Properties

Label 570.2.k.b.77.8
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
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 77.8
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.34719 - 1.08861i) q^{3} -1.00000i q^{4} +(-0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.629843 - 2.93314i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(1.34719 - 1.08861i) q^{3} -1.00000i q^{4} +(-0.539236 - 2.17007i) q^{5} +(-0.182842 + 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.629843 - 2.93314i) q^{9} +(1.91577 + 1.15318i) q^{10} -4.60223i q^{11} +(-1.08861 - 1.34719i) q^{12} +(1.32932 - 1.32932i) q^{13} -4.05624 q^{14} +(-3.08883 - 2.33648i) q^{15} -1.00000 q^{16} +(-3.40435 + 3.40435i) q^{17} +(1.62868 + 2.51941i) q^{18} -1.00000i q^{19} +(-2.17007 + 0.539236i) q^{20} +(6.98636 + 0.741650i) q^{21} +(3.25427 + 3.25427i) q^{22} +(2.00597 + 2.00597i) q^{23} +(1.72237 + 0.182842i) q^{24} +(-4.41845 + 2.34036i) q^{25} +1.87994i q^{26} +(-2.34453 - 4.63715i) q^{27} +(2.86820 - 2.86820i) q^{28} +6.21092 q^{29} +(3.83627 - 0.531985i) q^{30} -3.91496 q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.01005 - 6.20008i) q^{33} -4.81448i q^{34} +(4.67757 - 7.77084i) q^{35} +(-2.93314 - 0.629843i) q^{36} +(-4.28573 - 4.28573i) q^{37} +(0.707107 + 0.707107i) q^{38} +(0.343732 - 3.23796i) q^{39} +(1.15318 - 1.91577i) q^{40} -1.74242i q^{41} +(-5.46453 + 4.41568i) q^{42} +(8.19327 - 8.19327i) q^{43} -4.60223 q^{44} +(-6.70476 + 0.214847i) q^{45} -2.83687 q^{46} +(5.22236 - 5.22236i) q^{47} +(-1.34719 + 1.08861i) q^{48} +9.45311i q^{49} +(1.46943 - 4.77920i) q^{50} +(-0.880287 + 8.29233i) q^{51} +(-1.32932 - 1.32932i) q^{52} +(4.96160 + 4.96160i) q^{53} +(4.93680 + 1.62112i) q^{54} +(-9.98719 + 2.48169i) q^{55} +4.05624i q^{56} +(-1.08861 - 1.34719i) q^{57} +(-4.39178 + 4.39178i) q^{58} -5.08697 q^{59} +(-2.33648 + 3.08883i) q^{60} -0.446018 q^{61} +(2.76830 - 2.76830i) q^{62} +(10.2193 - 6.60631i) q^{63} +1.00000i q^{64} +(-3.60154 - 2.16791i) q^{65} +(7.92676 + 0.841479i) q^{66} +(6.27966 + 6.27966i) q^{67} +(3.40435 + 3.40435i) q^{68} +(4.88616 + 0.518698i) q^{69} +(2.18727 + 8.80235i) q^{70} +15.5294i q^{71} +(2.51941 - 1.62868i) q^{72} +(-6.36719 + 6.36719i) q^{73} +6.06094 q^{74} +(-3.40474 + 7.96290i) q^{75} -1.00000 q^{76} +(13.2001 - 13.2001i) q^{77} +(2.04653 + 2.53264i) q^{78} -10.4449i q^{79} +(0.539236 + 2.17007i) q^{80} +(-8.20660 - 3.69483i) q^{81} +(1.23207 + 1.23207i) q^{82} +(-3.87813 - 3.87813i) q^{83} +(0.741650 - 6.98636i) q^{84} +(9.22345 + 5.55195i) q^{85} +11.5870i q^{86} +(8.36729 - 6.76129i) q^{87} +(3.25427 - 3.25427i) q^{88} -2.07373 q^{89} +(4.58906 - 4.89290i) q^{90} +7.62551 q^{91} +(2.00597 - 2.00597i) q^{92} +(-5.27420 + 4.26188i) q^{93} +7.38553i q^{94} +(-2.17007 + 0.539236i) q^{95} +(0.182842 - 1.72237i) q^{96} +(12.5075 + 12.5075i) q^{97} +(-6.68436 - 6.68436i) q^{98} +(-13.4990 - 2.89868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} + 16q^{21} - 4q^{22} + 16q^{25} - 44q^{27} + 20q^{28} + 32q^{30} - 24q^{31} - 4q^{33} + 4q^{36} - 8q^{40} + 12q^{42} - 8q^{43} + 28q^{45} - 16q^{46} - 4q^{48} + 40q^{51} - 8q^{52} - 36q^{55} - 4q^{57} + 44q^{58} + 16q^{60} - 120q^{61} - 12q^{63} + 80q^{67} - 36q^{70} + 44q^{73} + 4q^{75} - 36q^{76} - 64q^{78} + 36q^{81} + 8q^{82} - 24q^{85} - 28q^{87} - 4q^{88} + 44q^{90} - 72q^{93} - 4q^{96} + 92q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) 1.34719 1.08861i 0.777801 0.628511i
\(4\) 1.00000i 0.500000i
\(5\) −0.539236 2.17007i −0.241153 0.970487i
\(6\) −0.182842 + 1.72237i −0.0746447 + 0.703156i
\(7\) 2.86820 + 2.86820i 1.08408 + 1.08408i 0.996125 + 0.0879519i \(0.0280322\pi\)
0.0879519 + 0.996125i \(0.471968\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.629843 2.93314i 0.209948 0.977713i
\(10\) 1.91577 + 1.15318i 0.605820 + 0.364667i
\(11\) 4.60223i 1.38763i −0.720156 0.693813i \(-0.755930\pi\)
0.720156 0.693813i \(-0.244070\pi\)
\(12\) −1.08861 1.34719i −0.314256 0.388900i
\(13\) 1.32932 1.32932i 0.368687 0.368687i −0.498311 0.866998i \(-0.666046\pi\)
0.866998 + 0.498311i \(0.166046\pi\)
\(14\) −4.05624 −1.08408
\(15\) −3.08883 2.33648i −0.797531 0.603278i
\(16\) −1.00000 −0.250000
\(17\) −3.40435 + 3.40435i −0.825677 + 0.825677i −0.986915 0.161239i \(-0.948451\pi\)
0.161239 + 0.986915i \(0.448451\pi\)
\(18\) 1.62868 + 2.51941i 0.383883 + 0.593830i
\(19\) 1.00000i 0.229416i
\(20\) −2.17007 + 0.539236i −0.485243 + 0.120577i
\(21\) 6.98636 + 0.741650i 1.52455 + 0.161841i
\(22\) 3.25427 + 3.25427i 0.693813 + 0.693813i
\(23\) 2.00597 + 2.00597i 0.418274 + 0.418274i 0.884609 0.466334i \(-0.154426\pi\)
−0.466334 + 0.884609i \(0.654426\pi\)
\(24\) 1.72237 + 0.182842i 0.351578 + 0.0373224i
\(25\) −4.41845 + 2.34036i −0.883690 + 0.468073i
\(26\) 1.87994i 0.368687i
\(27\) −2.34453 4.63715i −0.451206 0.892420i
\(28\) 2.86820 2.86820i 0.542038 0.542038i
\(29\) 6.21092 1.15334 0.576670 0.816978i \(-0.304352\pi\)
0.576670 + 0.816978i \(0.304352\pi\)
\(30\) 3.83627 0.531985i 0.700404 0.0971267i
\(31\) −3.91496 −0.703148 −0.351574 0.936160i \(-0.614353\pi\)
−0.351574 + 0.936160i \(0.614353\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −5.01005 6.20008i −0.872138 1.07930i
\(34\) 4.81448i 0.825677i
\(35\) 4.67757 7.77084i 0.790653 1.31351i
\(36\) −2.93314 0.629843i −0.488856 0.104974i
\(37\) −4.28573 4.28573i −0.704570 0.704570i 0.260818 0.965388i \(-0.416008\pi\)
−0.965388 + 0.260818i \(0.916008\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) 0.343732 3.23796i 0.0550411 0.518489i
\(40\) 1.15318 1.91577i 0.182333 0.302910i
\(41\) 1.74242i 0.272120i −0.990701 0.136060i \(-0.956556\pi\)
0.990701 0.136060i \(-0.0434440\pi\)
\(42\) −5.46453 + 4.41568i −0.843195 + 0.681354i
\(43\) 8.19327 8.19327i 1.24946 1.24946i 0.293504 0.955958i \(-0.405178\pi\)
0.955958 0.293504i \(-0.0948215\pi\)
\(44\) −4.60223 −0.693813
\(45\) −6.70476 + 0.214847i −0.999487 + 0.0320275i
\(46\) −2.83687 −0.418274
\(47\) 5.22236 5.22236i 0.761759 0.761759i −0.214881 0.976640i \(-0.568936\pi\)
0.976640 + 0.214881i \(0.0689365\pi\)
\(48\) −1.34719 + 1.08861i −0.194450 + 0.157128i
\(49\) 9.45311i 1.35044i
\(50\) 1.46943 4.77920i 0.207809 0.675881i
\(51\) −0.880287 + 8.29233i −0.123265 + 1.16116i
\(52\) −1.32932 1.32932i −0.184344 0.184344i
\(53\) 4.96160 + 4.96160i 0.681527 + 0.681527i 0.960344 0.278817i \(-0.0899422\pi\)
−0.278817 + 0.960344i \(0.589942\pi\)
\(54\) 4.93680 + 1.62112i 0.671813 + 0.220607i
\(55\) −9.98719 + 2.48169i −1.34667 + 0.334631i
\(56\) 4.05624i 0.542038i
\(57\) −1.08861 1.34719i −0.144190 0.178440i
\(58\) −4.39178 + 4.39178i −0.576670 + 0.576670i
\(59\) −5.08697 −0.662268 −0.331134 0.943584i \(-0.607431\pi\)
−0.331134 + 0.943584i \(0.607431\pi\)
\(60\) −2.33648 + 3.08883i −0.301639 + 0.398766i
\(61\) −0.446018 −0.0571067 −0.0285534 0.999592i \(-0.509090\pi\)
−0.0285534 + 0.999592i \(0.509090\pi\)
\(62\) 2.76830 2.76830i 0.351574 0.351574i
\(63\) 10.2193 6.60631i 1.28751 0.832316i
\(64\) 1.00000i 0.125000i
\(65\) −3.60154 2.16791i −0.446716 0.268896i
\(66\) 7.92676 + 0.841479i 0.975717 + 0.103579i
\(67\) 6.27966 + 6.27966i 0.767183 + 0.767183i 0.977610 0.210427i \(-0.0674854\pi\)
−0.210427 + 0.977610i \(0.567485\pi\)
\(68\) 3.40435 + 3.40435i 0.412838 + 0.412838i
\(69\) 4.88616 + 0.518698i 0.588224 + 0.0624440i
\(70\) 2.18727 + 8.80235i 0.261429 + 1.05208i
\(71\) 15.5294i 1.84300i 0.388380 + 0.921499i \(0.373035\pi\)
−0.388380 + 0.921499i \(0.626965\pi\)
\(72\) 2.51941 1.62868i 0.296915 0.191941i
\(73\) −6.36719 + 6.36719i −0.745223 + 0.745223i −0.973578 0.228355i \(-0.926665\pi\)
0.228355 + 0.973578i \(0.426665\pi\)
\(74\) 6.06094 0.704570
\(75\) −3.40474 + 7.96290i −0.393146 + 0.919476i
\(76\) −1.00000 −0.114708
\(77\) 13.2001 13.2001i 1.50429 1.50429i
\(78\) 2.04653 + 2.53264i 0.231724 + 0.286765i
\(79\) 10.4449i 1.17514i −0.809173 0.587571i \(-0.800084\pi\)
0.809173 0.587571i \(-0.199916\pi\)
\(80\) 0.539236 + 2.17007i 0.0602884 + 0.242622i
\(81\) −8.20660 3.69483i −0.911844 0.410537i
\(82\) 1.23207 + 1.23207i 0.136060 + 0.136060i
\(83\) −3.87813 3.87813i −0.425680 0.425680i 0.461474 0.887154i \(-0.347321\pi\)
−0.887154 + 0.461474i \(0.847321\pi\)
\(84\) 0.741650 6.98636i 0.0809206 0.762275i
\(85\) 9.22345 + 5.55195i 1.00042 + 0.602194i
\(86\) 11.5870i 1.24946i
\(87\) 8.36729 6.76129i 0.897068 0.724886i
\(88\) 3.25427 3.25427i 0.346906 0.346906i
\(89\) −2.07373 −0.219814 −0.109907 0.993942i \(-0.535055\pi\)
−0.109907 + 0.993942i \(0.535055\pi\)
\(90\) 4.58906 4.89290i 0.483730 0.515757i
\(91\) 7.62551 0.799370
\(92\) 2.00597 2.00597i 0.209137 0.209137i
\(93\) −5.27420 + 4.26188i −0.546909 + 0.441936i
\(94\) 7.38553i 0.761759i
\(95\) −2.17007 + 0.539236i −0.222645 + 0.0553244i
\(96\) 0.182842 1.72237i 0.0186612 0.175789i
\(97\) 12.5075 + 12.5075i 1.26994 + 1.26994i 0.946116 + 0.323828i \(0.104970\pi\)
0.323828 + 0.946116i \(0.395030\pi\)
\(98\) −6.68436 6.68436i −0.675222 0.675222i
\(99\) −13.4990 2.89868i −1.35670 0.291328i
\(100\) 2.34036 + 4.41845i 0.234036 + 0.441845i
\(101\) 1.85435i 0.184514i 0.995735 + 0.0922571i \(0.0294082\pi\)
−0.995735 + 0.0922571i \(0.970592\pi\)
\(102\) −5.24111 6.48602i −0.518947 0.642212i
\(103\) −11.4600 + 11.4600i −1.12919 + 1.12919i −0.138882 + 0.990309i \(0.544351\pi\)
−0.990309 + 0.138882i \(0.955649\pi\)
\(104\) 1.87994 0.184344
\(105\) −2.15786 15.5609i −0.210586 1.51858i
\(106\) −7.01675 −0.681527
\(107\) −8.61306 + 8.61306i −0.832656 + 0.832656i −0.987879 0.155223i \(-0.950390\pi\)
0.155223 + 0.987879i \(0.450390\pi\)
\(108\) −4.63715 + 2.34453i −0.446210 + 0.225603i
\(109\) 6.32736i 0.606051i 0.952982 + 0.303025i \(0.0979967\pi\)
−0.952982 + 0.303025i \(0.902003\pi\)
\(110\) 5.30719 8.81683i 0.506021 0.840651i
\(111\) −10.4392 1.10819i −0.990845 0.105185i
\(112\) −2.86820 2.86820i −0.271019 0.271019i
\(113\) 0.984759 + 0.984759i 0.0926383 + 0.0926383i 0.751907 0.659269i \(-0.229134\pi\)
−0.659269 + 0.751907i \(0.729134\pi\)
\(114\) 1.72237 + 0.182842i 0.161315 + 0.0171247i
\(115\) 3.27142 5.43480i 0.305061 0.506798i
\(116\) 6.21092i 0.576670i
\(117\) −3.06182 4.73634i −0.283065 0.437875i
\(118\) 3.59703 3.59703i 0.331134 0.331134i
\(119\) −19.5287 −1.79019
\(120\) −0.531985 3.83627i −0.0485634 0.350202i
\(121\) −10.1805 −0.925503
\(122\) 0.315382 0.315382i 0.0285534 0.0285534i
\(123\) −1.89682 2.34737i −0.171030 0.211655i
\(124\) 3.91496i 0.351574i
\(125\) 7.46135 + 8.32636i 0.667363 + 0.744732i
\(126\) −2.55479 + 11.8975i −0.227599 + 1.05992i
\(127\) 8.32109 + 8.32109i 0.738378 + 0.738378i 0.972264 0.233886i \(-0.0751443\pi\)
−0.233886 + 0.972264i \(0.575144\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) 2.11859 19.9572i 0.186532 1.75713i
\(130\) 4.07962 1.01373i 0.357806 0.0889102i
\(131\) 18.6781i 1.63191i 0.578115 + 0.815955i \(0.303789\pi\)
−0.578115 + 0.815955i \(0.696211\pi\)
\(132\) −6.20008 + 5.01005i −0.539648 + 0.436069i
\(133\) 2.86820 2.86820i 0.248704 0.248704i
\(134\) −8.88078 −0.767183
\(135\) −8.79871 + 7.58833i −0.757272 + 0.653100i
\(136\) −4.81448 −0.412838
\(137\) 14.3208 14.3208i 1.22351 1.22351i 0.257137 0.966375i \(-0.417221\pi\)
0.966375 0.257137i \(-0.0827792\pi\)
\(138\) −3.82181 + 3.08826i −0.325334 + 0.262890i
\(139\) 11.2626i 0.955283i 0.878555 + 0.477642i \(0.158508\pi\)
−0.878555 + 0.477642i \(0.841492\pi\)
\(140\) −7.77084 4.67757i −0.656756 0.395327i
\(141\) 1.35038 12.7206i 0.113723 1.07127i
\(142\) −10.9809 10.9809i −0.921499 0.921499i
\(143\) −6.11784 6.11784i −0.511600 0.511600i
\(144\) −0.629843 + 2.93314i −0.0524869 + 0.244428i
\(145\) −3.34915 13.4782i −0.278132 1.11930i
\(146\) 9.00456i 0.745223i
\(147\) 10.2908 + 12.7351i 0.848769 + 1.05038i
\(148\) −4.28573 + 4.28573i −0.352285 + 0.352285i
\(149\) −5.59268 −0.458170 −0.229085 0.973406i \(-0.573573\pi\)
−0.229085 + 0.973406i \(0.573573\pi\)
\(150\) −3.22310 8.03813i −0.263165 0.656311i
\(151\) −4.62138 −0.376083 −0.188041 0.982161i \(-0.560214\pi\)
−0.188041 + 0.982161i \(0.560214\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) 7.84123 + 12.1296i 0.633926 + 0.980623i
\(154\) 18.6678i 1.50429i
\(155\) 2.11109 + 8.49576i 0.169567 + 0.682396i
\(156\) −3.23796 0.343732i −0.259245 0.0275206i
\(157\) −10.3075 10.3075i −0.822626 0.822626i 0.163858 0.986484i \(-0.447606\pi\)
−0.986484 + 0.163858i \(0.947606\pi\)
\(158\) 7.38565 + 7.38565i 0.587571 + 0.587571i
\(159\) 12.0855 + 1.28295i 0.958440 + 0.101745i
\(160\) −1.91577 1.15318i −0.151455 0.0911667i
\(161\) 11.5071i 0.906883i
\(162\) 8.41558 3.19030i 0.661190 0.250654i
\(163\) −11.0783 + 11.0783i −0.867718 + 0.867718i −0.992219 0.124502i \(-0.960267\pi\)
0.124502 + 0.992219i \(0.460267\pi\)
\(164\) −1.74242 −0.136060
\(165\) −10.7530 + 14.2155i −0.837123 + 1.10667i
\(166\) 5.48450 0.425680
\(167\) 4.00388 4.00388i 0.309830 0.309830i −0.535014 0.844843i \(-0.679694\pi\)
0.844843 + 0.535014i \(0.179694\pi\)
\(168\) 4.41568 + 5.46453i 0.340677 + 0.421598i
\(169\) 9.46581i 0.728140i
\(170\) −10.4478 + 2.59614i −0.801308 + 0.199115i
\(171\) −2.93314 0.629843i −0.224303 0.0481653i
\(172\) −8.19327 8.19327i −0.624731 0.624731i
\(173\) 8.19231 + 8.19231i 0.622850 + 0.622850i 0.946259 0.323409i \(-0.104829\pi\)
−0.323409 + 0.946259i \(0.604829\pi\)
\(174\) −1.13561 + 10.6975i −0.0860907 + 0.810977i
\(175\) −19.3856 5.96036i −1.46541 0.450561i
\(176\) 4.60223i 0.346906i
\(177\) −6.85312 + 5.53775i −0.515112 + 0.416243i
\(178\) 1.46635 1.46635i 0.109907 0.109907i
\(179\) −5.97757 −0.446784 −0.223392 0.974729i \(-0.571713\pi\)
−0.223392 + 0.974729i \(0.571713\pi\)
\(180\) 0.214847 + 6.70476i 0.0160137 + 0.499743i
\(181\) 8.47586 0.630006 0.315003 0.949091i \(-0.397994\pi\)
0.315003 + 0.949091i \(0.397994\pi\)
\(182\) −5.39205 + 5.39205i −0.399685 + 0.399685i
\(183\) −0.600871 + 0.485541i −0.0444177 + 0.0358922i
\(184\) 2.83687i 0.209137i
\(185\) −6.98934 + 11.6114i −0.513866 + 0.853685i
\(186\) 0.715817 6.74302i 0.0524863 0.494422i
\(187\) 15.6676 + 15.6676i 1.14573 + 1.14573i
\(188\) −5.22236 5.22236i −0.380879 0.380879i
\(189\) 6.57567 20.0248i 0.478310 1.45659i
\(190\) 1.15318 1.91577i 0.0836603 0.138985i
\(191\) 6.45739i 0.467240i −0.972328 0.233620i \(-0.924943\pi\)
0.972328 0.233620i \(-0.0750572\pi\)
\(192\) 1.08861 + 1.34719i 0.0785639 + 0.0972251i
\(193\) 4.32749 4.32749i 0.311500 0.311500i −0.533991 0.845490i \(-0.679308\pi\)
0.845490 + 0.533991i \(0.179308\pi\)
\(194\) −17.6883 −1.26994
\(195\) −7.21197 + 1.00010i −0.516460 + 0.0716188i
\(196\) 9.45311 0.675222
\(197\) 14.8702 14.8702i 1.05946 1.05946i 0.0613383 0.998117i \(-0.480463\pi\)
0.998117 0.0613383i \(-0.0195368\pi\)
\(198\) 11.5949 7.49554i 0.824014 0.532685i
\(199\) 0.789726i 0.0559822i −0.999608 0.0279911i \(-0.991089\pi\)
0.999608 0.0279911i \(-0.00891101\pi\)
\(200\) −4.77920 1.46943i −0.337941 0.103904i
\(201\) 15.2960 + 1.62378i 1.07890 + 0.114532i
\(202\) −1.31122 1.31122i −0.0922571 0.0922571i
\(203\) 17.8141 + 17.8141i 1.25031 + 1.25031i
\(204\) 8.29233 + 0.880287i 0.580579 + 0.0616324i
\(205\) −3.78118 + 0.939573i −0.264089 + 0.0656226i
\(206\) 16.2069i 1.12919i
\(207\) 7.14724 4.62035i 0.496768 0.321136i
\(208\) −1.32932 + 1.32932i −0.0921718 + 0.0921718i
\(209\) −4.60223 −0.318343
\(210\) 12.5290 + 9.47735i 0.864585 + 0.653999i
\(211\) −19.8686 −1.36781 −0.683905 0.729571i \(-0.739720\pi\)
−0.683905 + 0.729571i \(0.739720\pi\)
\(212\) 4.96160 4.96160i 0.340764 0.340764i
\(213\) 16.9055 + 20.9210i 1.15834 + 1.43349i
\(214\) 12.1807i 0.832656i
\(215\) −22.1981 13.3619i −1.51390 0.911275i
\(216\) 1.62112 4.93680i 0.110303 0.335906i
\(217\) −11.2289 11.2289i −0.762266 0.762266i
\(218\) −4.47412 4.47412i −0.303025 0.303025i
\(219\) −1.64641 + 15.5092i −0.111254 + 1.04802i
\(220\) 2.48169 + 9.98719i 0.167315 + 0.673336i
\(221\) 9.05095i 0.608833i
\(222\) 8.16524 6.59802i 0.548015 0.442830i
\(223\) 10.1226 10.1226i 0.677856 0.677856i −0.281659 0.959515i \(-0.590885\pi\)
0.959515 + 0.281659i \(0.0908845\pi\)
\(224\) 4.05624 0.271019
\(225\) 4.08168 + 14.4340i 0.272112 + 0.962266i
\(226\) −1.39266 −0.0926383
\(227\) −13.7553 + 13.7553i −0.912969 + 0.912969i −0.996505 0.0835359i \(-0.973379\pi\)
0.0835359 + 0.996505i \(0.473379\pi\)
\(228\) −1.34719 + 1.08861i −0.0892198 + 0.0720952i
\(229\) 6.47050i 0.427583i −0.976879 0.213791i \(-0.931419\pi\)
0.976879 0.213791i \(-0.0685813\pi\)
\(230\) 1.52974 + 6.15623i 0.100868 + 0.405930i
\(231\) 3.41324 32.1529i 0.224575 2.11550i
\(232\) 4.39178 + 4.39178i 0.288335 + 0.288335i
\(233\) 4.00499 + 4.00499i 0.262376 + 0.262376i 0.826019 0.563643i \(-0.190601\pi\)
−0.563643 + 0.826019i \(0.690601\pi\)
\(234\) 5.51413 + 1.18407i 0.360470 + 0.0774050i
\(235\) −14.1490 8.51682i −0.922978 0.555576i
\(236\) 5.08697i 0.331134i
\(237\) −11.3704 14.0713i −0.738590 0.914026i
\(238\) 13.8089 13.8089i 0.895097 0.895097i
\(239\) −1.96845 −0.127329 −0.0636643 0.997971i \(-0.520279\pi\)
−0.0636643 + 0.997971i \(0.520279\pi\)
\(240\) 3.08883 + 2.33648i 0.199383 + 0.150819i
\(241\) 23.9008 1.53959 0.769794 0.638292i \(-0.220359\pi\)
0.769794 + 0.638292i \(0.220359\pi\)
\(242\) 7.19873 7.19873i 0.462752 0.462752i
\(243\) −15.0781 + 3.95617i −0.967260 + 0.253788i
\(244\) 0.446018i 0.0285534i
\(245\) 20.5140 5.09745i 1.31059 0.325664i
\(246\) 3.00109 + 0.318586i 0.191343 + 0.0203123i
\(247\) −1.32932 1.32932i −0.0845826 0.0845826i
\(248\) −2.76830 2.76830i −0.175787 0.175787i
\(249\) −9.44635 1.00279i −0.598638 0.0635495i
\(250\) −11.1636 0.611655i −0.706048 0.0386845i
\(251\) 6.34592i 0.400551i −0.979740 0.200275i \(-0.935816\pi\)
0.979740 0.200275i \(-0.0641837\pi\)
\(252\) −6.60631 10.2193i −0.416158 0.643757i
\(253\) 9.23195 9.23195i 0.580408 0.580408i
\(254\) −11.7678 −0.738378
\(255\) 18.4697 2.56123i 1.15662 0.160391i
\(256\) 1.00000 0.0625000
\(257\) −3.25382 + 3.25382i −0.202968 + 0.202968i −0.801270 0.598302i \(-0.795842\pi\)
0.598302 + 0.801270i \(0.295842\pi\)
\(258\) 12.6138 + 15.6099i 0.785301 + 0.971832i
\(259\) 24.5846i 1.52762i
\(260\) −2.16791 + 3.60154i −0.134448 + 0.223358i
\(261\) 3.91190 18.2175i 0.242141 1.12763i
\(262\) −13.2074 13.2074i −0.815955 0.815955i
\(263\) −20.2705 20.2705i −1.24993 1.24993i −0.955749 0.294183i \(-0.904952\pi\)
−0.294183 0.955749i \(-0.595048\pi\)
\(264\) 0.841479 7.92676i 0.0517895 0.487858i
\(265\) 8.09156 13.4425i 0.497061 0.825766i
\(266\) 4.05624i 0.248704i
\(267\) −2.79370 + 2.25748i −0.170972 + 0.138156i
\(268\) 6.27966 6.27966i 0.383591 0.383591i
\(269\) 16.9049 1.03071 0.515354 0.856977i \(-0.327660\pi\)
0.515354 + 0.856977i \(0.327660\pi\)
\(270\) 0.855863 11.5874i 0.0520861 0.705186i
\(271\) −2.93733 −0.178430 −0.0892149 0.996012i \(-0.528436\pi\)
−0.0892149 + 0.996012i \(0.528436\pi\)
\(272\) 3.40435 3.40435i 0.206419 0.206419i
\(273\) 10.2730 8.30123i 0.621751 0.502413i
\(274\) 20.2527i 1.22351i
\(275\) 10.7709 + 20.3347i 0.649509 + 1.22623i
\(276\) 0.518698 4.88616i 0.0312220 0.294112i
\(277\) −4.03864 4.03864i −0.242659 0.242659i 0.575291 0.817949i \(-0.304889\pi\)
−0.817949 + 0.575291i \(0.804889\pi\)
\(278\) −7.96388 7.96388i −0.477642 0.477642i
\(279\) −2.46581 + 11.4831i −0.147624 + 0.687476i
\(280\) 8.80235 2.18727i 0.526041 0.130714i
\(281\) 14.0877i 0.840400i 0.907431 + 0.420200i \(0.138040\pi\)
−0.907431 + 0.420200i \(0.861960\pi\)
\(282\) 8.03998 + 9.94971i 0.478774 + 0.592496i
\(283\) 15.0689 15.0689i 0.895756 0.895756i −0.0993018 0.995057i \(-0.531661\pi\)
0.995057 + 0.0993018i \(0.0316609\pi\)
\(284\) 15.5294 0.921499
\(285\) −2.33648 + 3.08883i −0.138401 + 0.182966i
\(286\) 8.65193 0.511600
\(287\) 4.99760 4.99760i 0.294999 0.294999i
\(288\) −1.62868 2.51941i −0.0959706 0.148458i
\(289\) 6.17923i 0.363484i
\(290\) 11.8987 + 7.16229i 0.698716 + 0.420584i
\(291\) 30.4658 + 3.23415i 1.78594 + 0.189589i
\(292\) 6.36719 + 6.36719i 0.372611 + 0.372611i
\(293\) −4.92404 4.92404i −0.287665 0.287665i 0.548491 0.836156i \(-0.315202\pi\)
−0.836156 + 0.548491i \(0.815202\pi\)
\(294\) −16.2818 1.72842i −0.949573 0.100804i
\(295\) 2.74308 + 11.0391i 0.159708 + 0.642722i
\(296\) 6.06094i 0.352285i
\(297\) −21.3412 + 10.7901i −1.23834 + 0.626105i
\(298\) 3.95462 3.95462i 0.229085 0.229085i
\(299\) 5.33316 0.308425
\(300\) 7.96290 + 3.40474i 0.459738 + 0.196573i
\(301\) 46.9998 2.70903
\(302\) 3.26781 3.26781i 0.188041 0.188041i
\(303\) 2.01866 + 2.49816i 0.115969 + 0.143515i
\(304\) 1.00000i 0.0573539i
\(305\) 0.240509 + 0.967892i 0.0137715 + 0.0554214i
\(306\) −14.1215 3.03237i −0.807275 0.173349i
\(307\) −7.41152 7.41152i −0.422998 0.422998i 0.463237 0.886235i \(-0.346688\pi\)
−0.886235 + 0.463237i \(0.846688\pi\)
\(308\) −13.2001 13.2001i −0.752146 0.752146i
\(309\) −2.96330 + 27.9144i −0.168576 + 1.58799i
\(310\) −7.50017 4.51465i −0.425981 0.256415i
\(311\) 22.6059i 1.28186i 0.767598 + 0.640931i \(0.221452\pi\)
−0.767598 + 0.640931i \(0.778548\pi\)
\(312\) 2.53264 2.04653i 0.143383 0.115862i
\(313\) −17.6638 + 17.6638i −0.998419 + 0.998419i −0.999999 0.00158010i \(-0.999497\pi\)
0.00158010 + 0.999999i \(0.499497\pi\)
\(314\) 14.5770 0.822626
\(315\) −19.8468 18.6144i −1.11824 1.04880i
\(316\) −10.4449 −0.587571
\(317\) −0.617852 + 0.617852i −0.0347020 + 0.0347020i −0.724245 0.689543i \(-0.757811\pi\)
0.689543 + 0.724245i \(0.257811\pi\)
\(318\) −9.45290 + 7.63853i −0.530092 + 0.428348i
\(319\) 28.5841i 1.60040i
\(320\) 2.17007 0.539236i 0.121311 0.0301442i
\(321\) −2.22714 + 20.9797i −0.124307 + 1.17097i
\(322\) −8.13672 8.13672i −0.453441 0.453441i
\(323\) 3.40435 + 3.40435i 0.189423 + 0.189423i
\(324\) −3.69483 + 8.20660i −0.205268 + 0.455922i
\(325\) −2.76244 + 8.98463i −0.153233 + 0.498377i
\(326\) 15.6671i 0.867718i
\(327\) 6.88804 + 8.52415i 0.380910 + 0.471387i
\(328\) 1.23207 1.23207i 0.0680300 0.0680300i
\(329\) 29.9575 1.65161
\(330\) −2.44832 17.6554i −0.134776 0.971899i
\(331\) 16.7769 0.922142 0.461071 0.887363i \(-0.347465\pi\)
0.461071 + 0.887363i \(0.347465\pi\)
\(332\) −3.87813 + 3.87813i −0.212840 + 0.212840i
\(333\) −15.2700 + 9.87131i −0.836790 + 0.540944i
\(334\) 5.66235i 0.309830i
\(335\) 10.2411 17.0135i 0.559532 0.929550i
\(336\) −6.98636 0.741650i −0.381137 0.0404603i
\(337\) 19.3140 + 19.3140i 1.05210 + 1.05210i 0.998566 + 0.0535356i \(0.0170491\pi\)
0.0535356 + 0.998566i \(0.482951\pi\)
\(338\) −6.69334 6.69334i −0.364070 0.364070i
\(339\) 2.39868 + 0.254636i 0.130278 + 0.0138299i
\(340\) 5.55195 9.22345i 0.301097 0.500212i
\(341\) 18.0176i 0.975706i
\(342\) 2.51941 1.62868i 0.136234 0.0880687i
\(343\) −7.03600 + 7.03600i −0.379908 + 0.379908i
\(344\) 11.5870 0.624731
\(345\) −1.50917 10.8830i −0.0812512 0.585922i
\(346\) −11.5857 −0.622850
\(347\) 20.8770 20.8770i 1.12074 1.12074i 0.129107 0.991631i \(-0.458789\pi\)
0.991631 0.129107i \(-0.0412109\pi\)
\(348\) −6.76129 8.36729i −0.362443 0.448534i
\(349\) 11.2937i 0.604537i −0.953223 0.302269i \(-0.902256\pi\)
0.953223 0.302269i \(-0.0977440\pi\)
\(350\) 17.9223 9.49308i 0.957988 0.507427i
\(351\) −9.28090 3.04762i −0.495378 0.162670i
\(352\) −3.25427 3.25427i −0.173453 0.173453i
\(353\) 0.723576 + 0.723576i 0.0385121 + 0.0385121i 0.726101 0.687589i \(-0.241331\pi\)
−0.687589 + 0.726101i \(0.741331\pi\)
\(354\) 0.930110 8.76167i 0.0494348 0.465677i
\(355\) 33.6999 8.37399i 1.78861 0.444445i
\(356\) 2.07373i 0.109907i
\(357\) −26.3089 + 21.2592i −1.39241 + 1.12516i
\(358\) 4.22678 4.22678i 0.223392 0.223392i
\(359\) −25.4403 −1.34269 −0.671345 0.741145i \(-0.734283\pi\)
−0.671345 + 0.741145i \(0.734283\pi\)
\(360\) −4.89290 4.58906i −0.257879 0.241865i
\(361\) −1.00000 −0.0526316
\(362\) −5.99334 + 5.99334i −0.315003 + 0.315003i
\(363\) −13.7151 + 11.0827i −0.719857 + 0.581689i
\(364\) 7.62551i 0.399685i
\(365\) 17.2507 + 10.3839i 0.902942 + 0.543516i
\(366\) 0.0815506 0.768209i 0.00426272 0.0401549i
\(367\) 14.0536 + 14.0536i 0.733593 + 0.733593i 0.971330 0.237737i \(-0.0764055\pi\)
−0.237737 + 0.971330i \(0.576406\pi\)
\(368\) −2.00597 2.00597i −0.104569 0.104569i
\(369\) −5.11075 1.09745i −0.266055 0.0571309i
\(370\) −3.26827 13.1527i −0.169910 0.683776i
\(371\) 28.4617i 1.47766i
\(372\) 4.26188 + 5.27420i 0.220968 + 0.273454i
\(373\) 5.52563 5.52563i 0.286106 0.286106i −0.549432 0.835538i \(-0.685156\pi\)
0.835538 + 0.549432i \(0.185156\pi\)
\(374\) −22.1574 −1.14573
\(375\) 19.1160 + 3.09467i 0.987148 + 0.159808i
\(376\) 7.38553 0.380879
\(377\) 8.25630 8.25630i 0.425221 0.425221i
\(378\) 9.51000 + 18.8094i 0.489142 + 0.967452i
\(379\) 8.19606i 0.421003i −0.977593 0.210502i \(-0.932490\pi\)
0.977593 0.210502i \(-0.0675098\pi\)
\(380\) 0.539236 + 2.17007i 0.0276622 + 0.111322i
\(381\) 20.2685 + 2.15164i 1.03839 + 0.110232i
\(382\) 4.56606 + 4.56606i 0.233620 + 0.233620i
\(383\) 11.6617 + 11.6617i 0.595886 + 0.595886i 0.939215 0.343329i \(-0.111555\pi\)
−0.343329 + 0.939215i \(0.611555\pi\)
\(384\) −1.72237 0.182842i −0.0878945 0.00933059i
\(385\) −35.7632 21.5273i −1.82266 1.09713i
\(386\) 6.12000i 0.311500i
\(387\) −18.8715 29.1925i −0.959293 1.48394i
\(388\) 12.5075 12.5075i 0.634972 0.634972i
\(389\) −15.6133 −0.791625 −0.395813 0.918331i \(-0.629537\pi\)
−0.395813 + 0.918331i \(0.629537\pi\)
\(390\) 4.39246 5.80681i 0.222421 0.294039i
\(391\) −13.6581 −0.690719
\(392\) −6.68436 + 6.68436i −0.337611 + 0.337611i
\(393\) 20.3332 + 25.1629i 1.02567 + 1.26930i
\(394\) 21.0296i 1.05946i
\(395\) −22.6662 + 5.63226i −1.14046 + 0.283390i
\(396\) −2.89868 + 13.4990i −0.145664 + 0.678349i
\(397\) −23.3976 23.3976i −1.17429 1.17429i −0.981176 0.193114i \(-0.938141\pi\)
−0.193114 0.981176i \(-0.561859\pi\)
\(398\) 0.558421 + 0.558421i 0.0279911 + 0.0279911i
\(399\) 0.741650 6.98636i 0.0371289 0.349756i
\(400\) 4.41845 2.34036i 0.220922 0.117018i
\(401\) 4.91777i 0.245582i −0.992433 0.122791i \(-0.960816\pi\)
0.992433 0.122791i \(-0.0391844\pi\)
\(402\) −11.9641 + 9.66774i −0.596715 + 0.482183i
\(403\) −5.20424 + 5.20424i −0.259242 + 0.259242i
\(404\) 1.85435 0.0922571
\(405\) −3.59277 + 19.8013i −0.178526 + 0.983935i
\(406\) −25.1930 −1.25031
\(407\) −19.7239 + 19.7239i −0.977679 + 0.977679i
\(408\) −6.48602 + 5.24111i −0.321106 + 0.259473i
\(409\) 3.39494i 0.167869i 0.996471 + 0.0839345i \(0.0267487\pi\)
−0.996471 + 0.0839345i \(0.973251\pi\)
\(410\) 2.00932 3.33807i 0.0992331 0.164856i
\(411\) 3.70304 34.8828i 0.182657 1.72064i
\(412\) 11.4600 + 11.4600i 0.564596 + 0.564596i
\(413\) −14.5904 14.5904i −0.717949 0.717949i
\(414\) −1.78678 + 8.32094i −0.0878157 + 0.408952i
\(415\) −6.32460 + 10.5070i −0.310462 + 0.515771i
\(416\) 1.87994i 0.0921718i
\(417\) 12.2606 + 15.1729i 0.600406 + 0.743020i
\(418\) 3.25427 3.25427i 0.159172 0.159172i
\(419\) −12.5500 −0.613105 −0.306553 0.951854i \(-0.599176\pi\)
−0.306553 + 0.951854i \(0.599176\pi\)
\(420\) −15.5609 + 2.15786i −0.759292 + 0.105293i
\(421\) −14.3230 −0.698060 −0.349030 0.937112i \(-0.613489\pi\)
−0.349030 + 0.937112i \(0.613489\pi\)
\(422\) 14.0492 14.0492i 0.683905 0.683905i
\(423\) −12.0286 18.6072i −0.584852 0.904711i
\(424\) 7.01675i 0.340764i
\(425\) 7.07454 23.0094i 0.343166 1.11612i
\(426\) −26.7474 2.83942i −1.29591 0.137570i
\(427\) −1.27927 1.27927i −0.0619081 0.0619081i
\(428\) 8.61306 + 8.61306i 0.416328 + 0.416328i
\(429\) −14.9019 1.58193i −0.719468 0.0763764i
\(430\) 25.1447 6.24814i 1.21259 0.301312i
\(431\) 8.30157i 0.399873i −0.979809 0.199936i \(-0.935926\pi\)
0.979809 0.199936i \(-0.0640735\pi\)
\(432\) 2.34453 + 4.63715i 0.112801 + 0.223105i
\(433\) −10.8163 + 10.8163i −0.519799 + 0.519799i −0.917510 0.397712i \(-0.869804\pi\)
0.397712 + 0.917510i \(0.369804\pi\)
\(434\) 15.8800 0.762266
\(435\) −19.1844 14.5117i −0.919824 0.695784i
\(436\) 6.32736 0.303025
\(437\) 2.00597 2.00597i 0.0959587 0.0959587i
\(438\) −9.80248 12.1309i −0.468381 0.579635i
\(439\) 17.0396i 0.813258i −0.913593 0.406629i \(-0.866704\pi\)
0.913593 0.406629i \(-0.133296\pi\)
\(440\) −8.81683 5.30719i −0.420326 0.253010i
\(441\) 27.7273 + 5.95397i 1.32035 + 0.283522i
\(442\) −6.39999 6.39999i −0.304416 0.304416i
\(443\) −25.4820 25.4820i −1.21069 1.21069i −0.970802 0.239884i \(-0.922891\pi\)
−0.239884 0.970802i \(-0.577109\pi\)
\(444\) −1.10819 + 10.4392i −0.0525924 + 0.495422i
\(445\) 1.11823 + 4.50014i 0.0530090 + 0.213327i
\(446\) 14.3154i 0.677856i
\(447\) −7.53441 + 6.08827i −0.356365 + 0.287965i
\(448\) −2.86820 + 2.86820i −0.135510 + 0.135510i
\(449\) 7.40137 0.349292 0.174646 0.984631i \(-0.444122\pi\)
0.174646 + 0.984631i \(0.444122\pi\)
\(450\) −13.0926 7.32018i −0.617189 0.345077i
\(451\) −8.01901 −0.377600
\(452\) 0.984759 0.984759i 0.0463192 0.0463192i
\(453\) −6.22588 + 5.03090i −0.292517 + 0.236372i
\(454\) 19.4529i 0.912969i
\(455\) −4.11194 16.5479i −0.192771 0.775778i
\(456\) 0.182842 1.72237i 0.00856234 0.0806575i
\(457\) 14.6959 + 14.6959i 0.687447 + 0.687447i 0.961667 0.274220i \(-0.0884196\pi\)
−0.274220 + 0.961667i \(0.588420\pi\)
\(458\) 4.57533 + 4.57533i 0.213791 + 0.213791i
\(459\) 23.7681 + 7.80487i 1.10940 + 0.364300i
\(460\) −5.43480 3.27142i −0.253399 0.152531i
\(461\) 37.8041i 1.76071i −0.474314 0.880356i \(-0.657304\pi\)
0.474314 0.880356i \(-0.342696\pi\)
\(462\) 20.3220 + 25.1490i 0.945464 + 1.17004i
\(463\) −0.789669 + 0.789669i −0.0366990 + 0.0366990i −0.725218 0.688519i \(-0.758261\pi\)
0.688519 + 0.725218i \(0.258261\pi\)
\(464\) −6.21092 −0.288335
\(465\) 12.0926 + 9.14725i 0.560782 + 0.424193i
\(466\) −5.66392 −0.262376
\(467\) −28.1504 + 28.1504i −1.30265 + 1.30265i −0.376045 + 0.926601i \(0.622716\pi\)
−0.926601 + 0.376045i \(0.877284\pi\)
\(468\) −4.73634 + 3.06182i −0.218938 + 0.141533i
\(469\) 36.0226i 1.66337i
\(470\) 16.0271 3.98254i 0.739277 0.183701i
\(471\) −25.1070 2.66528i −1.15687 0.122809i
\(472\) −3.59703 3.59703i −0.165567 0.165567i
\(473\) −37.7073 37.7073i −1.73378 1.73378i
\(474\) 17.9900 + 1.90976i 0.826308 + 0.0877182i
\(475\) 2.34036 + 4.41845i 0.107383 + 0.202732i
\(476\) 19.5287i 0.895097i
\(477\) 17.6781 11.4280i 0.809423 0.523253i
\(478\) 1.39191 1.39191i 0.0636643 0.0636643i
\(479\) −23.0077 −1.05125 −0.525624 0.850717i \(-0.676168\pi\)
−0.525624 + 0.850717i \(0.676168\pi\)
\(480\) −3.83627 + 0.531985i −0.175101 + 0.0242817i
\(481\) −11.3942 −0.519532
\(482\) −16.9005 + 16.9005i −0.769794 + 0.769794i
\(483\) 12.5267 + 15.5022i 0.569986 + 0.705374i
\(484\) 10.1805i 0.462752i
\(485\) 20.3977 33.8867i 0.926213 1.53872i
\(486\) 7.86438 13.4593i 0.356736 0.610524i
\(487\) 20.5042 + 20.5042i 0.929134 + 0.929134i 0.997650 0.0685156i \(-0.0218263\pi\)
−0.0685156 + 0.997650i \(0.521826\pi\)
\(488\) −0.315382 0.315382i −0.0142767 0.0142767i
\(489\) −2.86459 + 26.9845i −0.129541 + 1.22028i
\(490\) −10.9011 + 18.1100i −0.492462 + 0.818126i
\(491\) 16.9198i 0.763581i −0.924249 0.381791i \(-0.875308\pi\)
0.924249 0.381791i \(-0.124692\pi\)
\(492\) −2.34737 + 1.89682i −0.105827 + 0.0855152i
\(493\) −21.1442 + 21.1442i −0.952285 + 0.952285i
\(494\) 1.87994 0.0845826
\(495\) 0.988774 + 30.8569i 0.0444421 + 1.38691i
\(496\) 3.91496 0.175787
\(497\) −44.5413 + 44.5413i −1.99795 + 1.99795i
\(498\) 7.38866 5.97050i 0.331094 0.267544i
\(499\) 26.0020i 1.16401i −0.813185 0.582005i \(-0.802268\pi\)
0.813185 0.582005i \(-0.197732\pi\)
\(500\) 8.32636 7.46135i 0.372366 0.333682i
\(501\) 1.03531 9.75267i 0.0462543 0.435717i
\(502\) 4.48724 + 4.48724i 0.200275 + 0.200275i
\(503\) 3.80551 + 3.80551i 0.169679 + 0.169679i 0.786838 0.617159i \(-0.211716\pi\)
−0.617159 + 0.786838i \(0.711716\pi\)
\(504\) 11.8975 + 2.55479i 0.529958 + 0.113800i
\(505\) 4.02407 0.999929i 0.179069 0.0444963i
\(506\) 13.0560i 0.580408i
\(507\) 10.3046 + 12.7523i 0.457644 + 0.566347i
\(508\) 8.32109 8.32109i 0.369189 0.369189i
\(509\) −7.97379 −0.353432 −0.176716 0.984262i \(-0.556547\pi\)
−0.176716 + 0.984262i \(0.556547\pi\)
\(510\) −11.2490 + 14.8711i −0.498112 + 0.658503i
\(511\) −36.5247 −1.61576
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −4.63715 + 2.34453i −0.204735 + 0.103514i
\(514\) 4.60160i 0.202968i
\(515\) 31.0488 + 18.6895i 1.36817 + 0.823557i
\(516\) −19.9572 2.11859i −0.878567 0.0932658i
\(517\) −24.0345 24.0345i −1.05704 1.05704i
\(518\) 17.3840 + 17.3840i 0.763808 + 0.763808i
\(519\) 19.9549 + 2.11834i 0.875921 + 0.0929849i
\(520\) −1.01373 4.07962i −0.0444551 0.178903i
\(521\) 21.6995i 0.950673i −0.879804 0.475336i \(-0.842326\pi\)
0.879804 0.475336i \(-0.157674\pi\)
\(522\) 10.1156 + 15.6478i 0.442747 + 0.684887i
\(523\) −24.3202 + 24.3202i −1.06345 + 1.06345i −0.0656023 + 0.997846i \(0.520897\pi\)
−0.997846 + 0.0656023i \(0.979103\pi\)
\(524\) 18.6781 0.815955
\(525\) −32.6046 + 13.0737i −1.42298 + 0.570583i
\(526\) 28.6668 1.24993
\(527\) 13.3279 13.3279i 0.580573 0.580573i
\(528\) 5.01005 + 6.20008i 0.218034 + 0.269824i
\(529\) 14.9521i 0.650093i
\(530\) 3.78368 + 15.2269i 0.164353 + 0.661414i
\(531\) −3.20399 + 14.9208i −0.139041 + 0.647507i
\(532\) −2.86820 2.86820i −0.124352 0.124352i
\(533\) −2.31623 2.31623i −0.100327 0.100327i
\(534\) 0.379163 3.57173i 0.0164080 0.154564i
\(535\) 23.3355 + 14.0465i 1.00888 + 0.607284i
\(536\) 8.88078i 0.383591i
\(537\) −8.05292 + 6.50726i −0.347509 + 0.280809i
\(538\) −11.9535 + 11.9535i −0.515354 + 0.515354i
\(539\) 43.5054 1.87391
\(540\) 7.58833 + 8.79871i 0.326550 + 0.378636i
\(541\) −14.0695 −0.604893 −0.302447 0.953166i \(-0.597803\pi\)
−0.302447 + 0.953166i \(0.597803\pi\)
\(542\) 2.07700 2.07700i 0.0892149 0.0892149i
\(543\) 11.4186 9.22694i 0.490019 0.395966i
\(544\) 4.81448i 0.206419i
\(545\) 13.7308 3.41194i 0.588164 0.146151i
\(546\) −1.39426 + 13.1340i −0.0596688 + 0.562082i
\(547\) 13.8517 + 13.8517i 0.592256 + 0.592256i 0.938240 0.345984i \(-0.112455\pi\)
−0.345984 + 0.938240i \(0.612455\pi\)
\(548\) −14.3208 14.3208i −0.611756 0.611756i
\(549\) −0.280921 + 1.30823i −0.0119894 + 0.0558340i
\(550\) −21.9950 6.76265i −0.937870 0.288361i
\(551\) 6.21092i 0.264594i
\(552\) 3.08826 + 3.82181i 0.131445 + 0.162667i
\(553\) 29.9580 29.9580i 1.27394 1.27394i
\(554\) 5.71150 0.242659
\(555\) 3.22433 + 23.2514i 0.136865 + 0.986968i
\(556\) 11.2626 0.477642
\(557\) 15.4865 15.4865i 0.656182 0.656182i −0.298292 0.954475i \(-0.596417\pi\)
0.954475 + 0.298292i \(0.0964170\pi\)
\(558\) −6.37620 9.86338i −0.269926 0.417550i
\(559\) 21.7830i 0.921321i
\(560\) −4.67757 + 7.77084i −0.197663 + 0.328378i
\(561\) 38.1632 + 4.05129i 1.61125 + 0.171045i
\(562\) −9.96149 9.96149i −0.420200 0.420200i
\(563\) 21.7376 + 21.7376i 0.916131 + 0.916131i 0.996745 0.0806140i \(-0.0256881\pi\)
−0.0806140 + 0.996745i \(0.525688\pi\)
\(564\) −12.7206 1.35038i −0.535635 0.0568613i
\(565\) 1.60598 2.66802i 0.0675642 0.112244i
\(566\) 21.3107i 0.895756i
\(567\) −12.9406 34.1356i −0.543456 1.43356i
\(568\) −10.9809 + 10.9809i −0.460750 + 0.460750i
\(569\) 33.8572 1.41937 0.709684 0.704520i \(-0.248838\pi\)
0.709684 + 0.704520i \(0.248838\pi\)
\(570\) −0.531985 3.83627i −0.0222824 0.160684i
\(571\) −10.2627 −0.429480 −0.214740 0.976671i \(-0.568890\pi\)
−0.214740 + 0.976671i \(0.568890\pi\)
\(572\) −6.11784 + 6.11784i −0.255800 + 0.255800i
\(573\) −7.02960 8.69933i −0.293666 0.363420i
\(574\) 7.06767i 0.294999i
\(575\) −13.5580 4.16859i −0.565408 0.173842i
\(576\) 2.93314 + 0.629843i 0.122214 + 0.0262434i
\(577\) −13.9733 13.9733i −0.581717 0.581717i 0.353658 0.935375i \(-0.384938\pi\)
−0.935375 + 0.353658i \(0.884938\pi\)
\(578\) 4.36937 + 4.36937i 0.181742 + 0.181742i
\(579\) 1.11899 10.5409i 0.0465036 0.438066i
\(580\) −13.4782 + 3.34915i −0.559650 + 0.139066i
\(581\) 22.2465i 0.922939i
\(582\) −23.8295 + 19.2557i −0.987763 + 0.798174i
\(583\) 22.8344 22.8344i 0.945705 0.945705i
\(584\) −9.00456 −0.372611
\(585\) −8.62718 + 9.19838i −0.356690 + 0.380306i
\(586\) 6.96364 0.287665
\(587\) −22.9650 + 22.9650i −0.947869 + 0.947869i −0.998707 0.0508382i \(-0.983811\pi\)
0.0508382 + 0.998707i \(0.483811\pi\)
\(588\) 12.7351 10.2908i 0.525188 0.424385i
\(589\) 3.91496i 0.161313i
\(590\) −9.74548 5.86618i −0.401215 0.241507i
\(591\) 3.84508 36.2208i 0.158166 1.48992i
\(592\) 4.28573 + 4.28573i 0.176142 + 0.176142i
\(593\) −2.14305 2.14305i −0.0880044 0.0880044i 0.661734 0.749739i \(-0.269821\pi\)
−0.749739 + 0.661734i \(0.769821\pi\)
\(594\) 7.46079 22.7203i 0.306120 0.932224i
\(595\) 10.5306 + 42.3788i 0.431711 + 1.73736i
\(596\) 5.59268i 0.229085i
\(597\) −0.859707 1.06391i −0.0351855 0.0435430i
\(598\) −3.77111 + 3.77111i −0.154212 + 0.154212i
\(599\) −28.0055 −1.14427 −0.572137 0.820158i \(-0.693885\pi\)
−0.572137 + 0.820158i \(0.693885\pi\)
\(600\) −8.03813 + 3.22310i −0.328155 + 0.131583i
\(601\) −10.4827 −0.427599 −0.213800 0.976878i \(-0.568584\pi\)
−0.213800 + 0.976878i \(0.568584\pi\)
\(602\) −33.2339 + 33.2339i −1.35451 + 1.35451i
\(603\) 22.3743 14.4639i 0.911152 0.589016i
\(604\) 4.62138i 0.188041i
\(605\) 5.48971 + 22.0925i 0.223188 + 0.898189i
\(606\) −3.19387 0.339051i −0.129742 0.0137730i
\(607\) −25.3869 25.3869i −1.03042 1.03042i −0.999522 0.0308996i \(-0.990163\pi\)
−0.0308996 0.999522i \(-0.509837\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) 43.3918 + 4.60633i 1.75832 + 0.186658i
\(610\) −0.854469 0.514338i −0.0345964 0.0208249i
\(611\) 13.8844i 0.561701i
\(612\) 12.1296 7.84123i 0.490312 0.316963i
\(613\) −3.65006 + 3.65006i −0.147425 + 0.147425i −0.776967 0.629542i \(-0.783243\pi\)
0.629542 + 0.776967i \(0.283243\pi\)
\(614\) 10.4815 0.422998
\(615\) −4.07113 + 5.38202i −0.164164 + 0.217024i
\(616\) 18.6678 0.752146
\(617\) 25.7417 25.7417i 1.03632 1.03632i 0.0370077 0.999315i \(-0.488217\pi\)
0.999315 0.0370077i \(-0.0117826\pi\)
\(618\) −17.6431 21.8338i −0.709709 0.878286i
\(619\) 26.4712i 1.06397i −0.846755 0.531984i \(-0.821447\pi\)
0.846755 0.531984i \(-0.178553\pi\)
\(620\) 8.49576 2.11109i 0.341198 0.0847833i
\(621\) 4.59892 14.0051i 0.184548 0.562004i
\(622\) −15.9848 15.9848i −0.640931 0.640931i
\(623\) −5.94785 5.94785i −0.238296 0.238296i
\(624\) −0.343732 + 3.23796i −0.0137603 + 0.129622i
\(625\) 14.0454 20.6816i 0.561816 0.827262i
\(626\) 24.9804i 0.998419i
\(627\) −6.20008 + 5.01005i −0.247607 + 0.200082i
\(628\) −10.3075 + 10.3075i −0.411313 + 0.411313i
\(629\) 29.1803 1.16349
\(630\) 27.1961 0.871471i 1.08352 0.0347202i
\(631\) −0.953154 −0.0379445 −0.0189722 0.999820i \(-0.506039\pi\)
−0.0189722 + 0.999820i \(0.506039\pi\)
\(632\) 7.38565 7.38565i 0.293786 0.293786i
\(633\) −26.7668 + 21.6292i −1.06388 + 0.859683i
\(634\) 0.873774i 0.0347020i
\(635\) 13.5704 22.5444i 0.538524 0.894648i
\(636\) 1.28295 12.0855i 0.0508724 0.479220i
\(637\) 12.5662 + 12.5662i 0.497891 + 0.497891i
\(638\) 20.2120 + 20.2120i 0.800201 + 0.800201i
\(639\) 45.5498 + 9.78106i 1.80192 + 0.386933i
\(640\) −1.15318 + 1.91577i −0.0455833 + 0.0757275i
\(641\) 9.36570i 0.369923i 0.982746 + 0.184961i \(0.0592160\pi\)
−0.982746 + 0.184961i \(0.940784\pi\)
\(642\) −13.2601 16.4097i −0.523334 0.647640i
\(643\) −21.9899 + 21.9899i −0.867197 + 0.867197i −0.992161 0.124964i \(-0.960118\pi\)
0.124964 + 0.992161i \(0.460118\pi\)
\(644\) 11.5071 0.453441
\(645\) −44.4510 + 6.16413i −1.75026 + 0.242712i
\(646\) −4.81448 −0.189423
\(647\) −6.75416 + 6.75416i −0.265533 + 0.265533i −0.827297 0.561764i \(-0.810123\pi\)
0.561764 + 0.827297i \(0.310123\pi\)
\(648\) −3.19030 8.41558i −0.125327 0.330595i
\(649\) 23.4114i 0.918979i
\(650\) −4.39975 8.30643i −0.172572 0.325805i
\(651\) −27.3513 2.90353i −1.07198 0.113798i
\(652\) 11.0783 + 11.0783i 0.433859 + 0.433859i
\(653\) 13.6366 + 13.6366i 0.533643 + 0.533643i 0.921655 0.388011i \(-0.126838\pi\)
−0.388011 + 0.921655i \(0.626838\pi\)
\(654\) −10.8981 1.15690i −0.426148 0.0452385i
\(655\) 40.5328 10.0719i 1.58375 0.393541i
\(656\) 1.74242i 0.0680300i
\(657\) 14.6655 + 22.6862i 0.572156 + 0.885071i
\(658\) −21.1831 + 21.1831i −0.825805 + 0.825805i
\(659\) 10.2941 0.401002 0.200501 0.979694i \(-0.435743\pi\)
0.200501 + 0.979694i \(0.435743\pi\)
\(660\) 14.2155 + 10.7530i 0.553337 + 0.418562i
\(661\) 3.04994 0.118629 0.0593145 0.998239i \(-0.481109\pi\)
0.0593145 + 0.998239i \(0.481109\pi\)
\(662\) −11.8631 + 11.8631i −0.461071 + 0.461071i
\(663\) 9.85298 + 12.1933i 0.382658 + 0.473550i
\(664\) 5.48450i 0.212840i
\(665\) −7.77084 4.67757i −0.301340 0.181388i
\(666\) 3.81744 17.7776i 0.147923 0.688867i
\(667\) 12.4589 + 12.4589i 0.482412 + 0.482412i
\(668\) −4.00388 4.00388i −0.154915 0.154915i
\(669\) 2.61746 24.6565i 0.101197 0.953277i
\(670\) 4.78883 + 19.2720i 0.185009 + 0.744541i
\(671\) 2.05268i 0.0792427i
\(672\) 5.46453 4.41568i 0.210799 0.170339i
\(673\) 2.16629 2.16629i 0.0835045 0.0835045i −0.664121 0.747625i \(-0.731194\pi\)
0.747625 + 0.664121i \(0.231194\pi\)
\(674\) −27.3141 −1.05210
\(675\) 21.2118 + 15.0020i 0.816444 + 0.577425i
\(676\) 9.46581 0.364070
\(677\) 6.41647 6.41647i 0.246605 0.246605i −0.572971 0.819576i \(-0.694209\pi\)
0.819576 + 0.572971i \(0.194209\pi\)
\(678\) −1.87618 + 1.51607i −0.0720541 + 0.0582242i
\(679\) 71.7479i 2.75343i
\(680\) 2.59614 + 10.4478i 0.0995574 + 0.400654i
\(681\) −3.55679 + 33.5051i −0.136297 + 1.28392i
\(682\) −12.7403 12.7403i −0.487853 0.487853i
\(683\) −19.7954 19.7954i −0.757448 0.757448i 0.218409 0.975857i \(-0.429913\pi\)
−0.975857 + 0.218409i \(0.929913\pi\)
\(684\) −0.629843 + 2.93314i −0.0240826 + 0.112151i
\(685\) −38.7996 23.3550i −1.48246 0.892348i
\(686\) 9.95041i 0.379908i
\(687\) −7.04387 8.71699i −0.268740 0.332574i
\(688\) −8.19327 + 8.19327i −0.312366 + 0.312366i
\(689\) 13.1911 0.502541
\(690\) 8.76261 + 6.62831i 0.333587 + 0.252336i
\(691\) 7.17293 0.272871 0.136436 0.990649i \(-0.456435\pi\)
0.136436 + 0.990649i \(0.456435\pi\)
\(692\) 8.19231 8.19231i 0.311425 0.311425i
\(693\) −30.4037 47.0317i −1.15494 1.78659i
\(694\) 29.5246i 1.12074i
\(695\) 24.4407 6.07321i 0.927090 0.230370i
\(696\) 10.6975 + 1.13561i 0.405489 + 0.0430453i
\(697\) 5.93180 + 5.93180i 0.224683 + 0.224683i
\(698\) 7.98584 + 7.98584i 0.302269 + 0.302269i
\(699\) 9.75538 + 1.03560i 0.368982 + 0.0391700i
\(700\) −5.96036 + 19.3856i −0.225281 + 0.732707i
\(701\) 28.7624i 1.08634i −0.839623 0.543170i \(-0.817224\pi\)
0.839623 0.543170i \(-0.182776\pi\)
\(702\) 8.71758 4.40759i 0.329024 0.166354i
\(703\) −4.28573 + 4.28573i −0.161639 + 0.161639i
\(704\) 4.60223 0.173453
\(705\) −28.3329 + 3.92899i −1.06708 + 0.147974i
\(706\) −1.02329 −0.0385121
\(707\) −5.31863 + 5.31863i −0.200028 + 0.200028i
\(708\) 5.53775 + 6.85312i 0.208121 + 0.257556i
\(709\) 15.0208i 0.564119i −0.959397 0.282060i \(-0.908982\pi\)
0.959397 0.282060i \(-0.0910176\pi\)
\(710\) −17.9081 + 29.7507i −0.672080 + 1.11653i
\(711\) −30.6363 6.57864i −1.14895 0.246718i
\(712\) −1.46635 1.46635i −0.0549536 0.0549536i
\(713\) −7.85331 7.85331i −0.294109 0.294109i
\(714\) 3.57066 33.6357i 0.133629 1.25879i
\(715\) −9.97721 + 16.5751i −0.373127 + 0.619875i
\(716\) 5.97757i 0.223392i
\(717\) −2.65188 + 2.14288i −0.0990362 + 0.0800274i
\(718\) 17.9890 17.9890i 0.671345 0.671345i
\(719\) −0.237709 −0.00886505 −0.00443253 0.999990i \(-0.501411\pi\)
−0.00443253 + 0.999990i \(0.501411\pi\)
\(720\) 6.70476 0.214847i 0.249872 0.00800686i
\(721\) −65.7393 −2.44826
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) 32.1990 26.0188i 1.19749 0.967649i
\(724\) 8.47586i 0.315003i
\(725\) −27.4426 + 14.5358i −1.01919 + 0.539846i
\(726\) 1.86143 17.5347i 0.0690840 0.650773i
\(727\) 29.5991 + 29.5991i 1.09777 + 1.09777i 0.994671 + 0.103098i \(0.0328754\pi\)
0.103098 + 0.994671i \(0.467125\pi\)
\(728\) 5.39205 + 5.39205i 0.199843 + 0.199843i
\(729\) −16.0063 + 21.7439i −0.592826 + 0.805330i
\(730\) −19.5406 + 4.85558i −0.723229 + 0.179713i
\(731\) 55.7856i 2.06330i
\(732\) 0.485541 + 0.600871i 0.0179461 + 0.0222088i
\(733\) 20.2570 20.2570i 0.748209 0.748209i −0.225933 0.974143i \(-0.572543\pi\)
0.974143 + 0.225933i \(0.0725432\pi\)
\(734\) −19.8748 −0.733593
\(735\) 22.0870 29.1990i 0.814693 1.07702i
\(736\) 2.83687 0.104569
\(737\) 28.9005 28.9005i 1.06456 1.06456i
\(738\) 4.38986 2.83783i 0.161593 0.104462i
\(739\) 48.1026i 1.76948i −0.466081 0.884742i \(-0.654334\pi\)
0.466081 0.884742i \(-0.345666\pi\)
\(740\) 11.6114 + 6.98934i 0.426843 + 0.256933i
\(741\) −3.23796 0.343732i −0.118950 0.0126273i
\(742\) −20.1254 20.1254i −0.738828 0.738828i
\(743\) −32.7093 32.7093i −1.19999 1.19999i −0.974170 0.225817i \(-0.927495\pi\)
−0.225817 0.974170i \(-0.572505\pi\)
\(744\) −6.74302 0.715817i −0.247211 0.0262431i
\(745\) 3.01577 + 12.1365i 0.110489 + 0.444648i
\(746\) 7.81442i 0.286106i
\(747\) −13.8177 + 8.93247i −0.505563 + 0.326822i
\(748\) 15.6676 15.6676i 0.572865 0.572865i
\(749\) −49.4079 −1.80533
\(750\) −15.7053 + 11.3288i −0.573478 + 0.413670i
\(751\) 20.7531 0.757292 0.378646 0.925542i \(-0.376390\pi\)
0.378646 + 0.925542i \(0.376390\pi\)
\(752\) −5.22236 + 5.22236i −0.190440 + 0.190440i
\(753\) −6.90825 8.54916i −0.251751 0.311549i
\(754\) 11.6762i 0.425221i
\(755\) 2.49201 + 10.0287i 0.0906937 + 0.364983i
\(756\) −20.0248 6.57567i −0.728297 0.239155i
\(757\) 36.1673 + 36.1673i 1.31452 + 1.31452i 0.918045 + 0.396477i \(0.129767\pi\)
0.396477 + 0.918045i \(0.370233\pi\)
\(758\) 5.79549 + 5.79549i 0.210502 + 0.210502i
\(759\) 2.38717 22.4872i 0.0866488 0.816234i
\(760\) −1.91577 1.15318i −0.0694923 0.0418301i
\(761\) 20.2602i 0.734432i −0.930136 0.367216i \(-0.880311\pi\)
0.930136 0.367216i \(-0.119689\pi\)
\(762\) −15.8535 + 12.8106i −0.574311 + 0.464079i
\(763\) −18.1481 + 18.1481i −0.657006 + 0.657006i
\(764\) −6.45739 −0.233620
\(765\) 22.0940 23.5568i 0.798809 0.851697i
\(766\) −16.4922 −0.595886
\(767\) −6.76222 + 6.76222i −0.244170 + 0.244170i
\(768\) 1.34719 1.08861i 0.0486125 0.0392819i
\(769\) 10.8266i 0.390416i −0.980762 0.195208i \(-0.937462\pi\)
0.980762 0.195208i \(-0.0625382\pi\)
\(770\) 40.5105 10.0663i 1.45990 0.362765i
\(771\) −0.841363 + 7.92567i −0.0303010 + 0.285436i
\(772\) −4.32749 4.32749i −0.155750 0.155750i
\(773\) −15.4031 15.4031i −0.554011 0.554011i 0.373585 0.927596i \(-0.378128\pi\)
−0.927596 + 0.373585i \(0.878128\pi\)
\(774\) 33.9864 + 7.29801i 1.22161 + 0.262321i
\(775\) 17.2981 9.16243i 0.621365 0.329124i
\(776\) 17.6883i 0.634972i
\(777\) −26.7632 33.1202i −0.960123 1.18818i
\(778\)