Properties

Label 637.2.u.h.30.3
Level $637$
Weight $2$
Character 637.30
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.3
Root \(-1.08105 + 0.911778i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.h.361.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.713220 + 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 + 1.14467i) q^{4} +(-2.73845 - 1.58105i) q^{5} +(-1.89737 + 1.09545i) q^{6} -2.73565i q^{8} +4.07715 q^{9} +O(q^{10})\) \(q+(-0.713220 + 0.411778i) q^{2} +2.66029 q^{3} +(-0.660878 + 1.14467i) q^{4} +(-2.73845 - 1.58105i) q^{5} +(-1.89737 + 1.09545i) q^{6} -2.73565i q^{8} +4.07715 q^{9} +2.60416 q^{10} -5.94270i q^{11} +(-1.75813 + 3.04517i) q^{12} +(-0.0766193 - 3.60474i) q^{13} +(-7.28508 - 4.20604i) q^{15} +(-0.195274 - 0.338225i) q^{16} +(-1.34982 + 2.33796i) q^{17} +(-2.90791 + 1.67888i) q^{18} +1.95705i q^{19} +(3.61956 - 2.08976i) q^{20} +(2.44707 + 4.23845i) q^{22} +(-1.36471 - 2.36374i) q^{23} -7.27763i q^{24} +(2.49941 + 4.32911i) q^{25} +(1.53900 + 2.53942i) q^{26} +2.86554 q^{27} +(2.99923 - 5.19481i) q^{29} +6.92783 q^{30} +(0.997270 - 0.575774i) q^{31} +(5.01684 + 2.89647i) q^{32} -15.8093i q^{33} -2.22331i q^{34} +(-2.69450 + 4.66701i) q^{36} +(5.63310 - 3.25227i) q^{37} +(-0.805869 - 1.39581i) q^{38} +(-0.203830 - 9.58965i) q^{39} +(-4.32519 + 7.49145i) q^{40} +(-3.23351 - 1.86687i) q^{41} +(3.49562 + 6.05460i) q^{43} +(6.80245 + 3.92740i) q^{44} +(-11.1651 - 6.44617i) q^{45} +(1.94667 + 1.12391i) q^{46} +(0.394969 + 0.228035i) q^{47} +(-0.519487 - 0.899778i) q^{48} +(-3.56527 - 2.05841i) q^{50} +(-3.59092 + 6.21965i) q^{51} +(4.17688 + 2.29459i) q^{52} +(-0.199643 - 0.345792i) q^{53} +(-2.04376 + 1.17997i) q^{54} +(-9.39568 + 16.2738i) q^{55} +5.20632i q^{57} +4.94006i q^{58} +(-4.16200 - 2.40293i) q^{59} +(9.62910 - 5.55936i) q^{60} -1.15703 q^{61} +(-0.474182 + 0.821308i) q^{62} -3.98971 q^{64} +(-5.48944 + 9.99254i) q^{65} +(6.50993 + 11.2755i) q^{66} +6.27918i q^{67} +(-1.78413 - 3.09021i) q^{68} +(-3.63052 - 6.28825i) q^{69} +(3.90335 - 2.25360i) q^{71} -11.1537i q^{72} +(-7.19299 + 4.15288i) q^{73} +(-2.67843 + 4.63917i) q^{74} +(6.64917 + 11.5167i) q^{75} +(-2.24018 - 1.29337i) q^{76} +(4.09418 + 6.75560i) q^{78} +(3.95705 - 6.85381i) q^{79} +1.23495i q^{80} -4.60828 q^{81} +3.07494 q^{82} -6.19795i q^{83} +(7.39284 - 4.26826i) q^{85} +(-4.98630 - 2.87884i) q^{86} +(7.97882 - 13.8197i) q^{87} -16.2571 q^{88} +(-3.08423 + 1.78068i) q^{89} +10.6176 q^{90} +3.60762 q^{92} +(2.65303 - 1.53173i) q^{93} -0.375600 q^{94} +(3.09418 - 5.35928i) q^{95} +(13.3462 + 7.70546i) q^{96} +(-2.96831 + 1.71375i) q^{97} -24.2293i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.713220 + 0.411778i −0.504323 + 0.291171i −0.730497 0.682916i \(-0.760712\pi\)
0.226174 + 0.974087i \(0.427378\pi\)
\(3\) 2.66029 1.53592 0.767960 0.640498i \(-0.221272\pi\)
0.767960 + 0.640498i \(0.221272\pi\)
\(4\) −0.660878 + 1.14467i −0.330439 + 0.572337i
\(5\) −2.73845 1.58105i −1.22467 0.707065i −0.258762 0.965941i \(-0.583315\pi\)
−0.965911 + 0.258876i \(0.916648\pi\)
\(6\) −1.89737 + 1.09545i −0.774600 + 0.447215i
\(7\) 0 0
\(8\) 2.73565i 0.967199i
\(9\) 4.07715 1.35905
\(10\) 2.60416 0.823508
\(11\) 5.94270i 1.79179i −0.444265 0.895895i \(-0.646535\pi\)
0.444265 0.895895i \(-0.353465\pi\)
\(12\) −1.75813 + 3.04517i −0.507528 + 0.879064i
\(13\) −0.0766193 3.60474i −0.0212504 0.999774i
\(14\) 0 0
\(15\) −7.28508 4.20604i −1.88100 1.08600i
\(16\) −0.195274 0.338225i −0.0488186 0.0845563i
\(17\) −1.34982 + 2.33796i −0.327380 + 0.567038i −0.981991 0.188927i \(-0.939499\pi\)
0.654611 + 0.755966i \(0.272832\pi\)
\(18\) −2.90791 + 1.67888i −0.685401 + 0.395716i
\(19\) 1.95705i 0.448978i 0.974477 + 0.224489i \(0.0720712\pi\)
−0.974477 + 0.224489i \(0.927929\pi\)
\(20\) 3.61956 2.08976i 0.809359 0.467284i
\(21\) 0 0
\(22\) 2.44707 + 4.23845i 0.521717 + 0.903641i
\(23\) −1.36471 2.36374i −0.284561 0.492874i 0.687941 0.725766i \(-0.258515\pi\)
−0.972503 + 0.232892i \(0.925181\pi\)
\(24\) 7.27763i 1.48554i
\(25\) 2.49941 + 4.32911i 0.499883 + 0.865822i
\(26\) 1.53900 + 2.53942i 0.301822 + 0.498022i
\(27\) 2.86554 0.551474
\(28\) 0 0
\(29\) 2.99923 5.19481i 0.556942 0.964652i −0.440807 0.897602i \(-0.645308\pi\)
0.997750 0.0670505i \(-0.0213589\pi\)
\(30\) 6.92783 1.26484
\(31\) 0.997270 0.575774i 0.179115 0.103412i −0.407762 0.913088i \(-0.633691\pi\)
0.586877 + 0.809676i \(0.300357\pi\)
\(32\) 5.01684 + 2.89647i 0.886860 + 0.512029i
\(33\) 15.8093i 2.75205i
\(34\) 2.22331i 0.381294i
\(35\) 0 0
\(36\) −2.69450 + 4.66701i −0.449083 + 0.777835i
\(37\) 5.63310 3.25227i 0.926075 0.534670i 0.0405072 0.999179i \(-0.487103\pi\)
0.885568 + 0.464509i \(0.153769\pi\)
\(38\) −0.805869 1.39581i −0.130729 0.226430i
\(39\) −0.203830 9.58965i −0.0326389 1.53557i
\(40\) −4.32519 + 7.49145i −0.683873 + 1.18450i
\(41\) −3.23351 1.86687i −0.504990 0.291556i 0.225782 0.974178i \(-0.427506\pi\)
−0.730772 + 0.682622i \(0.760840\pi\)
\(42\) 0 0
\(43\) 3.49562 + 6.05460i 0.533078 + 0.923318i 0.999254 + 0.0386258i \(0.0122980\pi\)
−0.466176 + 0.884692i \(0.654369\pi\)
\(44\) 6.80245 + 3.92740i 1.02551 + 0.592077i
\(45\) −11.1651 6.44617i −1.66439 0.960938i
\(46\) 1.94667 + 1.12391i 0.287021 + 0.165712i
\(47\) 0.394969 + 0.228035i 0.0576121 + 0.0332624i 0.528529 0.848915i \(-0.322744\pi\)
−0.470917 + 0.882177i \(0.656077\pi\)
\(48\) −0.519487 0.899778i −0.0749815 0.129872i
\(49\) 0 0
\(50\) −3.56527 2.05841i −0.504205 0.291103i
\(51\) −3.59092 + 6.21965i −0.502829 + 0.870926i
\(52\) 4.17688 + 2.29459i 0.579230 + 0.318202i
\(53\) −0.199643 0.345792i −0.0274231 0.0474982i 0.851988 0.523561i \(-0.175397\pi\)
−0.879411 + 0.476063i \(0.842063\pi\)
\(54\) −2.04376 + 1.17997i −0.278121 + 0.160573i
\(55\) −9.39568 + 16.2738i −1.26691 + 2.19436i
\(56\) 0 0
\(57\) 5.20632i 0.689594i
\(58\) 4.94006i 0.648662i
\(59\) −4.16200 2.40293i −0.541846 0.312835i 0.203981 0.978975i \(-0.434612\pi\)
−0.745827 + 0.666140i \(0.767945\pi\)
\(60\) 9.62910 5.55936i 1.24311 0.717711i
\(61\) −1.15703 −0.148142 −0.0740711 0.997253i \(-0.523599\pi\)
−0.0740711 + 0.997253i \(0.523599\pi\)
\(62\) −0.474182 + 0.821308i −0.0602212 + 0.104306i
\(63\) 0 0
\(64\) −3.98971 −0.498714
\(65\) −5.48944 + 9.99254i −0.680881 + 1.23942i
\(66\) 6.50993 + 11.2755i 0.801316 + 1.38792i
\(67\) 6.27918i 0.767124i 0.923515 + 0.383562i \(0.125303\pi\)
−0.923515 + 0.383562i \(0.874697\pi\)
\(68\) −1.78413 3.09021i −0.216358 0.374743i
\(69\) −3.63052 6.28825i −0.437063 0.757016i
\(70\) 0 0
\(71\) 3.90335 2.25360i 0.463242 0.267453i −0.250165 0.968203i \(-0.580485\pi\)
0.713406 + 0.700751i \(0.247151\pi\)
\(72\) 11.1537i 1.31447i
\(73\) −7.19299 + 4.15288i −0.841876 + 0.486057i −0.857901 0.513814i \(-0.828232\pi\)
0.0160254 + 0.999872i \(0.494899\pi\)
\(74\) −2.67843 + 4.63917i −0.311361 + 0.539293i
\(75\) 6.64917 + 11.5167i 0.767780 + 1.32983i
\(76\) −2.24018 1.29337i −0.256966 0.148360i
\(77\) 0 0
\(78\) 4.09418 + 6.75560i 0.463575 + 0.764921i
\(79\) 3.95705 6.85381i 0.445203 0.771114i −0.552864 0.833272i \(-0.686465\pi\)
0.998066 + 0.0621581i \(0.0197983\pi\)
\(80\) 1.23495i 0.138072i
\(81\) −4.60828 −0.512031
\(82\) 3.07494 0.339571
\(83\) 6.19795i 0.680313i −0.940369 0.340156i \(-0.889520\pi\)
0.940369 0.340156i \(-0.110480\pi\)
\(84\) 0 0
\(85\) 7.39284 4.26826i 0.801866 0.462958i
\(86\) −4.98630 2.87884i −0.537687 0.310434i
\(87\) 7.97882 13.8197i 0.855419 1.48163i
\(88\) −16.2571 −1.73302
\(89\) −3.08423 + 1.78068i −0.326928 + 0.188752i −0.654476 0.756083i \(-0.727111\pi\)
0.327549 + 0.944834i \(0.393778\pi\)
\(90\) 10.6176 1.11919
\(91\) 0 0
\(92\) 3.60762 0.376120
\(93\) 2.65303 1.53173i 0.275106 0.158833i
\(94\) −0.375600 −0.0387402
\(95\) 3.09418 5.35928i 0.317457 0.549851i
\(96\) 13.3462 + 7.70546i 1.36215 + 0.786435i
\(97\) −2.96831 + 1.71375i −0.301386 + 0.174005i −0.643065 0.765811i \(-0.722338\pi\)
0.341679 + 0.939817i \(0.389004\pi\)
\(98\) 0 0
\(99\) 24.2293i 2.43513i
\(100\) −6.60723 −0.660723
\(101\) 13.3295 1.32633 0.663167 0.748472i \(-0.269212\pi\)
0.663167 + 0.748472i \(0.269212\pi\)
\(102\) 5.91465i 0.585637i
\(103\) 5.82248 10.0848i 0.573706 0.993688i −0.422475 0.906375i \(-0.638839\pi\)
0.996181 0.0873131i \(-0.0278281\pi\)
\(104\) −9.86130 + 0.209604i −0.966981 + 0.0205533i
\(105\) 0 0
\(106\) 0.284779 + 0.164417i 0.0276602 + 0.0159696i
\(107\) −1.96483 3.40318i −0.189947 0.328998i 0.755285 0.655396i \(-0.227498\pi\)
−0.945232 + 0.326398i \(0.894165\pi\)
\(108\) −1.89377 + 3.28011i −0.182228 + 0.315629i
\(109\) −9.74566 + 5.62666i −0.933465 + 0.538936i −0.887906 0.460025i \(-0.847840\pi\)
−0.0455595 + 0.998962i \(0.514507\pi\)
\(110\) 15.4757i 1.47555i
\(111\) 14.9857 8.65199i 1.42238 0.821210i
\(112\) 0 0
\(113\) 2.88709 + 5.00059i 0.271595 + 0.470416i 0.969270 0.245998i \(-0.0791157\pi\)
−0.697676 + 0.716414i \(0.745782\pi\)
\(114\) −2.14385 3.71325i −0.200790 0.347778i
\(115\) 8.63066i 0.804813i
\(116\) 3.96424 + 6.86627i 0.368071 + 0.637517i
\(117\) −0.312389 14.6971i −0.0288803 1.35874i
\(118\) 3.95790 0.364354
\(119\) 0 0
\(120\) −11.5063 + 19.9294i −1.05037 + 1.81930i
\(121\) −24.3156 −2.21051
\(122\) 0.825215 0.476438i 0.0747115 0.0431347i
\(123\) −8.60209 4.96642i −0.775625 0.447807i
\(124\) 1.52207i 0.136686i
\(125\) 0.00370455i 0.000331345i
\(126\) 0 0
\(127\) 3.06558 5.30975i 0.272027 0.471164i −0.697354 0.716727i \(-0.745639\pi\)
0.969381 + 0.245563i \(0.0789728\pi\)
\(128\) −7.18812 + 4.15007i −0.635346 + 0.366817i
\(129\) 9.29938 + 16.1070i 0.818765 + 1.41814i
\(130\) −0.199529 9.38731i −0.0174998 0.823322i
\(131\) −5.11084 + 8.85224i −0.446537 + 0.773424i −0.998158 0.0606707i \(-0.980676\pi\)
0.551621 + 0.834095i \(0.314009\pi\)
\(132\) 18.0965 + 10.4480i 1.57510 + 0.909383i
\(133\) 0 0
\(134\) −2.58563 4.47844i −0.223364 0.386878i
\(135\) −7.84715 4.53056i −0.675375 0.389928i
\(136\) 6.39584 + 3.69264i 0.548439 + 0.316641i
\(137\) 17.2751 + 9.97376i 1.47591 + 0.852116i 0.999631 0.0271788i \(-0.00865233\pi\)
0.476278 + 0.879295i \(0.341986\pi\)
\(138\) 5.17872 + 2.98994i 0.440842 + 0.254520i
\(139\) 10.1637 + 17.6041i 0.862077 + 1.49316i 0.869921 + 0.493192i \(0.164170\pi\)
−0.00784365 + 0.999969i \(0.502497\pi\)
\(140\) 0 0
\(141\) 1.05073 + 0.606641i 0.0884877 + 0.0510884i
\(142\) −1.85596 + 3.21462i −0.155749 + 0.269765i
\(143\) −21.4219 + 0.455325i −1.79139 + 0.0380762i
\(144\) −0.796164 1.37900i −0.0663470 0.114916i
\(145\) −16.4265 + 9.48383i −1.36414 + 0.787589i
\(146\) 3.42013 5.92383i 0.283052 0.490260i
\(147\) 0 0
\(148\) 8.59741i 0.706703i
\(149\) 10.7162i 0.877901i −0.898511 0.438951i \(-0.855350\pi\)
0.898511 0.438951i \(-0.144650\pi\)
\(150\) −9.48465 5.47597i −0.774418 0.447111i
\(151\) 7.57267 4.37208i 0.616255 0.355795i −0.159155 0.987254i \(-0.550877\pi\)
0.775409 + 0.631459i \(0.217544\pi\)
\(152\) 5.35380 0.434251
\(153\) −5.50343 + 9.53222i −0.444926 + 0.770634i
\(154\) 0 0
\(155\) −3.64130 −0.292476
\(156\) 11.1117 + 6.10427i 0.889651 + 0.488733i
\(157\) −3.25367 5.63552i −0.259671 0.449763i 0.706483 0.707730i \(-0.250281\pi\)
−0.966154 + 0.257967i \(0.916947\pi\)
\(158\) 6.51770i 0.518520i
\(159\) −0.531109 0.919907i −0.0421197 0.0729534i
\(160\) −9.15891 15.8637i −0.724075 1.25414i
\(161\) 0 0
\(162\) 3.28672 1.89759i 0.258229 0.149089i
\(163\) 2.61267i 0.204640i 0.994752 + 0.102320i \(0.0326266\pi\)
−0.994752 + 0.102320i \(0.967373\pi\)
\(164\) 4.27392 2.46755i 0.333737 0.192683i
\(165\) −24.9952 + 43.2930i −1.94588 + 3.37036i
\(166\) 2.55218 + 4.42050i 0.198087 + 0.343097i
\(167\) −3.36558 1.94312i −0.260436 0.150363i 0.364097 0.931361i \(-0.381378\pi\)
−0.624534 + 0.780998i \(0.714711\pi\)
\(168\) 0 0
\(169\) −12.9883 + 0.552385i −0.999097 + 0.0424911i
\(170\) −3.51515 + 6.08842i −0.269600 + 0.466961i
\(171\) 7.97919i 0.610184i
\(172\) −9.24072 −0.704599
\(173\) −13.9768 −1.06263 −0.531317 0.847173i \(-0.678303\pi\)
−0.531317 + 0.847173i \(0.678303\pi\)
\(174\) 13.1420i 0.996293i
\(175\) 0 0
\(176\) −2.00997 + 1.16046i −0.151507 + 0.0874727i
\(177\) −11.0721 6.39250i −0.832232 0.480490i
\(178\) 1.46649 2.54004i 0.109918 0.190384i
\(179\) 25.2843 1.88984 0.944919 0.327305i \(-0.106140\pi\)
0.944919 + 0.327305i \(0.106140\pi\)
\(180\) 14.7575 8.52026i 1.09996 0.635063i
\(181\) −0.864474 −0.0642559 −0.0321279 0.999484i \(-0.510228\pi\)
−0.0321279 + 0.999484i \(0.510228\pi\)
\(182\) 0 0
\(183\) −3.07803 −0.227535
\(184\) −6.46638 + 3.73336i −0.476708 + 0.275227i
\(185\) −20.5680 −1.51219
\(186\) −1.26146 + 2.18492i −0.0924950 + 0.160206i
\(187\) 13.8938 + 8.02158i 1.01601 + 0.586596i
\(188\) −0.522052 + 0.301407i −0.0380746 + 0.0219824i
\(189\) 0 0
\(190\) 5.09647i 0.369737i
\(191\) 14.6676 1.06131 0.530657 0.847587i \(-0.321945\pi\)
0.530657 + 0.847587i \(0.321945\pi\)
\(192\) −10.6138 −0.765985
\(193\) 16.4959i 1.18740i −0.804686 0.593700i \(-0.797667\pi\)
0.804686 0.593700i \(-0.202333\pi\)
\(194\) 1.41137 2.44457i 0.101331 0.175510i
\(195\) −14.6035 + 26.5831i −1.04578 + 1.90365i
\(196\) 0 0
\(197\) 9.53510 + 5.50509i 0.679348 + 0.392222i 0.799609 0.600521i \(-0.205040\pi\)
−0.120262 + 0.992742i \(0.538373\pi\)
\(198\) 9.97709 + 17.2808i 0.709041 + 1.22809i
\(199\) −10.6059 + 18.3699i −0.751829 + 1.30221i 0.195106 + 0.980782i \(0.437495\pi\)
−0.946935 + 0.321425i \(0.895838\pi\)
\(200\) 11.8429 6.83753i 0.837423 0.483486i
\(201\) 16.7045i 1.17824i
\(202\) −9.50686 + 5.48879i −0.668901 + 0.386190i
\(203\) 0 0
\(204\) −4.74632 8.22086i −0.332309 0.575576i
\(205\) 5.90322 + 10.2247i 0.412299 + 0.714122i
\(206\) 9.59027i 0.668186i
\(207\) −5.56412 9.63734i −0.386733 0.669842i
\(208\) −1.20425 + 0.729828i −0.0834998 + 0.0506044i
\(209\) 11.6301 0.804474
\(210\) 0 0
\(211\) 8.96788 15.5328i 0.617375 1.06932i −0.372588 0.927997i \(-0.621530\pi\)
0.989963 0.141327i \(-0.0451370\pi\)
\(212\) 0.527759 0.0362466
\(213\) 10.3840 5.99523i 0.711503 0.410786i
\(214\) 2.80271 + 1.61815i 0.191589 + 0.110614i
\(215\) 22.1070i 1.50768i
\(216\) 7.83913i 0.533385i
\(217\) 0 0
\(218\) 4.63387 8.02610i 0.313845 0.543596i
\(219\) −19.1355 + 11.0479i −1.29305 + 0.746545i
\(220\) −12.4188 21.5100i −0.837275 1.45020i
\(221\) 8.53115 + 4.68662i 0.573867 + 0.315256i
\(222\) −7.12540 + 12.3415i −0.478225 + 0.828311i
\(223\) −13.8834 8.01558i −0.929700 0.536763i −0.0429835 0.999076i \(-0.513686\pi\)
−0.886717 + 0.462313i \(0.847020\pi\)
\(224\) 0 0
\(225\) 10.1905 + 17.6505i 0.679366 + 1.17670i
\(226\) −4.11826 2.37768i −0.273943 0.158161i
\(227\) 14.1812 + 8.18751i 0.941239 + 0.543424i 0.890348 0.455280i \(-0.150461\pi\)
0.0508902 + 0.998704i \(0.483794\pi\)
\(228\) −5.95954 3.44074i −0.394680 0.227869i
\(229\) 23.3917 + 13.5052i 1.54577 + 0.892449i 0.998458 + 0.0555193i \(0.0176814\pi\)
0.547310 + 0.836930i \(0.315652\pi\)
\(230\) −3.55392 6.15556i −0.234338 0.405886i
\(231\) 0 0
\(232\) −14.2112 8.20484i −0.933011 0.538674i
\(233\) 5.78406 10.0183i 0.378926 0.656320i −0.611980 0.790873i \(-0.709627\pi\)
0.990906 + 0.134554i \(0.0429601\pi\)
\(234\) 6.27473 + 10.3536i 0.410192 + 0.676837i
\(235\) −0.721069 1.24893i −0.0470374 0.0814711i
\(236\) 5.50114 3.17609i 0.358094 0.206746i
\(237\) 10.5269 18.2331i 0.683796 1.18437i
\(238\) 0 0
\(239\) 14.6731i 0.949122i 0.880223 + 0.474561i \(0.157393\pi\)
−0.880223 + 0.474561i \(0.842607\pi\)
\(240\) 3.28533i 0.212067i
\(241\) −12.4246 7.17334i −0.800338 0.462076i 0.0432510 0.999064i \(-0.486228\pi\)
−0.843589 + 0.536989i \(0.819562\pi\)
\(242\) 17.3424 10.0126i 1.11481 0.643637i
\(243\) −20.8560 −1.33791
\(244\) 0.764654 1.32442i 0.0489519 0.0847872i
\(245\) 0 0
\(246\) 8.18025 0.521554
\(247\) 7.05464 0.149948i 0.448876 0.00954094i
\(248\) −1.57512 2.72818i −0.100020 0.173240i
\(249\) 16.4883i 1.04491i
\(250\) −0.00152545 0.00264216i −9.64781e−5 0.000167105i
\(251\) 4.30726 + 7.46040i 0.271872 + 0.470896i 0.969341 0.245719i \(-0.0790239\pi\)
−0.697469 + 0.716615i \(0.745691\pi\)
\(252\) 0 0
\(253\) −14.0470 + 8.11004i −0.883128 + 0.509874i
\(254\) 5.04936i 0.316825i
\(255\) 19.6671 11.3548i 1.23160 0.711066i
\(256\) 7.40753 12.8302i 0.462970 0.801888i
\(257\) 5.18197 + 8.97544i 0.323243 + 0.559873i 0.981155 0.193222i \(-0.0618936\pi\)
−0.657912 + 0.753094i \(0.728560\pi\)
\(258\) −13.2650 7.65856i −0.825844 0.476801i
\(259\) 0 0
\(260\) −7.81035 12.8875i −0.484377 0.799247i
\(261\) 12.2283 21.1800i 0.756913 1.31101i
\(262\) 8.41813i 0.520074i
\(263\) −22.0826 −1.36167 −0.680835 0.732436i \(-0.738383\pi\)
−0.680835 + 0.732436i \(0.738383\pi\)
\(264\) −43.2488 −2.66178
\(265\) 1.26258i 0.0775596i
\(266\) 0 0
\(267\) −8.20495 + 4.73713i −0.502135 + 0.289908i
\(268\) −7.18761 4.14977i −0.439053 0.253488i
\(269\) −6.46995 + 11.2063i −0.394480 + 0.683259i −0.993035 0.117823i \(-0.962409\pi\)
0.598555 + 0.801082i \(0.295742\pi\)
\(270\) 7.46233 0.454143
\(271\) 15.3069 8.83745i 0.929829 0.536837i 0.0430712 0.999072i \(-0.486286\pi\)
0.886757 + 0.462235i \(0.152952\pi\)
\(272\) 1.05434 0.0639289
\(273\) 0 0
\(274\) −16.4279 −0.992446
\(275\) 25.7266 14.8533i 1.55137 0.895685i
\(276\) 9.59732 0.577691
\(277\) −9.00751 + 15.6015i −0.541209 + 0.937401i 0.457626 + 0.889145i \(0.348700\pi\)
−0.998835 + 0.0482562i \(0.984634\pi\)
\(278\) −14.4980 8.37041i −0.869530 0.502024i
\(279\) 4.06602 2.34752i 0.243426 0.140542i
\(280\) 0 0
\(281\) 2.44178i 0.145665i −0.997344 0.0728323i \(-0.976796\pi\)
0.997344 0.0728323i \(-0.0232038\pi\)
\(282\) −0.999205 −0.0595018
\(283\) 28.7240 1.70746 0.853732 0.520713i \(-0.174334\pi\)
0.853732 + 0.520713i \(0.174334\pi\)
\(284\) 5.95741i 0.353507i
\(285\) 8.23143 14.2573i 0.487588 0.844527i
\(286\) 15.0910 9.14580i 0.892350 0.540802i
\(287\) 0 0
\(288\) 20.4544 + 11.8094i 1.20529 + 0.695873i
\(289\) 4.85596 + 8.41078i 0.285645 + 0.494752i
\(290\) 7.81046 13.5281i 0.458646 0.794399i
\(291\) −7.89657 + 4.55909i −0.462905 + 0.267258i
\(292\) 10.9782i 0.642449i
\(293\) 25.4013 14.6654i 1.48396 0.856763i 0.484124 0.874999i \(-0.339138\pi\)
0.999834 + 0.0182359i \(0.00580499\pi\)
\(294\) 0 0
\(295\) 7.59829 + 13.1606i 0.442390 + 0.766241i
\(296\) −8.89708 15.4102i −0.517132 0.895699i
\(297\) 17.0291i 0.988126i
\(298\) 4.41267 + 7.64298i 0.255619 + 0.442746i
\(299\) −8.41611 + 5.10052i −0.486716 + 0.294971i
\(300\) −17.5772 −1.01482
\(301\) 0 0
\(302\) −3.60065 + 6.23651i −0.207194 + 0.358871i
\(303\) 35.4603 2.03714
\(304\) 0.661923 0.382161i 0.0379639 0.0219185i
\(305\) 3.16846 + 1.82931i 0.181426 + 0.104746i
\(306\) 9.06476i 0.518198i
\(307\) 7.06910i 0.403455i 0.979442 + 0.201728i \(0.0646555\pi\)
−0.979442 + 0.201728i \(0.935344\pi\)
\(308\) 0 0
\(309\) 15.4895 26.8286i 0.881166 1.52623i
\(310\) 2.59705 1.49941i 0.147503 0.0851607i
\(311\) −11.1343 19.2852i −0.631368 1.09356i −0.987272 0.159039i \(-0.949160\pi\)
0.355904 0.934522i \(-0.384173\pi\)
\(312\) −26.2340 + 0.557607i −1.48520 + 0.0315683i
\(313\) 14.0420 24.3214i 0.793700 1.37473i −0.129961 0.991519i \(-0.541485\pi\)
0.923661 0.383210i \(-0.125181\pi\)
\(314\) 4.64117 + 2.67958i 0.261916 + 0.151217i
\(315\) 0 0
\(316\) 5.23025 + 9.05906i 0.294225 + 0.509612i
\(317\) −16.9009 9.75774i −0.949249 0.548049i −0.0564015 0.998408i \(-0.517963\pi\)
−0.892848 + 0.450359i \(0.851296\pi\)
\(318\) 0.757595 + 0.437398i 0.0424838 + 0.0245281i
\(319\) −30.8712 17.8235i −1.72845 0.997924i
\(320\) 10.9256 + 6.30792i 0.610762 + 0.352624i
\(321\) −5.22702 9.05346i −0.291744 0.505315i
\(322\) 0 0
\(323\) −4.57550 2.64167i −0.254588 0.146986i
\(324\) 3.04551 5.27498i 0.169195 0.293054i
\(325\) 15.4138 9.34142i 0.855004 0.518169i
\(326\) −1.07584 1.86341i −0.0595853 0.103205i
\(327\) −25.9263 + 14.9686i −1.43373 + 0.827764i
\(328\) −5.10711 + 8.84577i −0.281993 + 0.488426i
\(329\) 0 0
\(330\) 41.1700i 2.26633i
\(331\) 15.6308i 0.859145i 0.903032 + 0.429573i \(0.141336\pi\)
−0.903032 + 0.429573i \(0.858664\pi\)
\(332\) 7.09463 + 4.09609i 0.389368 + 0.224802i
\(333\) 22.9670 13.2600i 1.25858 0.726644i
\(334\) 3.20053 0.175125
\(335\) 9.92767 17.1952i 0.542407 0.939476i
\(336\) 0 0
\(337\) 21.7501 1.18480 0.592401 0.805643i \(-0.298180\pi\)
0.592401 + 0.805643i \(0.298180\pi\)
\(338\) 9.03603 5.74225i 0.491495 0.312337i
\(339\) 7.68050 + 13.3030i 0.417148 + 0.722521i
\(340\) 11.2832i 0.611917i
\(341\) −3.42165 5.92647i −0.185293 0.320937i
\(342\) −3.28565 5.69092i −0.177668 0.307730i
\(343\) 0 0
\(344\) 16.5633 9.56281i 0.893032 0.515592i
\(345\) 22.9601i 1.23613i
\(346\) 9.96851 5.75532i 0.535910 0.309408i
\(347\) 7.97952 13.8209i 0.428363 0.741946i −0.568365 0.822777i \(-0.692424\pi\)
0.996728 + 0.0808303i \(0.0257572\pi\)
\(348\) 10.5460 + 18.2663i 0.565327 + 0.979176i
\(349\) 5.90375 + 3.40853i 0.316021 + 0.182455i 0.649617 0.760261i \(-0.274929\pi\)
−0.333597 + 0.942716i \(0.608262\pi\)
\(350\) 0 0
\(351\) −0.219556 10.3295i −0.0117190 0.551349i
\(352\) 17.2128 29.8135i 0.917448 1.58907i
\(353\) 14.0033i 0.745318i −0.927968 0.372659i \(-0.878446\pi\)
0.927968 0.372659i \(-0.121554\pi\)
\(354\) 10.5292 0.559619
\(355\) −14.2522 −0.756427
\(356\) 4.70725i 0.249484i
\(357\) 0 0
\(358\) −18.0333 + 10.4115i −0.953088 + 0.550266i
\(359\) 4.68947 + 2.70747i 0.247501 + 0.142895i 0.618619 0.785691i \(-0.287692\pi\)
−0.371119 + 0.928586i \(0.621026\pi\)
\(360\) −17.6345 + 30.5438i −0.929418 + 1.60980i
\(361\) 15.1700 0.798419
\(362\) 0.616561 0.355972i 0.0324057 0.0187094i
\(363\) −64.6867 −3.39517
\(364\) 0 0
\(365\) 26.2636 1.37470
\(366\) 2.19531 1.26747i 0.114751 0.0662515i
\(367\) 30.0317 1.56764 0.783822 0.620985i \(-0.213267\pi\)
0.783822 + 0.620985i \(0.213267\pi\)
\(368\) −0.532985 + 0.923157i −0.0277838 + 0.0481229i
\(369\) −13.1835 7.61152i −0.686307 0.396240i
\(370\) 14.6695 8.46943i 0.762630 0.440305i
\(371\) 0 0
\(372\) 4.04914i 0.209938i
\(373\) 21.4098 1.10856 0.554278 0.832332i \(-0.312995\pi\)
0.554278 + 0.832332i \(0.312995\pi\)
\(374\) −13.2124 −0.683199
\(375\) 0.00985519i 0.000508920i
\(376\) 0.623826 1.08050i 0.0321713 0.0557224i
\(377\) −18.9557 10.4134i −0.976270 0.536317i
\(378\) 0 0
\(379\) −8.20693 4.73827i −0.421562 0.243389i 0.274184 0.961677i \(-0.411592\pi\)
−0.695745 + 0.718289i \(0.744926\pi\)
\(380\) 4.08975 + 7.08366i 0.209800 + 0.363384i
\(381\) 8.15535 14.1255i 0.417811 0.723670i
\(382\) −10.4613 + 6.03982i −0.535245 + 0.309024i
\(383\) 5.43061i 0.277491i −0.990328 0.138746i \(-0.955693\pi\)
0.990328 0.138746i \(-0.0443070\pi\)
\(384\) −19.1225 + 11.0404i −0.975842 + 0.563402i
\(385\) 0 0
\(386\) 6.79264 + 11.7652i 0.345736 + 0.598833i
\(387\) 14.2522 + 24.6855i 0.724480 + 1.25484i
\(388\) 4.53033i 0.229993i
\(389\) −5.32109 9.21640i −0.269790 0.467290i 0.699018 0.715105i \(-0.253621\pi\)
−0.968807 + 0.247815i \(0.920288\pi\)
\(390\) −0.530805 24.9730i −0.0268784 1.26456i
\(391\) 7.36845 0.372638
\(392\) 0 0
\(393\) −13.5963 + 23.5495i −0.685845 + 1.18792i
\(394\) −9.06750 −0.456814
\(395\) −21.6724 + 12.5126i −1.09046 + 0.629575i
\(396\) 27.7346 + 16.0126i 1.39372 + 0.804663i
\(397\) 37.1854i 1.86628i 0.359512 + 0.933140i \(0.382943\pi\)
−0.359512 + 0.933140i \(0.617057\pi\)
\(398\) 17.4690i 0.875644i
\(399\) 0 0
\(400\) 0.976143 1.69073i 0.0488072 0.0845365i
\(401\) 0.776487 0.448305i 0.0387759 0.0223873i −0.480487 0.877002i \(-0.659540\pi\)
0.519263 + 0.854615i \(0.326207\pi\)
\(402\) −6.87853 11.9140i −0.343070 0.594214i
\(403\) −2.15192 3.55078i −0.107195 0.176877i
\(404\) −8.80916 + 15.2579i −0.438272 + 0.759110i
\(405\) 12.6196 + 7.28590i 0.627071 + 0.362039i
\(406\) 0 0
\(407\) −19.3273 33.4758i −0.958016 1.65933i
\(408\) 17.0148 + 9.82350i 0.842359 + 0.486336i
\(409\) −21.2846 12.2886i −1.05245 0.607635i −0.129119 0.991629i \(-0.541215\pi\)
−0.923335 + 0.383995i \(0.874548\pi\)
\(410\) −8.42059 4.86163i −0.415863 0.240099i
\(411\) 45.9567 + 26.5331i 2.26688 + 1.30878i
\(412\) 7.69589 + 13.3297i 0.379149 + 0.656706i
\(413\) 0 0
\(414\) 7.93689 + 4.58237i 0.390077 + 0.225211i
\(415\) −9.79924 + 16.9728i −0.481026 + 0.833161i
\(416\) 10.0566 18.3063i 0.493067 0.897540i
\(417\) 27.0385 + 46.8321i 1.32408 + 2.29338i
\(418\) −8.29486 + 4.78904i −0.405715 + 0.234239i
\(419\) 3.82279 6.62126i 0.186755 0.323470i −0.757411 0.652938i \(-0.773536\pi\)
0.944167 + 0.329468i \(0.106869\pi\)
\(420\) 0 0
\(421\) 25.0780i 1.22223i −0.791544 0.611113i \(-0.790722\pi\)
0.791544 0.611113i \(-0.209278\pi\)
\(422\) 14.7711i 0.719046i
\(423\) 1.61035 + 0.929736i 0.0782979 + 0.0452053i
\(424\) −0.945966 + 0.546154i −0.0459402 + 0.0265236i
\(425\) −13.4951 −0.654606
\(426\) −4.93741 + 8.55184i −0.239218 + 0.414338i
\(427\) 0 0
\(428\) 5.19405 0.251064
\(429\) −56.9884 + 1.21130i −2.75143 + 0.0584820i
\(430\) 9.10317 + 15.7671i 0.438994 + 0.760359i
\(431\) 7.75404i 0.373499i −0.982408 0.186750i \(-0.940205\pi\)
0.982408 0.186750i \(-0.0597953\pi\)
\(432\) −0.559567 0.969199i −0.0269222 0.0466306i
\(433\) 17.9880 + 31.1561i 0.864448 + 1.49727i 0.867594 + 0.497273i \(0.165665\pi\)
−0.00314644 + 0.999995i \(0.501002\pi\)
\(434\) 0 0
\(435\) −43.6992 + 25.2298i −2.09522 + 1.20967i
\(436\) 14.8741i 0.712342i
\(437\) 4.62596 2.67080i 0.221290 0.127762i
\(438\) 9.09853 15.7591i 0.434745 0.753000i
\(439\) −14.1175 24.4523i −0.673792 1.16704i −0.976820 0.214061i \(-0.931331\pi\)
0.303028 0.952982i \(-0.402002\pi\)
\(440\) 44.5194 + 25.7033i 2.12238 + 1.22536i
\(441\) 0 0
\(442\) −8.01444 + 0.170348i −0.381208 + 0.00810264i
\(443\) −14.3959 + 24.9344i −0.683970 + 1.18467i 0.289790 + 0.957090i \(0.406415\pi\)
−0.973759 + 0.227580i \(0.926919\pi\)
\(444\) 22.8716i 1.08544i
\(445\) 11.2614 0.533840
\(446\) 13.2026 0.625159
\(447\) 28.5081i 1.34839i
\(448\) 0 0
\(449\) −25.2795 + 14.5951i −1.19301 + 0.688785i −0.958988 0.283446i \(-0.908522\pi\)
−0.234023 + 0.972231i \(0.575189\pi\)
\(450\) −14.5361 8.39244i −0.685240 0.395624i
\(451\) −11.0942 + 19.2158i −0.522408 + 0.904836i
\(452\) −7.63205 −0.358982
\(453\) 20.1455 11.6310i 0.946518 0.546473i
\(454\) −13.4858 −0.632918
\(455\) 0 0
\(456\) 14.2427 0.666974
\(457\) 27.4399 15.8424i 1.28358 0.741077i 0.306081 0.952006i \(-0.400982\pi\)
0.977501 + 0.210929i \(0.0676489\pi\)
\(458\) −22.2446 −1.03942
\(459\) −3.86797 + 6.69952i −0.180541 + 0.312707i
\(460\) −9.87929 5.70381i −0.460624 0.265942i
\(461\) −19.1407 + 11.0509i −0.891471 + 0.514691i −0.874424 0.485163i \(-0.838760\pi\)
−0.0170480 + 0.999855i \(0.505427\pi\)
\(462\) 0 0
\(463\) 38.8811i 1.80696i 0.428632 + 0.903479i \(0.358996\pi\)
−0.428632 + 0.903479i \(0.641004\pi\)
\(464\) −2.34269 −0.108757
\(465\) −9.68693 −0.449220
\(466\) 9.52699i 0.441329i
\(467\) 6.64116 11.5028i 0.307316 0.532287i −0.670458 0.741947i \(-0.733902\pi\)
0.977774 + 0.209660i \(0.0672358\pi\)
\(468\) 17.0298 + 9.35538i 0.787203 + 0.432453i
\(469\) 0 0
\(470\) 1.02856 + 0.593841i 0.0474440 + 0.0273918i
\(471\) −8.65571 14.9921i −0.398834 0.690801i
\(472\) −6.57358 + 11.3858i −0.302574 + 0.524073i
\(473\) 35.9807 20.7734i 1.65439 0.955164i
\(474\) 17.3390i 0.796406i
\(475\) −8.47228 + 4.89147i −0.388735 + 0.224436i
\(476\) 0 0
\(477\) −0.813975 1.40985i −0.0372694 0.0645524i
\(478\) −6.04205 10.4651i −0.276357 0.478664i
\(479\) 6.63512i 0.303166i −0.988445 0.151583i \(-0.951563\pi\)
0.988445 0.151583i \(-0.0484371\pi\)
\(480\) −24.3654 42.2021i −1.11212 1.92625i
\(481\) −12.1552 20.0566i −0.554229 0.914504i
\(482\) 11.8153 0.538172
\(483\) 0 0
\(484\) 16.0697 27.8335i 0.730439 1.26516i
\(485\) 10.8381 0.492133
\(486\) 14.8749 8.58804i 0.674740 0.389561i
\(487\) −28.9860 16.7351i −1.31348 0.758338i −0.330809 0.943698i \(-0.607322\pi\)
−0.982671 + 0.185359i \(0.940655\pi\)
\(488\) 3.16522i 0.143283i
\(489\) 6.95047i 0.314311i
\(490\) 0 0
\(491\) −18.6643 + 32.3276i −0.842310 + 1.45892i 0.0456264 + 0.998959i \(0.485472\pi\)
−0.887937 + 0.459966i \(0.847862\pi\)
\(492\) 11.3699 6.56439i 0.512593 0.295946i
\(493\) 8.09684 + 14.0241i 0.364663 + 0.631615i
\(494\) −4.96977 + 3.01189i −0.223601 + 0.135511i
\(495\) −38.3076 + 66.3507i −1.72180 + 2.98224i
\(496\) −0.389483 0.224868i −0.0174883 0.0100969i
\(497\) 0 0
\(498\) 6.78954 + 11.7598i 0.304246 + 0.526970i
\(499\) −29.5598 17.0663i −1.32328 0.763994i −0.339027 0.940777i \(-0.610098\pi\)
−0.984250 + 0.176783i \(0.943431\pi\)
\(500\) −0.00424050 0.00244826i −0.000189641 0.000109489i
\(501\) −8.95342 5.16926i −0.400009 0.230946i
\(502\) −6.14405 3.54727i −0.274223 0.158322i
\(503\) −7.65447 13.2579i −0.341296 0.591142i 0.643378 0.765549i \(-0.277533\pi\)
−0.984674 + 0.174407i \(0.944199\pi\)
\(504\) 0 0
\(505\) −36.5022 21.0745i −1.62433 0.937805i
\(506\) 6.67907 11.5685i 0.296921 0.514282i
\(507\) −34.5526 + 1.46950i −1.53453 + 0.0652630i
\(508\) 4.05195 + 7.01819i 0.179776 + 0.311382i
\(509\) 16.0189 9.24851i 0.710025 0.409933i −0.101046 0.994882i \(-0.532219\pi\)
0.811070 + 0.584949i \(0.198885\pi\)
\(510\) −9.35133 + 16.1970i −0.414084 + 0.717214i
\(511\) 0 0
\(512\) 4.39924i 0.194421i
\(513\) 5.60801i 0.247599i
\(514\) −7.39178 4.26765i −0.326037 0.188238i
\(515\) −31.8892 + 18.4112i −1.40520 + 0.811295i
\(516\) −24.5830 −1.08221
\(517\) 1.35515 2.34718i 0.0595992 0.103229i
\(518\) 0 0
\(519\) −37.1823 −1.63212
\(520\) 27.3361 + 15.0172i 1.19877 + 0.658547i
\(521\) −11.7932 20.4265i −0.516671 0.894901i −0.999813 0.0193585i \(-0.993838\pi\)
0.483141 0.875542i \(-0.339496\pi\)
\(522\) 20.1414i 0.881564i
\(523\) −6.15294 10.6572i −0.269049 0.466007i 0.699567 0.714567i \(-0.253376\pi\)
−0.968617 + 0.248560i \(0.920043\pi\)
\(524\) −6.75529 11.7005i −0.295106 0.511139i
\(525\) 0 0
\(526\) 15.7498 9.09312i 0.686722 0.396479i
\(527\) 3.10877i 0.135420i
\(528\) −5.34711 + 3.08715i −0.232703 + 0.134351i
\(529\) 7.77515 13.4670i 0.338050 0.585520i
\(530\) −0.519902 0.900497i −0.0225831 0.0391151i
\(531\) −16.9691 9.79712i −0.736397 0.425159i
\(532\) 0 0
\(533\) −6.48183 + 11.7990i −0.280759 + 0.511072i
\(534\) 3.90129 6.75724i 0.168825 0.292414i
\(535\) 12.4259i 0.537220i
\(536\) 17.1777 0.741962
\(537\) 67.2636 2.90264
\(538\) 10.6567i 0.459444i
\(539\) 0 0
\(540\) 10.3720 5.98829i 0.446341 0.257695i
\(541\) 16.8365 + 9.72054i 0.723857 + 0.417919i 0.816170 0.577811i \(-0.196093\pi\)
−0.0923139 + 0.995730i \(0.529426\pi\)
\(542\) −7.27813 + 12.6061i −0.312623 + 0.541478i
\(543\) −2.29975 −0.0986919
\(544\) −13.5437 + 7.81944i −0.580680 + 0.335256i
\(545\) 35.5841 1.52425
\(546\) 0 0
\(547\) 40.2163 1.71953 0.859763 0.510693i \(-0.170611\pi\)
0.859763 + 0.510693i \(0.170611\pi\)
\(548\) −22.8334 + 13.1829i −0.975395 + 0.563145i
\(549\) −4.71738 −0.201333
\(550\) −12.2325 + 21.1873i −0.521595 + 0.903429i
\(551\) 10.1665 + 5.86963i 0.433107 + 0.250055i
\(552\) −17.2024 + 9.93184i −0.732185 + 0.422727i
\(553\) 0 0
\(554\) 14.8364i 0.630337i
\(555\) −54.7168 −2.32260
\(556\) −26.8680 −1.13945
\(557\) 7.96399i 0.337445i −0.985664 0.168722i \(-0.946036\pi\)
0.985664 0.168722i \(-0.0539642\pi\)
\(558\) −1.93331 + 3.34860i −0.0818437 + 0.141757i
\(559\) 21.5574 13.0647i 0.911781 0.552578i
\(560\) 0 0
\(561\) 36.9615 + 21.3397i 1.56052 + 0.900965i
\(562\) 1.00547 + 1.74153i 0.0424133 + 0.0734620i
\(563\) −0.711981 + 1.23319i −0.0300064 + 0.0519726i −0.880639 0.473789i \(-0.842886\pi\)
0.850632 + 0.525761i \(0.176219\pi\)
\(564\) −1.38881 + 0.801831i −0.0584795 + 0.0337632i
\(565\) 18.2585i 0.768140i
\(566\) −20.4865 + 11.8279i −0.861113 + 0.497164i
\(567\) 0 0
\(568\) −6.16506 10.6782i −0.258680 0.448047i
\(569\) −9.25946 16.0379i −0.388177 0.672342i 0.604028 0.796963i \(-0.293562\pi\)
−0.992204 + 0.124622i \(0.960228\pi\)
\(570\) 13.5581i 0.567886i
\(571\) 2.17883 + 3.77384i 0.0911812 + 0.157930i 0.908008 0.418952i \(-0.137602\pi\)
−0.816827 + 0.576882i \(0.804269\pi\)
\(572\) 13.6360 24.8220i 0.570151 1.03786i
\(573\) 39.0202 1.63009
\(574\) 0 0
\(575\) 6.82194 11.8159i 0.284494 0.492759i
\(576\) −16.2667 −0.677778
\(577\) −8.28280 + 4.78208i −0.344818 + 0.199081i −0.662400 0.749150i \(-0.730462\pi\)
0.317583 + 0.948231i \(0.397129\pi\)
\(578\) −6.92674 3.99916i −0.288115 0.166343i
\(579\) 43.8839i 1.82375i
\(580\) 25.0706i 1.04100i
\(581\) 0 0
\(582\) 3.75466 6.50327i 0.155636 0.269569i
\(583\) −2.05494 + 1.18642i −0.0851068 + 0.0491364i
\(584\) 11.3608 + 19.6775i 0.470114 + 0.814262i
\(585\) −22.3813 + 40.7411i −0.925352 + 1.68444i
\(586\) −12.0778 + 20.9194i −0.498929 + 0.864171i
\(587\) −2.04428 1.18027i −0.0843765 0.0487148i 0.457218 0.889355i \(-0.348846\pi\)
−0.541595 + 0.840640i \(0.682179\pi\)
\(588\) 0 0
\(589\) 1.12682 + 1.95171i 0.0464297 + 0.0804186i
\(590\) −10.8385 6.25762i −0.446214 0.257622i
\(591\) 25.3661 + 14.6452i 1.04342 + 0.602421i
\(592\) −2.20000 1.27017i −0.0904194 0.0522037i
\(593\) 35.0127 + 20.2146i 1.43780 + 0.830114i 0.997697 0.0678337i \(-0.0216087\pi\)
0.440103 + 0.897947i \(0.354942\pi\)
\(594\) 7.01219 + 12.1455i 0.287714 + 0.498335i
\(595\) 0 0
\(596\) 12.2665 + 7.08207i 0.502455 + 0.290093i
\(597\) −28.2147 + 48.8693i −1.15475 + 2.00009i
\(598\) 3.90226 7.10336i 0.159575 0.290478i
\(599\) 19.2936 + 33.4176i 0.788316 + 1.36540i 0.926998 + 0.375067i \(0.122380\pi\)
−0.138681 + 0.990337i \(0.544286\pi\)
\(600\) 31.5057 18.1898i 1.28621 0.742596i
\(601\) −4.08115 + 7.06877i −0.166474 + 0.288341i −0.937178 0.348852i \(-0.886571\pi\)
0.770704 + 0.637193i \(0.219905\pi\)
\(602\) 0 0
\(603\) 25.6012i 1.04256i
\(604\) 11.5576i 0.470274i
\(605\) 66.5872 + 38.4442i 2.70716 + 1.56298i
\(606\) −25.2910 + 14.6018i −1.02738 + 0.593157i
\(607\) 7.58525 0.307876 0.153938 0.988081i \(-0.450804\pi\)
0.153938 + 0.988081i \(0.450804\pi\)
\(608\) −5.66853 + 9.81819i −0.229889 + 0.398180i
\(609\) 0 0
\(610\) −3.01308 −0.121996
\(611\) 0.791746 1.44123i 0.0320306 0.0583060i
\(612\) −7.27419 12.5993i −0.294042 0.509295i
\(613\) 15.5778i 0.629183i 0.949227 + 0.314592i \(0.101868\pi\)
−0.949227 + 0.314592i \(0.898132\pi\)
\(614\) −2.91090 5.04183i −0.117474 0.203472i
\(615\) 15.7043 + 27.2006i 0.633258 + 1.09683i
\(616\) 0 0
\(617\) 20.6709 11.9343i 0.832177 0.480458i −0.0224202 0.999749i \(-0.507137\pi\)
0.854598 + 0.519291i \(0.173804\pi\)
\(618\) 25.5129i 1.02628i
\(619\) 16.8843 9.74814i 0.678636 0.391811i −0.120705 0.992688i \(-0.538515\pi\)
0.799341 + 0.600878i \(0.205182\pi\)
\(620\) 2.40646 4.16810i 0.0966456 0.167395i
\(621\) −3.91063 6.77341i −0.156928 0.271807i
\(622\) 15.8824 + 9.16972i 0.636827 + 0.367672i
\(623\) 0 0
\(624\) −3.20366 + 1.94155i −0.128249 + 0.0777244i
\(625\) 12.5029 21.6557i 0.500117 0.866228i
\(626\) 23.1287i 0.924410i
\(627\) 30.9396 1.23561
\(628\) 8.60111 0.343222
\(629\) 17.5599i 0.700161i
\(630\) 0 0
\(631\) −22.2239 + 12.8309i −0.884718 + 0.510792i −0.872211 0.489130i \(-0.837314\pi\)
−0.0125066 + 0.999922i \(0.503981\pi\)
\(632\) −18.7496 10.8251i −0.745820 0.430600i
\(633\) 23.8572 41.3219i 0.948238 1.64240i
\(634\) 16.0721 0.638304
\(635\) −16.7899 + 9.69366i −0.666287 + 0.384681i
\(636\) 1.40399 0.0556719
\(637\) 0 0
\(638\) 29.3573 1.16227
\(639\) 15.9145 9.18826i 0.629569 0.363482i
\(640\) 26.2458 1.03746
\(641\) −0.553020 + 0.957859i −0.0218430 + 0.0378332i −0.876740 0.480964i \(-0.840287\pi\)
0.854897 + 0.518797i \(0.173620\pi\)
\(642\) 7.45603 + 4.30474i 0.294266 + 0.169895i
\(643\) 10.9437 6.31833i 0.431576 0.249171i −0.268442 0.963296i \(-0.586509\pi\)
0.700018 + 0.714125i \(0.253175\pi\)
\(644\) 0 0
\(645\) 58.8110i 2.31568i
\(646\) 4.35112 0.171192
\(647\) −25.7148 −1.01095 −0.505477 0.862840i \(-0.668683\pi\)
−0.505477 + 0.862840i \(0.668683\pi\)
\(648\) 12.6066i 0.495236i
\(649\) −14.2799 + 24.7335i −0.560535 + 0.970875i
\(650\) −7.14685 + 13.0096i −0.280323 + 0.510277i
\(651\) 0 0
\(652\) −2.99066 1.72666i −0.117123 0.0676211i
\(653\) −12.6303 21.8764i −0.494263 0.856089i 0.505715 0.862701i \(-0.331229\pi\)
−0.999978 + 0.00661158i \(0.997895\pi\)
\(654\) 12.3275 21.3518i 0.482041 0.834920i
\(655\) 27.9916 16.1610i 1.09372 0.631461i
\(656\) 1.45821i 0.0569335i
\(657\) −29.3269 + 16.9319i −1.14415 + 0.660577i
\(658\) 0 0
\(659\) −11.4882 19.8982i −0.447517 0.775123i 0.550707 0.834699i \(-0.314358\pi\)
−0.998224 + 0.0595764i \(0.981025\pi\)
\(660\) −33.0376 57.2228i −1.28599 2.22739i
\(661\) 30.4326i 1.18369i −0.806051 0.591845i \(-0.798400\pi\)
0.806051 0.591845i \(-0.201600\pi\)
\(662\) −6.43641 11.1482i −0.250158 0.433287i
\(663\) 22.6954 + 12.4678i 0.881415 + 0.484208i
\(664\) −16.9554 −0.657998
\(665\) 0 0
\(666\) −10.9204 + 18.9146i −0.423155 + 0.732926i
\(667\) −16.3723 −0.633937
\(668\) 4.44847 2.56833i 0.172117 0.0993715i
\(669\) −36.9339 21.3238i −1.42795 0.824425i
\(670\) 16.3520i 0.631733i
\(671\) 6.87586i 0.265440i
\(672\) 0 0
\(673\) 5.41933 9.38656i 0.208900 0.361825i −0.742468 0.669881i \(-0.766345\pi\)
0.951368 + 0.308056i \(0.0996784\pi\)
\(674\) −15.5126 + 8.95620i −0.597523 + 0.344980i
\(675\) 7.16218 + 12.4053i 0.275672 + 0.477479i
\(676\) 7.95135 15.2324i 0.305821 0.585861i
\(677\) 9.06044 15.6931i 0.348221 0.603137i −0.637712 0.770275i \(-0.720119\pi\)
0.985934 + 0.167138i \(0.0534525\pi\)
\(678\) −10.9558 6.32532i −0.420754 0.242923i
\(679\) 0 0
\(680\) −11.6765 20.2242i −0.447772 0.775564i
\(681\) 37.7261 + 21.7812i 1.44567 + 0.834656i
\(682\) 4.88078 + 2.81792i 0.186895 + 0.107904i
\(683\) −32.7662 18.9176i −1.25376 0.723861i −0.281909 0.959441i \(-0.590968\pi\)
−0.971855 + 0.235580i \(0.924301\pi\)
\(684\) −9.13357 5.27327i −0.349231 0.201628i
\(685\) −31.5380 54.6254i −1.20500 2.08713i
\(686\) 0 0
\(687\) 62.2288 + 35.9278i 2.37418 + 1.37073i
\(688\) 1.36521 2.36462i 0.0520482 0.0901502i
\(689\) −1.23119 + 0.746155i −0.0469047 + 0.0284262i
\(690\) −9.45446 16.3756i −0.359925 0.623408i
\(691\) −26.0034 + 15.0131i −0.989216 + 0.571124i −0.905040 0.425327i \(-0.860159\pi\)
−0.0841761 + 0.996451i \(0.526826\pi\)
\(692\) 9.23693 15.9988i 0.351135 0.608184i
\(693\) 0 0
\(694\) 13.1432i 0.498907i
\(695\) 64.2774i 2.43818i
\(696\) −37.8059 21.8273i −1.43303 0.827360i
\(697\) 8.72934 5.03988i 0.330647 0.190899i
\(698\) −5.61423 −0.212502
\(699\) 15.3873 26.6516i 0.582001 1.00805i
\(700\) 0 0
\(701\) 0.116177 0.00438796 0.00219398 0.999998i \(-0.499302\pi\)
0.00219398 + 0.999998i \(0.499302\pi\)
\(702\) 4.41006 + 7.27682i 0.166447 + 0.274646i
\(703\) 6.36485 + 11.0242i 0.240055 + 0.415787i
\(704\) 23.7097i 0.893591i
\(705\) −1.91825 3.32251i −0.0722456 0.125133i
\(706\) 5.76624 + 9.98741i 0.217015 + 0.375881i
\(707\) 0 0
\(708\) 14.6347 8.44932i 0.550004 0.317545i
\(709\) 6.72993i 0.252748i 0.991983 + 0.126374i \(0.0403339\pi\)
−0.991983 + 0.126374i \(0.959666\pi\)
\(710\) 10.1649 5.86873i 0.381483 0.220249i
\(711\) 16.1335 27.9440i 0.605053 1.04798i
\(712\) 4.87132 + 8.43738i 0.182561 + 0.316204i
\(713\) −2.72196 1.57153i −0.101938 0.0588541i
\(714\) 0 0
\(715\) 59.3826 + 32.6221i 2.22078 + 1.22000i
\(716\) −16.7098 + 28.9423i −0.624476 + 1.08162i
\(717\) 39.0347i 1.45778i
\(718\) −4.45950 −0.166427
\(719\) −46.8078 −1.74564 −0.872818 0.488046i \(-0.837710\pi\)
−0.872818 + 0.488046i \(0.837710\pi\)
\(720\) 5.03509i 0.187647i
\(721\) 0 0
\(722\) −10.8195 + 6.24666i −0.402661 + 0.232476i
\(723\) −33.0530 19.0832i −1.22926 0.709711i
\(724\) 0.571312 0.989541i 0.0212326 0.0367760i
\(725\) 29.9852 1.11362
\(726\) 46.1359 26.6366i 1.71226 0.988576i
\(727\) 13.3362 0.494611 0.247305 0.968938i \(-0.420455\pi\)
0.247305 + 0.968938i \(0.420455\pi\)
\(728\) 0 0
\(729\) −41.6582 −1.54290
\(730\) −18.7317 + 10.8148i −0.693291 + 0.400272i
\(731\) −18.8739 −0.698076
\(732\) 2.03420 3.52334i 0.0751863 0.130226i
\(733\) 25.5142 + 14.7306i 0.942387 + 0.544087i 0.890708 0.454576i \(-0.150209\pi\)
0.0516792 + 0.998664i \(0.483543\pi\)
\(734\) −21.4193 + 12.3664i −0.790599 + 0.456453i
\(735\) 0 0
\(736\) 15.8113i 0.582814i
\(737\) 37.3153 1.37453
\(738\) 12.5370 0.461494
\(739\) 12.0302i 0.442537i 0.975213 + 0.221269i \(0.0710198\pi\)
−0.975213 + 0.221269i \(0.928980\pi\)
\(740\) 13.5929 23.5436i 0.499685 0.865480i
\(741\) 18.7674 0.398904i 0.689438 0.0146541i
\(742\) 0 0
\(743\) −18.9509 10.9413i −0.695242 0.401398i 0.110331 0.993895i \(-0.464809\pi\)
−0.805573 + 0.592497i \(0.798142\pi\)
\(744\) −4.19027 7.25777i −0.153623 0.266083i
\(745\) −16.9427 + 29.3457i −0.620734 + 1.07514i
\(746\) −15.2699 + 8.81607i −0.559070 + 0.322779i
\(747\) 25.2700i 0.924580i
\(748\) −18.3642 + 10.6026i −0.671461 + 0.387668i
\(749\) 0 0
\(750\) −0.00405815 0.00702892i −0.000148183 0.000256660i
\(751\) 17.3746 + 30.0937i 0.634008 + 1.09813i 0.986724 + 0.162403i \(0.0519245\pi\)
−0.352717 + 0.935730i \(0.614742\pi\)
\(752\) 0.178118i 0.00649529i
\(753\) 11.4586 + 19.8468i 0.417574 + 0.723259i
\(754\) 17.8076 0.378504i 0.648515 0.0137843i
\(755\) −27.6498 −1.00628
\(756\) 0 0
\(757\) −21.9632 + 38.0413i −0.798265 + 1.38264i 0.122481 + 0.992471i \(0.460915\pi\)
−0.920745 + 0.390164i \(0.872418\pi\)
\(758\) 7.80447 0.283471
\(759\) −37.3691 + 21.5751i −1.35641 + 0.783126i
\(760\) −14.6611 8.46461i −0.531815 0.307044i
\(761\) 0.141391i 0.00512543i 0.999997 + 0.00256272i \(0.000815739\pi\)
−0.999997 + 0.00256272i \(0.999184\pi\)
\(762\) 13.4328i 0.486618i
\(763\) 0 0
\(764\) −9.69352 + 16.7897i −0.350699 + 0.607429i
\(765\) 30.1418 17.4024i 1.08978 0.629183i
\(766\) 2.23620 + 3.87322i 0.0807973 + 0.139945i
\(767\) −8.34305 + 15.1870i −0.301250 + 0.548372i
\(768\) 19.7062 34.1321i 0.711086 1.23164i
\(769\) 11.8200 + 6.82429i 0.426241 + 0.246090i 0.697744 0.716347i \(-0.254187\pi\)
−0.271503 + 0.962438i \(0.587521\pi\)
\(770\) 0 0
\(771\) 13.7856 + 23.8773i 0.496475 + 0.859920i
\(772\) 18.8824 + 10.9018i 0.679593 + 0.392363i
\(773\) −15.2328 8.79469i −0.547887 0.316323i 0.200382 0.979718i \(-0.435782\pi\)
−0.748269 + 0.663395i \(0.769115\pi\)
\(774\) −20.3299 11.7375i −0.730744 0.421895i
\(775\) 4.98518 + 2.87820i 0.179073 + 0.103388i
\(776\) 4.68824 + 8.12026i 0.168298 + 0.291500i
\(777\) 0 0
\(778\) 7.59022 + 4.38221i 0.272123 + 0.157110i
\(779\) 3.65356