(369\) 5.16787 1.65278i 0.269029 0.0860402i
\(370\) 75.8207 3.94173
\(371\) 0 0
\(372\) −19.5591 7.55992i −1.01409 0.391964i
\(373\) 12.7423 + 22.0703i 0.659771 + 1.14276i 0.980675 + 0.195645i \(0.0626799\pi\)
−0.320904 + 0.947112i \(0.603987\pi\)
\(374\) 10.6960 0.553075
\(375\) −6.92985 2.67851i −0.357856 0.138318i
\(376\) 16.1189 0.831271
\(377\) 1.52969 0.0787829
\(378\) 0 0
\(379\) 9.85497 0.506216 0.253108 0.967438i \(-0.418547\pi\)
0.253108 + 0.967438i \(0.418547\pi\)
\(380\) −23.8286 −1.22238
\(381\) −6.41250 2.47854i −0.328522 0.126980i
\(382\) −19.7803 −1.01205
\(383\) −13.6563 23.6535i −0.697806 1.20864i −0.969225 0.246175i \(-0.920826\pi\)
0.271419 0.962461i \(-0.412507\pi\)
\(384\) 33.5056 + 12.9505i 1.70983 + 0.660878i
\(385\) 0 0
\(386\) 44.8370 2.28214
\(387\) 2.76748 12.7304i 0.140679 0.647122i
\(388\) 15.3114 + 26.5202i 0.777321 + 1.34636i
\(389\) −2.09223 + 3.62385i −0.106080 + 0.183736i −0.914179 0.405311i \(-0.867163\pi\)
0.808099 + 0.589047i \(0.200497\pi\)
\(390\) 16.5120 + 6.38220i 0.836120 + 0.323175i
\(391\) −4.35019 + 7.53475i −0.219999 + 0.381049i
\(392\) 0 0
\(393\) 1.42274 + 9.11914i 0.0717676 + 0.460000i
\(394\) −14.3125 −0.721053
\(395\) −1.12114 1.94187i −0.0564107 0.0977062i
\(396\) 14.3011 4.57373i 0.718655 0.229839i
\(397\) −15.3354 + 26.5618i −0.769664 + 1.33310i 0.168082 + 0.985773i \(0.446243\pi\)
−0.937745 + 0.347323i \(0.887091\pi\)
\(398\) 17.1958 + 29.7840i 0.861948 + 1.49294i
\(399\) 0 0
\(400\) −4.01629 + 6.95642i −0.200815 + 0.347821i
\(401\) 3.42402 + 5.93057i 0.170987 + 0.296158i 0.938765 0.344557i \(-0.111971\pi\)
−0.767778 + 0.640716i \(0.778638\pi\)
\(402\) −49.4042 19.0956i −2.46406 0.952401i
\(403\) −2.40027 + 4.15739i −0.119566 + 0.207095i
\(404\) −29.9961 + 51.9547i −1.49236 + 2.58485i
\(405\) 21.4092 15.2543i 1.06383 0.757994i
\(406\) 0 0
\(407\) −7.36113 12.7499i −0.364878 0.631987i
\(408\) 3.58030 + 22.9482i 0.177251 + 1.13611i
\(409\) 18.2698 0.903384 0.451692 0.892174i \(-0.350821\pi\)
0.451692 + 0.892174i \(0.350821\pi\)
\(410\) 12.6089 0.622709
\(411\) 10.1081 8.14680i 0.498597 0.401852i
\(412\) −4.11646 7.12991i −0.202803 0.351265i
\(413\) 0 0
\(414\) −3.99798 + 18.3906i −0.196490 + 0.903851i
\(415\) 2.87328 4.97666i 0.141044 0.244295i
\(416\) 1.95901 3.39311i 0.0960485 0.166361i
\(417\) −18.9686 + 15.2880i −0.928896 + 0.748658i
\(418\) 3.56490 + 6.17458i 0.174365 + 0.302009i
\(419\) −11.2310 + 19.4526i −0.548669 + 0.950322i 0.449698 + 0.893181i \(0.351532\pi\)
−0.998366 + 0.0571410i \(0.981802\pi\)
\(420\) 0 0
\(421\) 10.4177 + 18.0440i 0.507728 + 0.879411i 0.999960 + 0.00894684i \(0.00284791\pi\)
−0.492232 + 0.870464i \(0.663819\pi\)
\(422\) 16.5271 28.6258i 0.804527 1.39348i
\(423\) −8.83422 8.02861i −0.429535 0.390364i
\(424\) 13.0739 + 22.6446i 0.634923 + 1.09972i
\(425\) 11.6901 0.567053
\(426\) −49.8127 19.2535i −2.41343 0.932834i
\(427\) 0 0
\(428\) −32.3649 + 56.0577i −1.56442 + 2.70965i
\(429\) −0.529872 3.39626i −0.0255825 0.163973i
\(430\) 15.1376 26.2191i 0.730001 1.26440i
\(431\) −10.1213 17.5307i −0.487527 0.844422i 0.512370 0.858765i \(-0.328768\pi\)
−0.999897 + 0.0143427i \(0.995434\pi\)
\(432\) 5.29261 + 10.5678i 0.254641 + 0.508444i
\(433\) 21.6764 1.04170 0.520851 0.853648i \(-0.325615\pi\)
0.520851 + 0.853648i \(0.325615\pi\)
\(434\) 0 0
\(435\) 4.11011 3.31260i 0.197065 0.158827i
\(436\) −28.8346 49.9431i −1.38093 2.39184i
\(437\) −5.79956 −0.277431
\(438\) 6.66315 + 42.7080i 0.318377 + 2.04067i
\(439\) 35.4781 1.69328 0.846639 0.532168i \(-0.178623\pi\)
0.846639 + 0.532168i \(0.178623\pi\)
\(440\) 16.0172 0.763589
\(441\) 0 0
\(442\) 11.5832 0.550955
\(443\) −19.2063 −0.912517 −0.456258 0.889847i \(-0.650811\pi\)
−0.456258 + 0.889847i \(0.650811\pi\)
\(444\) 54.2235 43.7023i 2.57333 2.07402i
\(445\) 18.7143 0.887144
\(446\) 5.57946 + 9.66391i 0.264195 + 0.457599i
\(447\) −0.581980 3.73025i −0.0275267 0.176435i
\(448\) 0 0
\(449\) −29.6082 −1.39730 −0.698648 0.715465i \(-0.746215\pi\)
−0.698648 + 0.715465i \(0.746215\pi\)
\(450\) 24.0856 7.70300i 1.13541 0.363123i
\(451\) −1.22415 2.12029i −0.0576429 0.0998405i
\(452\) −3.12244 + 5.40823i −0.146867 + 0.254382i
\(453\) −18.9174 + 15.2468i −0.888818 + 0.716356i
\(454\) −23.5257 + 40.7478i −1.10412 + 1.91239i
\(455\) 0 0
\(456\) −12.0543 + 9.71534i −0.564494 + 0.454963i
\(457\) −9.56196 −0.447290 −0.223645 0.974671i \(-0.571796\pi\)
−0.223645 + 0.974671i \(0.571796\pi\)
\(458\) −33.5031 58.0290i −1.56550 2.71152i
\(459\) 9.46795 14.3604i 0.441926 0.670287i
\(460\) −14.1913 + 24.5800i −0.661673 + 1.14605i
\(461\) −10.9187 18.9118i −0.508536 0.880809i −0.999951 0.00988416i \(-0.996854\pi\)
0.491416 0.870925i \(-0.336480\pi\)
\(462\) 0 0
\(463\) 13.0744 22.6456i 0.607621 1.05243i −0.384010 0.923329i \(-0.625457\pi\)
0.991631 0.129102i \(-0.0412094\pi\)
\(464\) 1.18670 + 2.05542i 0.0550909 + 0.0954203i
\(465\) 2.55374 + 16.3684i 0.118427 + 0.759065i
\(466\) 16.4721 28.5305i 0.763054 1.32165i
\(467\) 17.4764 30.2699i 0.808709 1.40073i −0.105049 0.994467i \(-0.533500\pi\)
0.913758 0.406258i \(-0.133167\pi\)
\(468\) 15.4873 4.95311i 0.715901 0.228958i
\(469\) 0 0
\(470\) −13.8707 24.0248i −0.639809 1.10818i
\(471\) −4.79215 1.85225i −0.220811 0.0853473i
\(472\) −49.4772 −2.27737
\(473\) −5.87861 −0.270299
\(474\) −2.96028 1.14420i −0.135970 0.0525549i
\(475\) 3.89623 + 6.74848i 0.178771 + 0.309641i
\(476\) 0 0
\(477\) 4.11362 18.9226i 0.188350 0.866407i
\(478\) −13.2010 + 22.8649i −0.603801 + 1.04581i
\(479\) −14.9054 + 25.8170i −0.681047 + 1.17961i 0.293615 + 0.955924i \(0.405142\pi\)
−0.974662 + 0.223684i \(0.928192\pi\)
\(480\) −2.08426 13.3593i −0.0951332 0.609764i
\(481\) −7.97172 13.8074i −0.363479 0.629565i
\(482\) 27.6516 47.8939i 1.25949 2.18151i
\(483\) 0 0
\(484\) 16.9467 + 29.3525i 0.770304 + 1.33421i
\(485\) 12.0965 20.9518i 0.549276 0.951374i
\(486\) 10.0446 35.8261i 0.455634 1.62511i
\(487\) −11.2253 19.4428i −0.508667 0.881037i −0.999950 0.0100365i \(-0.996805\pi\)
0.491283 0.871000i \(-0.336528\pi\)
\(488\) 2.26740 0.102640
\(489\) −0.523994 + 0.422321i −0.0236958 + 0.0190980i
\(490\) 0 0
\(491\) 17.5222 30.3494i 0.790767 1.36965i −0.134726 0.990883i \(-0.543016\pi\)
0.925493 0.378765i \(-0.123651\pi\)
\(492\) 9.01732 7.26764i 0.406532 0.327651i
\(493\) 1.72704 2.99132i 0.0777819 0.134722i
\(494\) 3.86060 + 6.68675i 0.173696 + 0.300851i
\(495\) −8.77845 7.97792i −0.394562 0.358581i
\(496\) −7.44830 −0.334438
\(497\) 0 0
\(498\) −1.25381 8.03642i −0.0561848 0.360121i
\(499\) 4.46760 + 7.73811i 0.199997 + 0.346405i 0.948527 0.316696i \(-0.102573\pi\)
−0.748530 + 0.663101i \(0.769240\pi\)
\(500\) −15.8586 −0.709217
\(501\) −9.84158 + 7.93197i −0.439689 + 0.354374i
\(502\) −18.5794 −0.829241
\(503\) 12.6403 0.563603 0.281802 0.959473i \(-0.409068\pi\)
0.281802 + 0.959473i \(0.409068\pi\)
\(504\) 0 0
\(505\) 47.3958 2.10909
\(506\) 8.49239 0.377533
\(507\) 2.89716 + 18.5696i 0.128667 + 0.824703i
\(508\) −14.6746 −0.651082
\(509\) −14.0555 24.3449i −0.623000 1.07907i −0.988924 0.148423i \(-0.952580\pi\)
0.365924 0.930645i \(-0.380753\pi\)
\(510\) 31.1228 25.0839i 1.37814 1.11073i
\(511\) 0 0
\(512\) 24.5070 1.08307
\(513\) 11.4456 + 0.679434i 0.505336 + 0.0299978i
\(514\) −12.3830 21.4480i −0.546192 0.946033i
\(515\) −3.25214 + 5.63287i −0.143306 + 0.248214i
\(516\) −4.28669 27.4759i −0.188711 1.20956i
\(517\) −2.69331 + 4.66495i −0.118452 + 0.205164i
\(518\) 0 0
\(519\) 6.55127 + 2.53218i 0.287569 + 0.111150i
\(520\) 17.3458 0.760662
\(521\) −4.23768 7.33988i −0.185656 0.321566i 0.758141 0.652090i \(-0.226108\pi\)
−0.943797 + 0.330524i \(0.892774\pi\)
\(522\) 1.58721 7.30114i 0.0694702 0.319562i
\(523\) −16.7236 + 28.9662i −0.731273 + 1.26660i 0.225066 + 0.974344i \(0.427740\pi\)
−0.956339 + 0.292259i \(0.905593\pi\)
\(524\) 9.85035 + 17.0613i 0.430315 + 0.745327i
\(525\) 0 0
\(526\) −22.8341 + 39.5498i −0.995613 + 1.72445i
\(527\) 5.41988 + 9.38751i 0.236094 + 0.408926i
\(528\) 4.15243 3.34672i 0.180711 0.145647i
\(529\) 8.04603 13.9361i 0.349827 0.605919i
\(530\) 22.5008 38.9725i 0.977371 1.69286i
\(531\) 27.1167 + 24.6439i 1.17677 + 1.06945i
\(532\) 0 0
\(533\) −1.32569 2.29616i −0.0574220 0.0994579i
\(534\) 20.6236 16.6219i 0.892471 0.719301i
\(535\) 51.1387 2.21092
\(536\) −51.8987 −2.24168
\(537\) 2.82614 + 18.1144i 0.121957 + 0.781693i
\(538\) −10.5461 18.2665i −0.454677 0.787523i
\(539\) 0 0
\(540\) 30.8866 46.8469i 1.32915 2.01597i
\(541\) −9.12929 + 15.8124i −0.392499 + 0.679828i −0.992778 0.119962i \(-0.961723\pi\)
0.600280 + 0.799790i \(0.295056\pi\)
\(542\) −21.8865 + 37.9085i −0.940106 + 1.62831i
\(543\) 31.7155 + 12.2586i 1.36104 + 0.526067i
\(544\) −4.42350 7.66173i −0.189656 0.328494i
\(545\) −22.7803 + 39.4567i −0.975802 + 1.69014i
\(546\) 0 0
\(547\) −2.88599 4.99869i −0.123396 0.213728i 0.797709 0.603043i \(-0.206045\pi\)
−0.921105 + 0.389315i \(0.872712\pi\)
\(548\) 13.8558 23.9990i 0.591892 1.02519i
\(549\) −1.24268 1.12936i −0.0530364 0.0481999i
\(550\) −5.70532 9.88190i −0.243276 0.421366i
\(551\) 2.30244 0.0980874
\(552\) 2.84269 + 18.2205i 0.120993 + 0.775515i
\(553\) 0 0
\(554\) 6.09227 10.5521i 0.258836 0.448317i
\(555\) −51.3198 19.8360i −2.17840 0.841992i
\(556\) −26.0014 + 45.0358i −1.10271 + 1.90994i
\(557\) 16.6911 + 28.9098i 0.707223 + 1.22495i 0.965883 + 0.258977i \(0.0833855\pi\)
−0.258661 + 0.965968i \(0.583281\pi\)
\(558\) 17.3526 + 15.7701i 0.734592 + 0.667603i
\(559\) −6.36623 −0.269263
\(560\) 0 0
\(561\) −7.23964 2.79825i −0.305658 0.118142i
\(562\) 2.03643 + 3.52720i 0.0859015 + 0.148786i
\(563\) −2.19131 −0.0923528 −0.0461764 0.998933i \(-0.514704\pi\)
−0.0461764 + 0.998933i \(0.514704\pi\)
\(564\) −23.7674 9.18652i −1.00079 0.386822i
\(565\) 4.93367 0.207561
\(566\) −29.8079 −1.25292
\(567\) 0 0
\(568\) −52.3278 −2.19563
\(569\) 18.9860 0.795936 0.397968 0.917399i \(-0.369716\pi\)
0.397968 + 0.917399i \(0.369716\pi\)
\(570\) 24.8535 + 9.60631i 1.04100 + 0.402364i
\(571\) −21.7380 −0.909709 −0.454854 0.890566i \(-0.650309\pi\)
−0.454854 + 0.890566i \(0.650309\pi\)
\(572\) −3.66858 6.35417i −0.153391 0.265681i
\(573\) 13.3885 + 5.17488i 0.559311 + 0.216184i
\(574\) 0 0
\(575\) 9.28172 0.387074
\(576\) −24.2622 22.0497i −1.01093 0.918738i
\(577\) 15.4516 + 26.7629i 0.643258 + 1.11416i 0.984701 + 0.174253i \(0.0557511\pi\)
−0.341443 + 0.939903i \(0.610916\pi\)
\(578\) −7.21083 + 12.4895i −0.299931 + 0.519496i
\(579\) −30.3482 11.7301i −1.26123 0.487488i
\(580\) 5.63398 9.75835i 0.233938 0.405193i
\(581\) 0 0
\(582\) −5.27858 33.8335i −0.218804 1.40244i
\(583\) −8.73804 −0.361893
\(584\) 21.1767 + 36.6792i 0.876299 + 1.51780i
\(585\) −9.50661 8.63968i −0.393050 0.357207i
\(586\) −6.21069 + 10.7572i −0.256561 + 0.444377i
\(587\) 9.18332 + 15.9060i 0.379036 + 0.656510i 0.990922 0.134436i \(-0.0429222\pi\)
−0.611886 + 0.790946i \(0.709589\pi\)
\(588\) 0 0
\(589\) −3.61282 + 6.25759i −0.148864 + 0.257840i
\(590\) 42.5763 + 73.7444i 1.75284 + 3.03601i
\(591\) 9.68751 + 3.74440i 0.398491 + 0.154024i
\(592\) 12.3685 21.4230i 0.508344 0.880478i
\(593\) −13.8775 + 24.0365i −0.569880 + 0.987061i 0.426698 + 0.904394i \(0.359677\pi\)
−0.996577 + 0.0826662i \(0.973656\pi\)
\(594\) −16.7600 0.994906i −0.687671 0.0408215i
\(595\) 0 0
\(596\) −4.02936 6.97905i −0.165049 0.285873i
\(597\) −3.84710 24.6583i −0.157451 1.00920i
\(598\) 9.19682 0.376086
\(599\) 0.402823 0.0164589 0.00822945 0.999966i \(-0.497380\pi\)
0.00822945 + 0.999966i \(0.497380\pi\)
\(600\) 19.2919 15.5486i 0.787589 0.634769i
\(601\) −12.3733 21.4312i −0.504717 0.874196i −0.999985 0.00545577i \(-0.998263\pi\)
0.495268 0.868740i \(-0.335070\pi\)
\(602\) 0 0
\(603\) 28.4438 + 25.8500i 1.15832 + 1.05269i
\(604\) −25.9313 + 44.9143i −1.05513 + 1.82754i
\(605\) 13.3885 23.1895i 0.544318 0.942787i
\(606\) 52.2313 42.0966i 2.12175 1.71006i
\(607\) 12.0348 + 20.8449i 0.488479 + 0.846070i 0.999912 0.0132531i \(-0.00421872\pi\)
−0.511434 + 0.859323i \(0.670885\pi\)
\(608\) 2.94865 5.10721i 0.119584 0.207125i
\(609\) 0 0
\(610\) −1.95115 3.37950i −0.0789999 0.136832i
\(611\) −2.91672 + 5.05190i −0.117998 + 0.204378i
\(612\) 7.79952 35.8777i 0.315277 1.45027i
\(613\) 10.1907 + 17.6509i 0.411600 + 0.712912i 0.995065 0.0992261i \(-0.0316367\pi\)
−0.583465 + 0.812138i \(0.698303\pi\)
\(614\) 11.9376 0.481762
\(615\) −8.53443 3.29871i −0.344142 0.133017i
\(616\) 0 0
\(617\) −20.9315 + 36.2544i −0.842669 + 1.45955i 0.0449604 + 0.998989i \(0.485684\pi\)
−0.887630 + 0.460558i \(0.847650\pi\)
\(618\) 1.41914 + 9.09607i 0.0570861 + 0.365898i
\(619\) 7.41095 12.8361i 0.297871 0.515928i −0.677777 0.735267i \(-0.737057\pi\)
0.975649 + 0.219339i \(0.0703900\pi\)
\(620\) 17.6809 + 30.6242i 0.710081 + 1.22990i
\(621\) 7.51737 11.4019i 0.301662 0.457543i
\(622\) −77.3270 −3.10053
\(623\) 0 0
\(624\) 4.49687 3.62432i 0.180019 0.145089i
\(625\) 15.0930 + 26.1419i 0.603722 + 1.04568i
\(626\) 3.62582 0.144917
\(627\) −0.797548 5.11195i −0.0318510 0.204152i
\(628\) −10.9666 −0.437614
\(629\) −36.0007 −1.43544
\(630\) 0 0
\(631\) −21.0294 −0.837169 −0.418585 0.908178i \(-0.637474\pi\)
−0.418585 + 0.908178i \(0.637474\pi\)
\(632\) −3.10975 −0.123699
\(633\) −18.6755 + 15.0518i −0.742285 + 0.598255i
\(634\) 51.3388 2.03893
\(635\) 5.79673 + 10.0402i 0.230036 + 0.398434i
\(636\) −6.37180 40.8406i −0.252658 1.61943i
\(637\) 0 0
\(638\) −3.37150 −0.133479
\(639\) 28.6790 + 26.0637i 1.13453 + 1.03107i
\(640\) −30.2882 52.4607i −1.19725 2.07369i
\(641\) −5.96592 + 10.3333i −0.235640 + 0.408140i −0.959458 0.281850i \(-0.909052\pi\)
0.723819 + 0.689990i \(0.242385\pi\)
\(642\) 56.3561 45.4210i 2.22420 1.79262i
\(643\) 19.9678 34.5852i 0.787452 1.36391i −0.140072 0.990141i \(-0.544733\pi\)
0.927524 0.373765i \(-0.121933\pi\)
\(644\) 0 0
\(645\) −17.1054 + 13.7863i −0.673524 + 0.542837i
\(646\) 17.4347 0.685958
\(647\) −0.494477 0.856459i −0.0194399 0.0336709i 0.856142 0.516741i \(-0.172855\pi\)
−0.875582 + 0.483070i \(0.839522\pi\)
\(648\) −3.47557 36.2917i −0.136533 1.42567i
\(649\) 8.26714 14.3191i 0.324514 0.562074i
\(650\) −6.17856 10.7016i −0.242343 0.419751i
\(651\) 0 0
\(652\) −0.718272 + 1.24408i −0.0281297 + 0.0487221i
\(653\) −11.3573 19.6715i −0.444447 0.769804i 0.553567 0.832805i \(-0.313266\pi\)
−0.998014 + 0.0630004i \(0.979933\pi\)
\(654\) 9.94067 + 63.7155i 0.388711 + 2.49147i
\(655\) 7.78211 13.4790i 0.304072 0.526668i
\(656\) 2.05688 3.56262i 0.0803076 0.139097i
\(657\) 6.66315 30.6504i 0.259954 1.19579i
\(658\) 0 0
\(659\) −19.1943 33.2454i −0.747702 1.29506i −0.948922 0.315512i \(-0.897824\pi\)
0.201220 0.979546i \(-0.435509\pi\)
\(660\) −23.6173 9.12852i −0.919304 0.355327i
\(661\) −33.9258 −1.31956 −0.659780 0.751459i \(-0.729351\pi\)
−0.659780 + 0.751459i \(0.729351\pi\)
\(662\) −46.4915 −1.80694
\(663\) −7.84015 3.03036i −0.304486 0.117689i
\(664\) −3.98486 6.90198i −0.154642 0.267849i
\(665\) 0 0
\(666\) −74.1738 + 23.7221i −2.87418 + 0.919213i
\(667\) 1.37124 2.37505i 0.0530944 0.0919623i
\(668\) −13.4905 + 23.3662i −0.521962 + 0.904064i
\(669\) −1.24825 8.00077i −0.0482602 0.309328i
\(670\) 44.6601 + 77.3535i 1.72537 + 2.98843i
\(671\) −0.378860 + 0.656205i −0.0146257 + 0.0253325i
\(672\) 0 0
\(673\) −16.1030 27.8912i −0.620725 1.07513i −0.989351 0.145549i \(-0.953505\pi\)
0.368626 0.929578i \(-0.379828\pi\)
\(674\) −11.5702 + 20.0401i −0.445666 + 0.771916i
\(675\) −18.3177 1.08738i −0.705050 0.0418532i
\(676\) 20.0585 + 34.7424i 0.771483 + 1.33625i
\(677\) 37.9684 1.45924 0.729622 0.683850i \(-0.239696\pi\)
0.729622 + 0.683850i \(0.239696\pi\)
\(678\) 5.43702 4.38204i 0.208807 0.168291i
\(679\) 0 0
\(680\) 19.5836 33.9198i 0.750997 1.30076i
\(681\) 26.5839 21.4257i 1.01870 0.821034i
\(682\) 5.29031 9.16309i 0.202577 0.350873i
\(683\) 7.59357 + 13.1525i 0.290560 + 0.503265i 0.973942 0.226796i \(-0.0728251\pi\)
−0.683382 + 0.730061i \(0.739492\pi\)
\(684\) 23.3111 7.45529i 0.891320 0.285060i
\(685\) −21.8932 −0.836495
\(686\) 0 0
\(687\) 7.49540 + 48.0424i 0.285967 + 1.83293i
\(688\) −4.93877 8.55420i −0.188289 0.326126i
\(689\) −9.46285 −0.360506
\(690\) 24.7109 19.9161i 0.940728 0.758193i
\(691\) −2.69148 −0.102389 −0.0511943 0.998689i \(-0.516303\pi\)
−0.0511943 + 0.998689i \(0.516303\pi\)
\(692\) 14.9922 0.569919
\(693\) 0 0
\(694\) −4.83589 −0.183568
\(695\) 41.0840 1.55841
\(696\) −1.12856 7.23358i −0.0427779 0.274188i
\(697\) −5.98689 −0.226770
\(698\) 19.4429 + 33.6761i 0.735924 + 1.27466i
\(699\) −18.6133 + 15.0017i −0.704021 + 0.567416i
\(700\) 0 0
\(701\) −11.8515 −0.447625 −0.223813 0.974632i \(-0.571850\pi\)
−0.223813 + 0.974632i \(0.571850\pi\)
\(702\) −18.1502 1.07743i −0.685035 0.0406650i
\(703\) −11.9988 20.7826i −0.452544 0.783829i
\(704\) −7.39689 + 12.8118i −0.278781 + 0.482862i
\(705\) 3.10320 + 19.8902i 0.116873 + 0.749109i
\(706\) −20.3617 + 35.2675i −0.766323 + 1.32731i
\(707\) 0 0
\(708\) 72.9542 + 28.1981i 2.74179 + 1.05975i
\(709\) −41.0333 −1.54104 −0.770520 0.637416i \(-0.780003\pi\)
−0.770520 + 0.637416i \(0.780003\pi\)
\(710\) 45.0294 + 77.9931i 1.68992 + 2.92703i
\(711\) 1.70434 + 1.54892i 0.0639179 + 0.0580891i
\(712\) 12.9772 22.4771i 0.486339 0.842364i
\(713\) 4.30328 + 7.45351i 0.161159 + 0.279136i
\(714\) 0 0
\(715\) −2.89830 + 5.02001i −0.108390 + 0.187738i
\(716\) 19.5669 + 33.8908i 0.731248 + 1.26656i
\(717\) 14.9171 12.0226i 0.557088 0.448993i
\(718\) −3.54123 + 6.13359i −0.132158 + 0.228904i
\(719\) −10.4555 + 18.1094i −0.389923 + 0.675366i −0.992439 0.122741i \(-0.960832\pi\)
0.602516 + 0.798107i \(0.294165\pi\)
\(720\) 4.23400 19.4763i 0.157792 0.725840i
\(721\) 0 0
\(722\) −16.8644 29.2100i −0.627628 1.08708i
\(723\) −31.2461 + 25.1832i −1.16205 + 0.936574i
\(724\) 72.5792 2.69738
\(725\) −3.68487 −0.136853
\(726\) −5.84233 37.4469i −0.216829 1.38978i
\(727\) −1.32165 2.28917i −0.0490173 0.0849005i 0.840476 0.541849i \(-0.182276\pi\)
−0.889493 + 0.456949i \(0.848942\pi\)
\(728\) 0 0
\(729\) −16.1715 + 21.6213i −0.598945 + 0.800790i
\(730\) 36.4462 63.1267i 1.34893 2.33642i
\(731\) −7.18756 + 12.4492i −0.265841 + 0.460451i
\(732\) −3.34329 1.29224i −0.123571 0.0477625i
\(733\) 7.07446 + 12.2533i 0.261301 + 0.452587i 0.966588 0.256335i \(-0.0825151\pi\)
−0.705287 + 0.708922i \(0.749182\pi\)
\(734\) 12.1223 20.9964i 0.447442 0.774992i
\(735\) 0 0
\(736\) −3.51218 6.08327i −0.129461 0.224232i
\(737\) 8.67174 15.0199i 0.319428 0.553265i
\(738\) −12.3350 + 3.94496i −0.454059 + 0.145216i
\(739\) −7.85905 13.6123i −0.289100 0.500736i 0.684495 0.729017i \(-0.260023\pi\)
−0.973595 + 0.228282i \(0.926689\pi\)
\(740\) −117.442 −4.31727
\(741\) −0.863704 5.53598i −0.0317289 0.203369i
\(742\) 0 0
\(743\) 10.5496 18.2724i 0.387026 0.670348i −0.605022 0.796208i \(-0.706836\pi\)
0.992048 + 0.125861i \(0.0401692\pi\)
\(744\) 21.4303 + 8.28320i 0.785673 + 0.303677i
\(745\) −3.18333 + 5.51368i −0.116628 + 0.202006i
\(746\) −30.4142 52.6789i −1.11354 1.92871i
\(747\) −1.25381 + 5.76753i −0.0458747 + 0.211023i
\(748\) −16.5675 −0.605768
\(749\) 0 0
\(750\) 16.5406 + 6.39325i 0.603979 + 0.233449i
\(751\) −6.51848 11.2903i −0.237863 0.411990i 0.722238 0.691644i \(-0.243113\pi\)
−0.960101 + 0.279654i \(0.909780\pi\)
\(752\) −9.05088 −0.330052
\(753\) 12.5756 + 4.86071i 0.458282 + 0.177134i
\(754\) −3.65116 −0.132968
\(755\) 40.9732 1.49117
\(756\) 0 0
\(757\) −12.6856 −0.461065 −0.230532 0.973065i \(-0.574047\pi\)
−0.230532 + 0.973065i \(0.574047\pi\)
\(758\) −23.5225 −0.854377
\(759\) −5.74814 2.22176i −0.208644 0.0806447i
\(760\) 26.1084 0.947050
\(761\) −3.02038 5.23146i −0.109489 0.189640i 0.806074 0.591814i \(-0.201588\pi\)
−0.915563 + 0.402174i \(0.868255\pi\)
\(762\) 15.3058 + 5.91596i 0.554470 + 0.214313i
\(763\) 0 0
\(764\) 30.6388 1.10847
\(765\) −27.6280 + 8.83594i −0.998894 + 0.319464i
\(766\) 32.5959 + 56.4577i 1.17774 + 2.03990i
\(767\) 8.95288 15.5068i 0.323270 0.559920i
\(768\) −44.6627 17.2629i −1.61163 0.622923i
\(769\) −0.108129 + 0.187285i −0.00389924 + 0.00675368i −0.867968 0.496619i \(-0.834575\pi\)
0.864069 + 0.503373i \(0.167908\pi\)
\(770\) 0 0
\(771\) 2.77037 + 17.7569i 0.0997724 + 0.639499i
\(772\) −69.4503 −2.49957
\(773\) −18.8132 32.5854i −0.676663 1.17202i −0.975980 0.217861i \(-0.930092\pi\)
0.299316 0.954154i \(-0.403241\pi\)
\(774\) −6.60562 + 30.3858i −0.237434 + 1.09219i
\(775\) 5.78202 10.0148i 0.207696 0.359741i
\(776\) −16.7763 29.0575i −0.602235 1.04310i
\(777\) 0 0
\(778\) 4.99388 8.64965i 0.179039 0.310105i
\(779\) −1.99539 3.45612i −0.0714923 0.123828i
\(780\) −25.5763 9.88571i −0.915780 0.353965i