Properties

Label 570.2.k.b.77.15
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 77.15
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.15

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(1.08861 - 1.34719i) q^{3} -1.00000i q^{4} +(0.539236 + 2.17007i) q^{5} +(-0.182842 - 1.72237i) q^{6} +(2.86820 + 2.86820i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-0.629843 - 2.93314i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(1.08861 - 1.34719i) 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} +(-1.34719 - 1.08861i) q^{12} +(1.32932 - 1.32932i) q^{13} +4.05624 q^{14} +(3.51052 + 1.63592i) q^{15} -1.00000 q^{16} +(3.40435 - 3.40435i) q^{17} +(-2.51941 - 1.62868i) 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} +(-4.63715 - 2.34453i) q^{27} +(2.86820 - 2.86820i) q^{28} -6.21092 q^{29} +(3.63908 - 1.32554i) q^{30} -3.91496 q^{31} +(-0.707107 + 0.707107i) q^{32} +(6.20008 + 5.01005i) 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} +(4.41568 - 5.46453i) q^{42} +(8.19327 - 8.19327i) q^{43} +4.60223 q^{44} +(6.02550 - 2.94846i) q^{45} -2.83687 q^{46} +(-5.22236 + 5.22236i) q^{47} +(-1.08861 + 1.34719i) 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} +(-1.34719 - 1.08861i) q^{57} +(-4.39178 + 4.39178i) q^{58} +5.08697 q^{59} +(1.63592 - 3.51052i) q^{60} -0.446018 q^{61} +(-2.76830 + 2.76830i) q^{62} +(6.60631 - 10.2193i) 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} +(-1.62868 + 2.51941i) q^{72} +(-6.36719 + 6.36719i) q^{73} -6.06094 q^{74} +(-1.65707 + 8.50024i) q^{75} -1.00000 q^{76} +(-13.2001 + 13.2001i) q^{77} +(-2.53264 - 2.04653i) 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} +(-6.76129 + 8.36729i) q^{87} +(3.25427 - 3.25427i) q^{88} +2.07373 q^{89} +(2.17579 - 6.34554i) q^{90} +7.62551 q^{91} +(-2.00597 + 2.00597i) q^{92} +(-4.26188 + 5.27420i) 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
\(3\) 1.08861 1.34719i 0.628511 0.777801i
\(4\) 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 \(0.244070\pi\)
−0.720156 + 0.693813i \(0.755930\pi\)
\(12\) −1.34719 1.08861i −0.388900 0.314256i
\(13\) 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
\(15\) 3.51052 + 1.63592i 0.906413 + 0.422393i
\(16\) −1.00000 −0.250000
\(17\) 3.40435 3.40435i 0.825677 0.825677i −0.161239 0.986915i \(-0.551549\pi\)
0.986915 + 0.161239i \(0.0515489\pi\)
\(18\) −2.51941 1.62868i −0.593830 0.383883i
\(19\) 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 0.466334 0.884609i \(-0.345574\pi\)
−0.884609 + 0.466334i \(0.845574\pi\)
\(24\) −1.72237 + 0.182842i −0.351578 + 0.0373224i
\(25\) −4.41845 + 2.34036i −0.883690 + 0.468073i
\(26\) 1.87994i 0.368687i
\(27\) −4.63715 2.34453i −0.892420 0.451206i
\(28\) 2.86820 2.86820i 0.542038 0.542038i
\(29\) −6.21092 −1.15334 −0.576670 0.816978i \(-0.695648\pi\)
−0.576670 + 0.816978i \(0.695648\pi\)
\(30\) 3.63908 1.32554i 0.664403 0.242010i
\(31\) −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
\(33\) 6.20008 + 5.01005i 1.07930 + 0.872138i
\(34\) 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 \(0.0434440\pi\)
−0.990701 + 0.136060i \(0.956556\pi\)
\(42\) 4.41568 5.46453i 0.681354 0.843195i
\(43\) 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
\(45\) 6.02550 2.94846i 0.898228 0.439530i
\(46\) −2.83687 −0.418274
\(47\) −5.22236 + 5.22236i −0.761759 + 0.761759i −0.976640 0.214881i \(-0.931064\pi\)
0.214881 + 0.976640i \(0.431064\pi\)
\(48\) −1.08861 + 1.34719i −0.157128 + 0.194450i
\(49\) 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 0.278817 0.960344i \(-0.410058\pi\)
−0.960344 + 0.278817i \(0.910058\pi\)
\(54\) −4.93680 + 1.62112i −0.671813 + 0.220607i
\(55\) −9.98719 + 2.48169i −1.34667 + 0.334631i
\(56\) 4.05624i 0.542038i
\(57\) −1.34719 1.08861i −0.178440 0.144190i
\(58\) −4.39178 + 4.39178i −0.576670 + 0.576670i
\(59\) 5.08697 0.662268 0.331134 0.943584i \(-0.392569\pi\)
0.331134 + 0.943584i \(0.392569\pi\)
\(60\) 1.63592 3.51052i 0.211196 0.453207i
\(61\) −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
\(63\) 6.60631 10.2193i 0.832316 1.28751i
\(64\) 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 \(-0.626965\pi\)
0.388380 0.921499i \(-0.373035\pi\)
\(72\) −1.62868 + 2.51941i −0.191941 + 0.296915i
\(73\) −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
\(75\) −1.65707 + 8.50024i −0.191342 + 0.981523i
\(76\) −1.00000 −0.114708
\(77\) −13.2001 + 13.2001i −1.50429 + 1.50429i
\(78\) −2.53264 2.04653i −0.286765 0.231724i
\(79\) 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 0.887154 0.461474i \(-0.152679\pi\)
−0.461474 + 0.887154i \(0.652679\pi\)
\(84\) −0.741650 6.98636i −0.0809206 0.762275i
\(85\) 9.22345 + 5.55195i 1.00042 + 0.602194i
\(86\) 11.5870i 1.24946i
\(87\) −6.76129 + 8.36729i −0.724886 + 0.897068i
\(88\) 3.25427 3.25427i 0.346906 0.346906i
\(89\) 2.07373 0.219814 0.109907 0.993942i \(-0.464945\pi\)
0.109907 + 0.993942i \(0.464945\pi\)
\(90\) 2.17579 6.34554i 0.229349 0.668879i
\(91\) 7.62551 0.799370
\(92\) −2.00597 + 2.00597i −0.209137 + 0.209137i
\(93\) −4.26188 + 5.27420i −0.441936 + 0.546909i
\(94\) 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 \(-0.970592\pi\)
0.995735 0.0922571i \(-0.0294082\pi\)
\(102\) −6.48602 5.24111i −0.642212 0.518947i
\(103\) −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
\(105\) 5.37673 + 14.7610i 0.524715 + 1.44053i
\(106\) −7.01675 −0.681527
\(107\) 8.61306 8.61306i 0.832656 0.832656i −0.155223 0.987879i \(-0.549610\pi\)
0.987879 + 0.155223i \(0.0496097\pi\)
\(108\) −2.34453 + 4.63715i −0.225603 + 0.446210i
\(109\) 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 0.659269 0.751907i \(-0.270866\pi\)
−0.751907 + 0.659269i \(0.770866\pi\)
\(114\) −1.72237 + 0.182842i −0.161315 + 0.0171247i
\(115\) 3.27142 5.43480i 0.305061 0.506798i
\(116\) 6.21092i 0.576670i
\(117\) −4.73634 3.06182i −0.437875 0.283065i
\(118\) 3.59703 3.59703i 0.331134 0.331134i
\(119\) 19.5287 1.79019
\(120\) −1.32554 3.63908i −0.121005 0.332201i
\(121\) −10.1805 −0.925503
\(122\) −0.315382 + 0.315382i −0.0285534 + 0.0285534i
\(123\) 2.34737 + 1.89682i 0.211655 + 0.171030i
\(124\) 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 \(-0.696211\pi\)
0.578115 0.815955i \(-0.303789\pi\)
\(132\) 5.01005 6.20008i 0.436069 0.539648i
\(133\) 2.86820 2.86820i 0.248704 0.248704i
\(134\) 8.88078 0.767183
\(135\) 2.58730 11.3272i 0.222679 0.974892i
\(136\) −4.81448 −0.412838
\(137\) −14.3208 + 14.3208i −1.22351 + 1.22351i −0.257137 + 0.966375i \(0.582779\pi\)
−0.966375 + 0.257137i \(0.917221\pi\)
\(138\) −3.08826 + 3.82181i −0.262890 + 0.325334i
\(139\) 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
\(147\) 12.7351 + 10.2908i 1.05038 + 0.848769i
\(148\) −4.28573 + 4.28573i −0.352285 + 0.352285i
\(149\) 5.59268 0.458170 0.229085 0.973406i \(-0.426427\pi\)
0.229085 + 0.973406i \(0.426427\pi\)
\(150\) 4.83885 + 7.18230i 0.395091 + 0.586433i
\(151\) −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
\(153\) −12.1296 7.84123i −0.980623 0.633926i
\(154\) 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
\(162\) −3.19030 + 8.41558i −0.250654 + 0.661190i
\(163\) −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
\(165\) −7.52888 + 16.1562i −0.586122 + 1.25776i
\(166\) 5.48450 0.425680
\(167\) −4.00388 + 4.00388i −0.309830 + 0.309830i −0.844843 0.535014i \(-0.820306\pi\)
0.535014 + 0.844843i \(0.320306\pi\)
\(168\) −5.46453 4.41568i −0.421598 0.340677i
\(169\) 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 0.323409 0.946259i \(-0.395171\pi\)
−0.946259 + 0.323409i \(0.895171\pi\)
\(174\) 1.13561 + 10.6975i 0.0860907 + 0.810977i
\(175\) −19.3856 5.96036i −1.46541 0.450561i
\(176\) 4.60223i 0.346906i
\(177\) 5.53775 6.85312i 0.416243 0.515112i
\(178\) 1.46635 1.46635i 0.109907 0.109907i
\(179\) 5.97757 0.446784 0.223392 0.974729i \(-0.428287\pi\)
0.223392 + 0.974729i \(0.428287\pi\)
\(180\) −2.94846 6.02550i −0.219765 0.449114i
\(181\) 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
\(183\) −0.485541 + 0.600871i −0.0358922 + 0.0444177i
\(184\) 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 \(0.0750572\pi\)
−0.972328 + 0.233620i \(0.924943\pi\)
\(192\) 1.34719 + 1.08861i 0.0972251 + 0.0785639i
\(193\) 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
\(195\) 6.84127 2.49195i 0.489914 0.178452i
\(196\) 9.45311 0.675222
\(197\) −14.8702 + 14.8702i −1.05946 + 1.05946i −0.0613383 + 0.998117i \(0.519537\pi\)
−0.998117 + 0.0613383i \(0.980463\pi\)
\(198\) 7.49554 11.5949i 0.532685 0.824014i
\(199\) 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
\(207\) −4.62035 + 7.14724i −0.321136 + 0.496768i
\(208\) −1.32932 + 1.32932i −0.0921718 + 0.0921718i
\(209\) 4.60223 0.318343
\(210\) 14.2395 + 6.63569i 0.982621 + 0.457906i
\(211\) −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
\(213\) −20.9210 16.9055i −1.43349 1.15834i
\(214\) 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
\(222\) −6.59802 + 8.16524i −0.442830 + 0.548015i
\(223\) 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
\(225\) 9.64754 + 11.4859i 0.643169 + 0.765724i
\(226\) −1.39266 −0.0926383
\(227\) 13.7553 13.7553i 0.912969 0.912969i −0.0835359 0.996505i \(-0.526621\pi\)
0.996505 + 0.0835359i \(0.0266213\pi\)
\(228\) −1.08861 + 1.34719i −0.0720952 + 0.0892198i
\(229\) 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 0.563643 0.826019i \(-0.309399\pi\)
−0.826019 + 0.563643i \(0.809399\pi\)
\(234\) −5.51413 + 1.18407i −0.360470 + 0.0774050i
\(235\) −14.1490 8.51682i −0.922978 0.555576i
\(236\) 5.08697i 0.331134i
\(237\) −14.0713 11.3704i −0.914026 0.738590i
\(238\) 13.8089 13.8089i 0.895097 0.895097i
\(239\) 1.96845 0.127329 0.0636643 0.997971i \(-0.479721\pi\)
0.0636643 + 0.997971i \(0.479721\pi\)
\(240\) −3.51052 1.63592i −0.226603 0.105598i
\(241\) 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
\(243\) −3.95617 + 15.0781i −0.253788 + 0.967260i
\(244\) 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 \(0.0641837\pi\)
−0.979740 + 0.200275i \(0.935816\pi\)
\(252\) −10.2193 6.60631i −0.643757 0.416158i
\(253\) 9.23195 9.23195i 0.580408 0.580408i
\(254\) 11.7678 0.738378
\(255\) 17.5203 6.38181i 1.09716 0.399644i
\(256\) 1.00000 0.0625000
\(257\) 3.25382 3.25382i 0.202968 0.202968i −0.598302 0.801270i \(-0.704158\pi\)
0.801270 + 0.598302i \(0.204158\pi\)
\(258\) −15.6099 12.6138i −0.971832 0.785301i
\(259\) 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 \(0.0950475\pi\)
0.294183 + 0.955749i \(0.404952\pi\)
\(264\) −0.841479 7.92676i −0.0517895 0.487858i
\(265\) 8.09156 13.4425i 0.497061 0.825766i
\(266\) 4.05624i 0.248704i
\(267\) 2.25748 2.79370i 0.138156 0.170972i
\(268\) 6.27966 6.27966i 0.383591 0.383591i
\(269\) −16.9049 −1.03071 −0.515354 0.856977i \(-0.672340\pi\)
−0.515354 + 0.856977i \(0.672340\pi\)
\(270\) −6.18006 9.83905i −0.376106 0.598786i
\(271\) −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
\(273\) 8.30123 10.2730i 0.502413 0.621751i
\(274\) 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 \(-0.861960\pi\)
0.907431 0.420200i \(-0.138040\pi\)
\(282\) 9.94971 + 8.03998i 0.592496 + 0.478774i
\(283\) 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
\(285\) 1.63592 3.51052i 0.0969035 0.207945i
\(286\) 8.65193 0.511600
\(287\) −4.99760 + 4.99760i −0.294999 + 0.294999i
\(288\) 2.51941 + 1.62868i 0.148458 + 0.0959706i
\(289\) 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 0.836156 0.548491i \(-0.184798\pi\)
−0.548491 + 0.836156i \(0.684798\pi\)
\(294\) 16.2818 1.72842i 0.949573 0.100804i
\(295\) 2.74308 + 11.0391i 0.159708 + 0.642722i
\(296\) 6.06094i 0.352285i
\(297\) 10.7901 21.3412i 0.626105 1.23834i
\(298\) 3.95462 3.95462i 0.229085 0.229085i
\(299\) −5.33316 −0.308425
\(300\) 8.50024 + 1.65707i 0.490762 + 0.0956709i
\(301\) 46.9998 2.70903
\(302\) −3.26781 + 3.26781i −0.188041 + 0.188041i
\(303\) −2.49816 2.01866i −0.143515 0.115969i
\(304\) 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 \(-0.778548\pi\)
0.767598 0.640931i \(-0.221452\pi\)
\(312\) −2.04653 + 2.53264i −0.115862 + 0.143383i
\(313\) −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
\(315\) 25.7391 + 8.82555i 1.45023 + 0.497263i
\(316\) −10.4449 −0.587571
\(317\) 0.617852 0.617852i 0.0347020 0.0347020i −0.689543 0.724245i \(-0.742189\pi\)
0.724245 + 0.689543i \(0.242189\pi\)
\(318\) −7.63853 + 9.45290i −0.428348 + 0.530092i
\(319\) 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
\(327\) 8.52415 + 6.88804i 0.471387 + 0.380910i
\(328\) 1.23207 1.23207i 0.0680300 0.0680300i
\(329\) −29.9575 −1.65161
\(330\) 6.10046 + 16.7479i 0.335819 + 0.921942i
\(331\) 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
\(333\) −9.87131 + 15.2700i −0.540944 + 0.836790i
\(334\) 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
\(342\) −1.62868 + 2.51941i −0.0880687 + 0.136234i
\(343\) −7.03600 + 7.03600i −0.379908 + 0.379908i
\(344\) −11.5870 −0.624731
\(345\) −3.76040 10.3236i −0.202453 0.555805i
\(346\) −11.5857 −0.622850
\(347\) −20.8770 + 20.8770i −1.12074 + 1.12074i −0.129107 + 0.991631i \(0.541211\pi\)
−0.991631 + 0.129107i \(0.958789\pi\)
\(348\) 8.36729 + 6.76129i 0.448534 + 0.362443i
\(349\) 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 0.687589 0.726101i \(-0.258669\pi\)
−0.726101 + 0.687589i \(0.758669\pi\)
\(354\) −0.930110 8.76167i −0.0494348 0.465677i
\(355\) 33.6999 8.37399i 1.78861 0.444445i
\(356\) 2.07373i 0.109907i
\(357\) 21.2592 26.3089i 1.12516 1.39241i
\(358\) 4.22678 4.22678i 0.223392 0.223392i
\(359\) 25.4403 1.34269 0.671345 0.741145i \(-0.265717\pi\)
0.671345 + 0.741145i \(0.265717\pi\)
\(360\) −6.34554 2.17579i −0.334439 0.114674i
\(361\) −1.00000 −0.0526316
\(362\) 5.99334 5.99334i 0.315003 0.315003i
\(363\) −11.0827 + 13.7151i −0.581689 + 0.719857i
\(364\) 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
\(372\) 5.27420 + 4.26188i 0.273454 + 0.220968i
\(373\) 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
\(375\) −19.3397 + 0.987670i −0.998698 + 0.0510031i
\(376\) 7.38553 0.380879
\(377\) −8.25630 + 8.25630i −0.425221 + 0.425221i
\(378\) −18.8094 9.51000i −0.967452 0.489142i
\(379\) 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 0.343329 0.939215i \(-0.388445\pi\)
−0.939215 + 0.343329i \(0.888445\pi\)
\(384\) 1.72237 0.182842i 0.0878945 0.00933059i
\(385\) −35.7632 21.5273i −1.82266 1.09713i
\(386\) 6.12000i 0.311500i
\(387\) −29.1925 18.8715i −1.48394 0.959293i
\(388\) 12.5075 12.5075i 0.634972 0.634972i
\(389\) 15.6133 0.791625 0.395813 0.918331i \(-0.370463\pi\)
0.395813 + 0.918331i \(0.370463\pi\)
\(390\) 3.07543 6.59958i 0.155731 0.334183i
\(391\) −13.6581 −0.690719
\(392\) 6.68436 6.68436i 0.337611 0.337611i
\(393\) −25.1629 20.3332i −1.26930 1.02567i
\(394\) 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 \(0.0391844\pi\)
−0.992433 + 0.122791i \(0.960816\pi\)
\(402\) 9.66774 11.9641i 0.482183 0.596715i
\(403\) −5.20424 + 5.20424i −0.259242 + 0.259242i
\(404\) −1.85435 −0.0922571
\(405\) −12.4433 15.8165i −0.618315 0.785930i
\(406\) −25.1930 −1.25031
\(407\) 19.7239 19.7239i 0.977679 0.977679i
\(408\) −5.24111 + 6.48602i −0.259473 + 0.321106i
\(409\) 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
\(417\) 15.1729 + 12.2606i 0.743020 + 0.600406i
\(418\) 3.25427 3.25427i 0.159172 0.159172i
\(419\) 12.5500 0.613105 0.306553 0.951854i \(-0.400824\pi\)
0.306553 + 0.951854i \(0.400824\pi\)
\(420\) 14.7610 5.37673i 0.720264 0.262358i
\(421\) −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
\(423\) 18.6072 + 12.0286i 0.904711 + 0.584852i
\(424\) 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 \(0.0640735\pi\)
−0.979809 + 0.199936i \(0.935926\pi\)
\(432\) 4.63715 + 2.34453i 0.223105 + 0.112801i
\(433\) −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
\(435\) −21.8036 10.1606i −1.04540 0.487162i
\(436\) 6.32736 0.303025
\(437\) −2.00597 + 2.00597i −0.0959587 + 0.0959587i
\(438\) 12.1309 + 9.80248i 0.579635 + 0.468381i
\(439\) 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 \(0.0771094\pi\)
0.239884 + 0.970802i \(0.422891\pi\)
\(444\) 1.10819 + 10.4392i 0.0525924 + 0.495422i
\(445\) 1.11823 + 4.50014i 0.0530090 + 0.213327i
\(446\) 14.3154i 0.677856i
\(447\) 6.08827 7.53441i 0.287965 0.356365i
\(448\) −2.86820 + 2.86820i −0.135510 + 0.135510i
\(449\) −7.40137 −0.349292 −0.174646 0.984631i \(-0.555878\pi\)
−0.174646 + 0.984631i \(0.555878\pi\)
\(450\) 14.9436 + 1.29989i 0.704447 + 0.0612776i
\(451\) −8.01901 −0.377600
\(452\) −0.984759 + 0.984759i −0.0463192 + 0.0463192i
\(453\) −5.03090 + 6.22588i −0.236372 + 0.292517i
\(454\) 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 \(0.342696\pi\)
−0.474314 + 0.880356i \(0.657304\pi\)
\(462\) 25.1490 + 20.3220i 1.17004 + 0.945464i
\(463\) −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
\(465\) −13.7436 6.40456i −0.637342 0.297004i
\(466\) −5.66392 −0.262376
\(467\) 28.1504 28.1504i 1.30265 1.30265i 0.376045 0.926601i \(-0.377284\pi\)
0.926601 0.376045i \(-0.122716\pi\)
\(468\) −3.06182 + 4.73634i −0.141533 + 0.218938i
\(469\) 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
\(477\) −11.4280 + 17.6781i −0.523253 + 0.809423i
\(478\) 1.39191 1.39191i 0.0636643 0.0636643i
\(479\) 23.0077 1.05125 0.525624 0.850717i \(-0.323832\pi\)
0.525624 + 0.850717i \(0.323832\pi\)
\(480\) −3.63908 + 1.32554i −0.166101 + 0.0605026i
\(481\) −11.3942 −0.519532
\(482\) 16.9005 16.9005i 0.769794 0.769794i
\(483\) −15.5022 12.5267i −0.705374 0.569986i
\(484\) 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 \(0.124692\pi\)
−0.924249 + 0.381791i \(0.875308\pi\)
\(492\) 1.89682 2.34737i 0.0855152 0.105827i
\(493\) −21.1442 + 21.1442i −0.952285 + 0.952285i
\(494\) −1.87994 −0.0845826
\(495\) 13.5695 + 27.7307i 0.609903 + 1.24640i
\(496\) 3.91496 0.175787
\(497\) 44.5413 44.5413i 1.99795 1.99795i
\(498\) 5.97050 7.38866i 0.267544 0.331094i
\(499\) 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 0.617159 0.786838i \(-0.288284\pi\)
−0.786838 + 0.617159i \(0.788284\pi\)
\(504\) −11.8975 + 2.55479i −0.529958 + 0.113800i
\(505\) 4.02407 0.999929i 0.179069 0.0444963i
\(506\) 13.0560i 0.580408i
\(507\) 12.7523 + 10.3046i 0.566347 + 0.457644i
\(508\) 8.32109 8.32109i 0.369189 0.369189i
\(509\) 7.97379 0.353432 0.176716 0.984262i \(-0.443453\pi\)
0.176716 + 0.984262i \(0.443453\pi\)
\(510\) 7.87610 16.9013i 0.348760 0.748404i
\(511\) −36.5247 −1.61576
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −2.34453 + 4.63715i −0.103514 + 0.204735i
\(514\) 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 \(0.157674\pi\)
−0.879804 + 0.475336i \(0.842326\pi\)
\(522\) 15.6478 + 10.1156i 0.684887 + 0.442747i
\(523\) −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
\(525\) −29.1332 + 19.6276i −1.27148 + 0.856617i
\(526\) 28.6668 1.24993
\(527\) −13.3279 + 13.3279i −0.580573 + 0.580573i
\(528\) −6.20008 5.01005i −0.269824 0.218034i
\(529\) 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
\(537\) 6.50726 8.05292i 0.280809 0.347509i
\(538\) −11.9535 + 11.9535i −0.515354 + 0.515354i
\(539\) −43.5054 −1.87391
\(540\) −11.3272 2.58730i −0.487446 0.111340i
\(541\) −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
\(543\) 9.22694 11.4186i 0.395966 0.490019i
\(544\) 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
\(552\) 3.82181 + 3.08826i 0.162667 + 0.131445i
\(553\) 29.9580 29.9580i 1.27394 1.27394i
\(554\) −5.71150 −0.242659
\(555\) −8.03405 22.0563i −0.341026 0.936236i
\(556\) 11.2626 0.477642
\(557\) −15.4865 + 15.4865i −0.656182 + 0.656182i −0.954475 0.298292i \(-0.903583\pi\)
0.298292 + 0.954475i \(0.403583\pi\)
\(558\) 9.86338 + 6.37620i 0.417550 + 0.269926i
\(559\) 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 0.0806140 0.996745i \(-0.474312\pi\)
−0.996745 + 0.0806140i \(0.974312\pi\)
\(564\) 12.7206 1.35038i 0.535635 0.0568613i
\(565\) 1.60598 2.66802i 0.0675642 0.112244i
\(566\) 21.3107i 0.895756i
\(567\) −34.1356 12.9406i −1.43356 0.543456i
\(568\) −10.9809 + 10.9809i −0.460750 + 0.460750i
\(569\) −33.8572 −1.41937 −0.709684 0.704520i \(-0.751162\pi\)
−0.709684 + 0.704520i \(0.751162\pi\)
\(570\) −1.32554 3.63908i −0.0555210 0.152424i
\(571\) −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
\(573\) 8.69933 + 7.02960i 0.363420 + 0.293666i
\(574\) 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
\(582\) 19.2557 23.8295i 0.798174 0.987763i
\(583\) 22.8344 22.8344i 0.945705 0.945705i
\(584\) 9.00456 0.372611
\(585\) 4.09037 11.9293i 0.169116 0.493214i
\(586\) 6.96364 0.287665
\(587\) 22.9650 22.9650i 0.947869 0.947869i −0.0508382 0.998707i \(-0.516189\pi\)
0.998707 + 0.0508382i \(0.0161893\pi\)
\(588\) 10.2908 12.7351i 0.424385 0.525188i
\(589\) 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 0.749739 0.661734i \(-0.230179\pi\)
−0.661734 + 0.749739i \(0.730179\pi\)
\(594\) −7.46079 22.7203i −0.306120 0.932224i
\(595\) 10.5306 + 42.3788i 0.431711 + 1.73736i
\(596\) 5.59268i 0.229085i
\(597\) −1.06391 0.859707i −0.0435430 0.0351855i
\(598\) −3.77111 + 3.77111i −0.154212 + 0.154212i
\(599\) 28.0055 1.14427 0.572137 0.820158i \(-0.306115\pi\)
0.572137 + 0.820158i \(0.306115\pi\)
\(600\) 7.18230 4.83885i 0.293216 0.197545i
\(601\) −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
\(603\) 14.4639 22.3743i 0.589016 0.911152i
\(604\) 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
\(612\) −7.84123 + 12.1296i −0.316963 + 0.490312i
\(613\) −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
\(615\) −2.85045 + 6.11679i −0.114941 + 0.246653i
\(616\) 18.6678 0.752146
\(617\) −25.7417 + 25.7417i −1.03632 + 1.03632i −0.0370077 + 0.999315i \(0.511783\pi\)
−0.999315 + 0.0370077i \(0.988217\pi\)
\(618\) 21.8338 + 17.6431i 0.878286 + 0.709709i
\(619\) 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
\(627\) 5.01005 6.20008i 0.200082 0.247607i
\(628\) −10.3075 + 10.3075i −0.411313 + 0.411313i
\(629\) −29.1803 −1.16349
\(630\) 24.4409 11.9597i 0.973748 0.476484i
\(631\) −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
\(633\) −21.6292 + 26.7668i −0.859683 + 1.06388i
\(634\) 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 \(-0.940784\pi\)
0.982746 0.184961i \(-0.0592160\pi\)
\(642\) −16.4097 13.2601i −0.647640 0.523334i
\(643\) −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
\(645\) 42.1662 15.3591i 1.66029 0.604765i
\(646\) −4.81448 −0.189423
\(647\) 6.75416 6.75416i 0.265533 0.265533i −0.561764 0.827297i \(-0.689877\pi\)
0.827297 + 0.561764i \(0.189877\pi\)
\(648\) 8.41558 + 3.19030i 0.330595 + 0.125327i
\(649\) 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 0.388011 0.921655i \(-0.373162\pi\)
−0.921655 + 0.388011i \(0.873162\pi\)
\(654\) 10.8981 1.15690i 0.426148 0.0452385i
\(655\) 40.5328 10.0719i 1.58375 0.393541i
\(656\) 1.74242i 0.0680300i
\(657\) 22.6862 + 14.6655i 0.885071 + 0.572156i
\(658\) −21.1831 + 21.1831i −0.825805 + 0.825805i
\(659\) −10.2941 −0.401002 −0.200501 0.979694i \(-0.564257\pi\)
−0.200501 + 0.979694i \(0.564257\pi\)
\(660\) 16.1562 + 7.52888i 0.628881 + 0.293061i
\(661\) 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
\(663\) −12.1933 9.85298i −0.473550 0.382658i
\(664\) 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
\(672\) −4.41568 + 5.46453i −0.170339 + 0.210799i
\(673\) 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
\(675\) 25.9761 0.493404i 0.999820 0.0189911i
\(676\) 9.46581 0.364070
\(677\) −6.41647 + 6.41647i −0.246605 + 0.246605i −0.819576 0.572971i \(-0.805791\pi\)
0.572971 + 0.819576i \(0.305791\pi\)
\(678\) −1.51607 + 1.87618i −0.0582242 + 0.0720541i
\(679\) 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 0.975857 0.218409i \(-0.0700867\pi\)
−0.218409 + 0.975857i \(0.570087\pi\)
\(684\) 0.629843 + 2.93314i 0.0240826 + 0.112151i
\(685\) −38.7996 23.3550i −1.48246 0.892348i
\(686\) 9.95041i 0.379908i
\(687\) −8.71699 7.04387i −0.332574 0.268740i
\(688\) −8.19327 + 8.19327i −0.312366 + 0.312366i
\(689\) −13.1911 −0.502541
\(690\) −9.95891 4.64090i −0.379129 0.176676i
\(691\) 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
\(693\) 47.0317 + 30.4037i 1.78659 + 1.15494i
\(694\) 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 \(0.182776\pi\)
−0.839623 + 0.543170i \(0.817224\pi\)
\(702\) −4.40759 + 8.71758i −0.166354 + 0.329024i
\(703\) −4.28573 + 4.28573i −0.161639 + 0.161639i
\(704\) −4.60223 −0.173453
\(705\) −26.8765 + 9.78984i −1.01223 + 0.368707i
\(706\) −1.02329 −0.0385121
\(707\) 5.31863 5.31863i 0.200028 0.200028i
\(708\) −6.85312 5.53775i −0.257556 0.208121i
\(709\) 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
\(717\) 2.14288 2.65188i 0.0800274 0.0990362i
\(718\) 17.9890 17.9890i 0.671345 0.671345i
\(719\) 0.237709 0.00886505 0.00443253 0.999990i \(-0.498589\pi\)
0.00443253 + 0.999990i \(0.498589\pi\)
\(720\) −6.02550 + 2.94846i −0.224557 + 0.109883i
\(721\) −65.7393 −2.44826
\(722\) −0.707107 + 0.707107i −0.0263158 + 0.0263158i
\(723\) 26.0188 32.1990i 0.967649 1.19749i
\(724\) 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
\(732\) 0.600871 + 0.485541i 0.0222088 + 0.0179461i
\(733\) 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
\(735\) −15.4645 + 33.1854i −0.570418 + 1.22406i
\(736\) 2.83687 0.104569
\(737\) −28.9005 + 28.9005i −1.06456 + 1.06456i
\(738\) 2.83783 4.38986i 0.104462 0.161593i
\(739\) 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 \(0.0725052\pi\)
0.225817 + 0.974170i \(0.427495\pi\)
\(744\) 6.74302 0.715817i 0.247211 0.0262431i
\(745\) 3.01577 + 12.1365i 0.110489 + 0.444648i
\(746\) 7.81442i 0.286106i
\(747\) 8.93247 13.8177i 0.326822 0.505563i
\(748\) 15.6676 15.6676i 0.572865 0.572865i
\(749\) 49.4079 1.80533
\(750\) −12.9769 + 14.3736i −0.473848 + 0.524851i
\(751\) 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
\(753\) 8.54916 + 6.90825i 0.311549 + 0.251751i
\(754\) 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 \(0.119689\pi\)
−0.930136 + 0.367216i \(0.880311\pi\)
\(762\) 12.8106 15.8535i 0.464079 0.574311i
\(763\) −18.1481 + 18.1481i −0.657006 + 0.657006i
\(764\) 6.45739 0.233620
\(765\) 10.4753 30.5505i 0.378736 1.10456i
\(766\) −16.4922 −0.595886
\(767\) 6.76222 6.76222i 0.244170 0.244170i
\(768\) 1.08861 1.34719i 0.0392819 0.0486125i
\(769\) 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 0.927596 0.373585i \(-0.121872\pi\)
−0.373585 + 0.927596i \(0.621872\pi\)
\(774\) −33.9864 + 7.29801i −1.22161 + 0.262321i
\(775\) 17.2981 9.16243i 0.621365 0.329124i
\(776\) 17.6883i 0.634972i
\(777\) −33.1202 26.7632i −1.18818 0.960123i
\(778\)