Properties

Label 950.2.u.g.199.5
Level $950$
Weight $2$
Character 950.199
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.u (of order \(18\), degree \(6\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(6\) over \(\Q(\zeta_{18})\)
Twist minimal: no (minimal twist has level 190)
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 199.5
Character \(\chi\) \(=\) 950.199
Dual form 950.2.u.g.549.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.984808 - 0.173648i) q^{2} +(0.712963 + 0.849676i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(-4.26875 - 2.46456i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.307311 - 1.74285i) q^{9} +O(q^{10})\) \(q+(0.984808 - 0.173648i) q^{2} +(0.712963 + 0.849676i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.849676 + 0.712963i) q^{6} +(-4.26875 - 2.46456i) q^{7} +(0.866025 - 0.500000i) q^{8} +(0.307311 - 1.74285i) q^{9} +(-2.20561 - 3.82023i) q^{11} +(0.960572 + 0.554587i) q^{12} +(1.69691 - 2.02230i) q^{13} +(-4.63187 - 1.68586i) q^{14} +(0.766044 - 0.642788i) q^{16} +(-4.94904 + 0.872649i) q^{17} -1.76973i q^{18} +(4.21347 - 1.11656i) q^{19} +(-0.949379 - 5.38420i) q^{21} +(-2.83548 - 3.37919i) q^{22} +(-0.351075 - 0.964570i) q^{23} +(1.04228 + 0.379360i) q^{24} +(1.31996 - 2.28624i) q^{26} +(4.58167 - 2.64523i) q^{27} +(-4.85424 - 0.855934i) q^{28} +(-0.462691 + 2.62405i) q^{29} +(-1.01615 + 1.76003i) q^{31} +(0.642788 - 0.766044i) q^{32} +(1.67344 - 4.59773i) q^{33} +(-4.72232 + 1.71878i) q^{34} +(-0.307311 - 1.74285i) q^{36} +2.00107i q^{37} +(3.95557 - 1.83126i) q^{38} +2.92813 q^{39} +(1.65005 - 1.38456i) q^{41} +(-1.86991 - 5.13754i) q^{42} +(-0.516578 + 1.41929i) q^{43} +(-3.37919 - 2.83548i) q^{44} +(-0.513237 - 0.888952i) q^{46} +(1.76317 + 0.310895i) q^{47} +(1.09232 + 0.192606i) q^{48} +(8.64815 + 14.9790i) q^{49} +(-4.26995 - 3.58291i) q^{51} +(0.902907 - 2.48072i) q^{52} +(1.92343 + 5.28457i) q^{53} +(4.05273 - 3.40064i) q^{54} -4.92913 q^{56} +(3.95276 + 2.78402i) q^{57} +2.66453i q^{58} +(-2.44041 - 13.8402i) q^{59} +(13.6360 - 4.96308i) q^{61} +(-0.695088 + 1.90974i) q^{62} +(-5.60720 + 6.68240i) q^{63} +(0.500000 - 0.866025i) q^{64} +(0.849627 - 4.81847i) q^{66} +(-13.4349 - 2.36894i) q^{67} +(-4.35211 + 2.51269i) q^{68} +(0.569269 - 0.986002i) q^{69} +(14.6575 + 5.33488i) q^{71} +(-0.605285 - 1.66301i) q^{72} +(8.10702 + 9.66157i) q^{73} +(0.347483 + 1.97067i) q^{74} +(3.57748 - 2.49031i) q^{76} +21.7435i q^{77} +(2.88365 - 0.508465i) q^{78} +(2.17143 - 1.82205i) q^{79} +(0.525132 + 0.191132i) q^{81} +(1.38456 - 1.65005i) q^{82} +(-6.30732 - 3.64153i) q^{83} +(-2.73363 - 4.73478i) q^{84} +(-0.262274 + 1.48743i) q^{86} +(-2.55947 + 1.47771i) q^{87} +(-3.82023 - 2.20561i) q^{88} +(-7.72995 - 6.48620i) q^{89} +(-12.2278 + 4.45054i) q^{91} +(-0.659805 - 0.786325i) q^{92} +(-2.21993 + 0.391433i) q^{93} +1.79037 q^{94} +1.10917 q^{96} +(-11.7266 + 2.06772i) q^{97} +(11.1179 + 13.2497i) q^{98} +(-7.33589 + 2.67005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 36q^{9} + O(q^{10}) \) \( 36q + 36q^{9} - 24q^{11} - 12q^{14} + 24q^{21} - 18q^{26} + 12q^{29} - 12q^{31} - 36q^{34} - 36q^{36} - 96q^{39} - 42q^{41} - 6q^{44} + 36q^{46} + 78q^{49} + 84q^{51} + 108q^{54} + 60q^{59} + 96q^{61} + 18q^{64} + 48q^{66} + 60q^{69} + 60q^{71} + 6q^{74} - 42q^{76} - 60q^{79} + 36q^{81} - 12q^{84} + 72q^{86} - 60q^{89} - 120q^{91} - 12q^{94} - 342q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.984808 0.173648i 0.696364 0.122788i
\(3\) 0.712963 + 0.849676i 0.411629 + 0.490561i 0.931529 0.363667i \(-0.118475\pi\)
−0.519900 + 0.854227i \(0.674031\pi\)
\(4\) 0.939693 0.342020i 0.469846 0.171010i
\(5\) 0 0
\(6\) 0.849676 + 0.712963i 0.346879 + 0.291066i
\(7\) −4.26875 2.46456i −1.61344 0.931518i −0.988566 0.150789i \(-0.951819\pi\)
−0.624870 0.780729i \(-0.714848\pi\)
\(8\) 0.866025 0.500000i 0.306186 0.176777i
\(9\) 0.307311 1.74285i 0.102437 0.580950i
\(10\) 0 0
\(11\) −2.20561 3.82023i −0.665016 1.15184i −0.979281 0.202507i \(-0.935091\pi\)
0.314264 0.949336i \(-0.398242\pi\)
\(12\) 0.960572 + 0.554587i 0.277293 + 0.160095i
\(13\) 1.69691 2.02230i 0.470638 0.560884i −0.477546 0.878607i \(-0.658474\pi\)
0.948184 + 0.317722i \(0.102918\pi\)
\(14\) −4.63187 1.68586i −1.23792 0.450565i
\(15\) 0 0
\(16\) 0.766044 0.642788i 0.191511 0.160697i
\(17\) −4.94904 + 0.872649i −1.20032 + 0.211649i −0.737836 0.674980i \(-0.764152\pi\)
−0.462483 + 0.886628i \(0.653041\pi\)
\(18\) 1.76973i 0.417131i
\(19\) 4.21347 1.11656i 0.966635 0.256156i
\(20\) 0 0
\(21\) −0.949379 5.38420i −0.207172 1.17493i
\(22\) −2.83548 3.37919i −0.604526 0.720446i
\(23\) −0.351075 0.964570i −0.0732041 0.201127i 0.897694 0.440619i \(-0.145241\pi\)
−0.970898 + 0.239493i \(0.923019\pi\)
\(24\) 1.04228 + 0.379360i 0.212755 + 0.0774364i
\(25\) 0 0
\(26\) 1.31996 2.28624i 0.258866 0.448368i
\(27\) 4.58167 2.64523i 0.881744 0.509075i
\(28\) −4.85424 0.855934i −0.917366 0.161756i
\(29\) −0.462691 + 2.62405i −0.0859196 + 0.487274i 0.911235 + 0.411887i \(0.135130\pi\)
−0.997154 + 0.0753868i \(0.975981\pi\)
\(30\) 0 0
\(31\) −1.01615 + 1.76003i −0.182506 + 0.316110i −0.942733 0.333547i \(-0.891754\pi\)
0.760227 + 0.649657i \(0.225088\pi\)
\(32\) 0.642788 0.766044i 0.113630 0.135419i
\(33\) 1.67344 4.59773i 0.291308 0.800363i
\(34\) −4.72232 + 1.71878i −0.809871 + 0.294769i
\(35\) 0 0
\(36\) −0.307311 1.74285i −0.0512185 0.290475i
\(37\) 2.00107i 0.328975i 0.986379 + 0.164487i \(0.0525970\pi\)
−0.986379 + 0.164487i \(0.947403\pi\)
\(38\) 3.95557 1.83126i 0.641678 0.297069i
\(39\) 2.92813 0.468876
\(40\) 0 0
\(41\) 1.65005 1.38456i 0.257695 0.216232i −0.504782 0.863247i \(-0.668427\pi\)
0.762477 + 0.647015i \(0.223983\pi\)
\(42\) −1.86991 5.13754i −0.288534 0.792740i
\(43\) −0.516578 + 1.41929i −0.0787775 + 0.216439i −0.972829 0.231525i \(-0.925629\pi\)
0.894052 + 0.447964i \(0.147851\pi\)
\(44\) −3.37919 2.83548i −0.509432 0.427464i
\(45\) 0 0
\(46\) −0.513237 0.888952i −0.0756727 0.131069i
\(47\) 1.76317 + 0.310895i 0.257185 + 0.0453486i 0.300754 0.953702i \(-0.402762\pi\)
−0.0435690 + 0.999050i \(0.513873\pi\)
\(48\) 1.09232 + 0.192606i 0.157663 + 0.0278003i
\(49\) 8.64815 + 14.9790i 1.23545 + 2.13986i
\(50\) 0 0
\(51\) −4.26995 3.58291i −0.597913 0.501708i
\(52\) 0.902907 2.48072i 0.125211 0.344013i
\(53\) 1.92343 + 5.28457i 0.264203 + 0.725891i 0.998873 + 0.0474667i \(0.0151148\pi\)
−0.734670 + 0.678425i \(0.762663\pi\)
\(54\) 4.05273 3.40064i 0.551507 0.462769i
\(55\) 0 0
\(56\) −4.92913 −0.658683
\(57\) 3.95276 + 2.78402i 0.523555 + 0.368752i
\(58\) 2.66453i 0.349870i
\(59\) −2.44041 13.8402i −0.317714 1.80184i −0.556583 0.830792i \(-0.687888\pi\)
0.238869 0.971052i \(-0.423223\pi\)
\(60\) 0 0
\(61\) 13.6360 4.96308i 1.74590 0.635457i 0.746358 0.665545i \(-0.231801\pi\)
0.999547 + 0.0300876i \(0.00957861\pi\)
\(62\) −0.695088 + 1.90974i −0.0882763 + 0.242537i
\(63\) −5.60720 + 6.68240i −0.706441 + 0.841903i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 0.849627 4.81847i 0.104582 0.593113i
\(67\) −13.4349 2.36894i −1.64134 0.289412i −0.724679 0.689086i \(-0.758012\pi\)
−0.916657 + 0.399674i \(0.869123\pi\)
\(68\) −4.35211 + 2.51269i −0.527771 + 0.304709i
\(69\) 0.569269 0.986002i 0.0685319 0.118701i
\(70\) 0 0
\(71\) 14.6575 + 5.33488i 1.73952 + 0.633134i 0.999233 0.0391574i \(-0.0124674\pi\)
0.740287 + 0.672291i \(0.234690\pi\)
\(72\) −0.605285 1.66301i −0.0713335 0.195987i
\(73\) 8.10702 + 9.66157i 0.948855 + 1.13080i 0.991289 + 0.131702i \(0.0420441\pi\)
−0.0424348 + 0.999099i \(0.513511\pi\)
\(74\) 0.347483 + 1.97067i 0.0403941 + 0.229086i
\(75\) 0 0
\(76\) 3.57748 2.49031i 0.410365 0.285658i
\(77\) 21.7435i 2.47790i
\(78\) 2.88365 0.508465i 0.326509 0.0575723i
\(79\) 2.17143 1.82205i 0.244305 0.204996i −0.512410 0.858741i \(-0.671247\pi\)
0.756716 + 0.653744i \(0.226803\pi\)
\(80\) 0 0
\(81\) 0.525132 + 0.191132i 0.0583480 + 0.0212369i
\(82\) 1.38456 1.65005i 0.152899 0.182218i
\(83\) −6.30732 3.64153i −0.692318 0.399710i 0.112162 0.993690i \(-0.464222\pi\)
−0.804480 + 0.593980i \(0.797556\pi\)
\(84\) −2.73363 4.73478i −0.298263 0.516607i
\(85\) 0 0
\(86\) −0.262274 + 1.48743i −0.0282817 + 0.160394i
\(87\) −2.55947 + 1.47771i −0.274404 + 0.158428i
\(88\) −3.82023 2.20561i −0.407238 0.235119i
\(89\) −7.72995 6.48620i −0.819373 0.687536i 0.133452 0.991055i \(-0.457394\pi\)
−0.952825 + 0.303520i \(0.901838\pi\)
\(90\) 0 0
\(91\) −12.2278 + 4.45054i −1.28182 + 0.466544i
\(92\) −0.659805 0.786325i −0.0687894 0.0819800i
\(93\) −2.21993 + 0.391433i −0.230196 + 0.0405897i
\(94\) 1.79037 0.184663
\(95\) 0 0
\(96\) 1.10917 0.113205
\(97\) −11.7266 + 2.06772i −1.19066 + 0.209945i −0.733656 0.679521i \(-0.762188\pi\)
−0.457002 + 0.889466i \(0.651077\pi\)
\(98\) 11.1179 + 13.2497i 1.12307 + 1.33843i
\(99\) −7.33589 + 2.67005i −0.737285 + 0.268350i
\(100\) 0 0
\(101\) −1.10632 0.928316i −0.110083 0.0923709i 0.586085 0.810250i \(-0.300669\pi\)
−0.696168 + 0.717879i \(0.745113\pi\)
\(102\) −4.82725 2.78701i −0.477969 0.275955i
\(103\) 3.86364 2.23068i 0.380696 0.219795i −0.297425 0.954745i \(-0.596128\pi\)
0.678121 + 0.734950i \(0.262794\pi\)
\(104\) 0.458418 2.59982i 0.0449515 0.254933i
\(105\) 0 0
\(106\) 2.81186 + 4.87029i 0.273112 + 0.473044i
\(107\) 6.80951 + 3.93147i 0.658300 + 0.380070i 0.791629 0.611002i \(-0.209233\pi\)
−0.133329 + 0.991072i \(0.542567\pi\)
\(108\) 3.40064 4.05273i 0.327227 0.389974i
\(109\) −2.37019 0.862678i −0.227023 0.0826296i 0.226004 0.974126i \(-0.427434\pi\)
−0.453027 + 0.891497i \(0.649656\pi\)
\(110\) 0 0
\(111\) −1.70027 + 1.42669i −0.161382 + 0.135416i
\(112\) −4.85424 + 0.855934i −0.458683 + 0.0808782i
\(113\) 2.59814i 0.244413i −0.992505 0.122206i \(-0.961003\pi\)
0.992505 0.122206i \(-0.0389970\pi\)
\(114\) 4.37615 + 2.05533i 0.409864 + 0.192499i
\(115\) 0 0
\(116\) 0.462691 + 2.62405i 0.0429598 + 0.243637i
\(117\) −3.00308 3.57893i −0.277635 0.330872i
\(118\) −4.80666 13.2062i −0.442489 1.21573i
\(119\) 23.2769 + 8.47211i 2.13379 + 0.776637i
\(120\) 0 0
\(121\) −4.22943 + 7.32559i −0.384494 + 0.665963i
\(122\) 12.5670 7.25554i 1.13776 0.656886i
\(123\) 2.35285 + 0.414871i 0.212150 + 0.0374077i
\(124\) −0.352906 + 2.00143i −0.0316919 + 0.179733i
\(125\) 0 0
\(126\) −4.36163 + 7.55456i −0.388564 + 0.673013i
\(127\) 13.3209 15.8752i 1.18204 1.40869i 0.289822 0.957080i \(-0.406404\pi\)
0.892213 0.451614i \(-0.149152\pi\)
\(128\) 0.342020 0.939693i 0.0302306 0.0830579i
\(129\) −1.57424 + 0.572975i −0.138604 + 0.0504476i
\(130\) 0 0
\(131\) −0.301638 1.71068i −0.0263543 0.149462i 0.968791 0.247879i \(-0.0797334\pi\)
−0.995145 + 0.0984163i \(0.968622\pi\)
\(132\) 4.89281i 0.425864i
\(133\) −20.7381 5.61805i −1.79822 0.487147i
\(134\) −13.6422 −1.17850
\(135\) 0 0
\(136\) −3.84967 + 3.23026i −0.330107 + 0.276992i
\(137\) −0.854249 2.34703i −0.0729834 0.200520i 0.897837 0.440328i \(-0.145138\pi\)
−0.970820 + 0.239808i \(0.922916\pi\)
\(138\) 0.389403 1.06988i 0.0331482 0.0910738i
\(139\) −9.06390 7.60552i −0.768790 0.645092i 0.171609 0.985165i \(-0.445104\pi\)
−0.940399 + 0.340074i \(0.889548\pi\)
\(140\) 0 0
\(141\) 0.992916 + 1.71978i 0.0836186 + 0.144832i
\(142\) 15.3612 + 2.70859i 1.28908 + 0.227300i
\(143\) −11.4684 2.02218i −0.959032 0.169103i
\(144\) −0.884867 1.53264i −0.0737390 0.127720i
\(145\) 0 0
\(146\) 9.66157 + 8.10702i 0.799597 + 0.670942i
\(147\) −6.56152 + 18.0276i −0.541185 + 1.48689i
\(148\) 0.684408 + 1.88040i 0.0562580 + 0.154568i
\(149\) 15.4299 12.9472i 1.26406 1.06068i 0.268828 0.963188i \(-0.413364\pi\)
0.995237 0.0974880i \(-0.0310808\pi\)
\(150\) 0 0
\(151\) −7.67871 −0.624885 −0.312442 0.949937i \(-0.601147\pi\)
−0.312442 + 0.949937i \(0.601147\pi\)
\(152\) 3.09069 3.07370i 0.250688 0.249310i
\(153\) 8.89360i 0.719005i
\(154\) 3.77571 + 21.4131i 0.304256 + 1.72552i
\(155\) 0 0
\(156\) 2.75154 1.00148i 0.220300 0.0801825i
\(157\) −1.98396 + 5.45088i −0.158337 + 0.435027i −0.993340 0.115218i \(-0.963243\pi\)
0.835003 + 0.550245i \(0.185466\pi\)
\(158\) 1.82205 2.17143i 0.144954 0.172750i
\(159\) −3.11884 + 5.40199i −0.247340 + 0.428406i
\(160\) 0 0
\(161\) −0.878594 + 4.98275i −0.0692429 + 0.392696i
\(162\) 0.550344 + 0.0970404i 0.0432391 + 0.00762422i
\(163\) 9.28767 5.36224i 0.727466 0.420003i −0.0900283 0.995939i \(-0.528696\pi\)
0.817495 + 0.575936i \(0.195362\pi\)
\(164\) 1.07700 1.86541i 0.0840992 0.145664i
\(165\) 0 0
\(166\) −6.84384 2.49095i −0.531185 0.193335i
\(167\) −3.38367 9.29655i −0.261836 0.719389i −0.999044 0.0437226i \(-0.986078\pi\)
0.737208 0.675666i \(-0.236144\pi\)
\(168\) −3.51429 4.18816i −0.271133 0.323124i
\(169\) 1.04724 + 5.93919i 0.0805569 + 0.456861i
\(170\) 0 0
\(171\) −0.651146 7.68657i −0.0497944 0.587806i
\(172\) 1.51037i 0.115165i
\(173\) −15.4634 + 2.72662i −1.17566 + 0.207301i −0.727151 0.686477i \(-0.759156\pi\)
−0.448510 + 0.893778i \(0.648045\pi\)
\(174\) −2.26399 + 1.89971i −0.171633 + 0.144017i
\(175\) 0 0
\(176\) −4.14519 1.50873i −0.312456 0.113725i
\(177\) 10.0198 11.9411i 0.753134 0.897550i
\(178\) −8.73883 5.04537i −0.655003 0.378166i
\(179\) 5.05642 + 8.75798i 0.377935 + 0.654602i 0.990762 0.135615i \(-0.0433010\pi\)
−0.612827 + 0.790217i \(0.709968\pi\)
\(180\) 0 0
\(181\) 0.465151 2.63800i 0.0345744 0.196081i −0.962628 0.270826i \(-0.912703\pi\)
0.997203 + 0.0747449i \(0.0238142\pi\)
\(182\) −11.2692 + 6.50626i −0.835326 + 0.482276i
\(183\) 13.9389 + 8.04765i 1.03040 + 0.594899i
\(184\) −0.786325 0.659805i −0.0579686 0.0486414i
\(185\) 0 0
\(186\) −2.11823 + 0.770973i −0.155316 + 0.0565305i
\(187\) 14.2494 + 16.9817i 1.04202 + 1.24183i
\(188\) 1.76317 0.310895i 0.128592 0.0226743i
\(189\) −26.0774 −1.89685
\(190\) 0 0
\(191\) 3.75100 0.271413 0.135706 0.990749i \(-0.456670\pi\)
0.135706 + 0.990749i \(0.456670\pi\)
\(192\) 1.09232 0.192606i 0.0788316 0.0139001i
\(193\) 9.27700 + 11.0559i 0.667773 + 0.795821i 0.988479 0.151358i \(-0.0483645\pi\)
−0.320706 + 0.947179i \(0.603920\pi\)
\(194\) −11.1894 + 4.07261i −0.803353 + 0.292397i
\(195\) 0 0
\(196\) 13.2497 + 11.1179i 0.946410 + 0.794132i
\(197\) 17.1473 + 9.89999i 1.22169 + 0.705345i 0.965279 0.261222i \(-0.0841254\pi\)
0.256415 + 0.966567i \(0.417459\pi\)
\(198\) −6.76079 + 3.90335i −0.480469 + 0.277399i
\(199\) −3.46951 + 19.6766i −0.245947 + 1.39484i 0.572335 + 0.820020i \(0.306038\pi\)
−0.818282 + 0.574817i \(0.805073\pi\)
\(200\) 0 0
\(201\) −7.56577 13.1043i −0.533648 0.924305i
\(202\) −1.25072 0.722101i −0.0880001 0.0508069i
\(203\) 8.44226 10.0611i 0.592530 0.706150i
\(204\) −5.23787 1.90643i −0.366724 0.133477i
\(205\) 0 0
\(206\) 3.41759 2.86770i 0.238115 0.199802i
\(207\) −1.78899 + 0.315447i −0.124343 + 0.0219251i
\(208\) 2.63992i 0.183046i
\(209\) −13.5588 13.6337i −0.937880 0.943064i
\(210\) 0 0
\(211\) 2.37072 + 13.4450i 0.163207 + 0.925594i 0.950894 + 0.309518i \(0.100168\pi\)
−0.787687 + 0.616076i \(0.788721\pi\)
\(212\) 3.61486 + 4.30802i 0.248269 + 0.295876i
\(213\) 5.91730 + 16.2577i 0.405447 + 1.11396i
\(214\) 7.38875 + 2.68928i 0.505084 + 0.183836i
\(215\) 0 0
\(216\) 2.64523 4.58167i 0.179985 0.311743i
\(217\) 8.67539 5.00874i 0.588924 0.340015i
\(218\) −2.48398 0.437993i −0.168237 0.0296646i
\(219\) −2.42920 + 13.7767i −0.164150 + 0.930941i
\(220\) 0 0
\(221\) −6.63332 + 11.4892i −0.446205 + 0.772850i
\(222\) −1.42669 + 1.70027i −0.0957533 + 0.114114i
\(223\) 7.92835 21.7830i 0.530922 1.45870i −0.327054 0.945006i \(-0.606056\pi\)
0.857976 0.513690i \(-0.171722\pi\)
\(224\) −4.63187 + 1.68586i −0.309480 + 0.112641i
\(225\) 0 0
\(226\) −0.451163 2.55867i −0.0300109 0.170200i
\(227\) 7.37892i 0.489756i −0.969554 0.244878i \(-0.921252\pi\)
0.969554 0.244878i \(-0.0787479\pi\)
\(228\) 4.66657 + 1.26420i 0.309051 + 0.0837235i
\(229\) 13.2440 0.875188 0.437594 0.899173i \(-0.355831\pi\)
0.437594 + 0.899173i \(0.355831\pi\)
\(230\) 0 0
\(231\) −18.4749 + 15.5023i −1.21556 + 1.01998i
\(232\) 0.911323 + 2.50384i 0.0598313 + 0.164385i
\(233\) −5.17822 + 14.2271i −0.339237 + 0.932045i 0.646375 + 0.763020i \(0.276284\pi\)
−0.985612 + 0.169025i \(0.945938\pi\)
\(234\) −3.57893 3.00308i −0.233962 0.196317i
\(235\) 0 0
\(236\) −7.02687 12.1709i −0.457410 0.792258i
\(237\) 3.09630 + 0.545962i 0.201126 + 0.0354640i
\(238\) 24.3945 + 4.30140i 1.58126 + 0.278818i
\(239\) 5.84319 + 10.1207i 0.377964 + 0.654653i 0.990766 0.135583i \(-0.0432909\pi\)
−0.612802 + 0.790237i \(0.709958\pi\)
\(240\) 0 0
\(241\) 9.77297 + 8.20049i 0.629532 + 0.528240i 0.900784 0.434268i \(-0.142993\pi\)
−0.271251 + 0.962509i \(0.587437\pi\)
\(242\) −2.89310 + 7.94873i −0.185976 + 0.510964i
\(243\) −5.21633 14.3318i −0.334628 0.919383i
\(244\) 11.1161 9.32754i 0.711637 0.597135i
\(245\) 0 0
\(246\) 2.38915 0.152327
\(247\) 4.89186 10.4156i 0.311261 0.662727i
\(248\) 2.03230i 0.129051i
\(249\) −1.40276 7.95545i −0.0888963 0.504156i
\(250\) 0 0
\(251\) −25.2367 + 9.18541i −1.59293 + 0.579778i −0.977963 0.208778i \(-0.933051\pi\)
−0.614964 + 0.788556i \(0.710829\pi\)
\(252\) −2.98353 + 8.19717i −0.187945 + 0.516373i
\(253\) −2.91054 + 3.46865i −0.182984 + 0.218072i
\(254\) 10.3618 17.9471i 0.650157 1.12610i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −0.157270 0.0277309i −0.00981023 0.00172981i 0.168741 0.985660i \(-0.446030\pi\)
−0.178551 + 0.983931i \(0.557141\pi\)
\(258\) −1.45082 + 0.837633i −0.0903243 + 0.0521488i
\(259\) 4.93178 8.54209i 0.306446 0.530780i
\(260\) 0 0
\(261\) 4.43113 + 1.61280i 0.274280 + 0.0998299i
\(262\) −0.594111 1.63231i −0.0367043 0.100844i
\(263\) −5.95157 7.09280i −0.366990 0.437361i 0.550673 0.834721i \(-0.314371\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(264\) −0.849627 4.81847i −0.0522909 0.296557i
\(265\) 0 0
\(266\) −21.3986 1.93157i −1.31203 0.118432i
\(267\) 11.1924i 0.684962i
\(268\) −13.4349 + 2.36894i −0.820668 + 0.144706i
\(269\) −9.55896 + 8.02092i −0.582820 + 0.489044i −0.885872 0.463930i \(-0.846439\pi\)
0.303052 + 0.952974i \(0.401995\pi\)
\(270\) 0 0
\(271\) 26.5079 + 9.64808i 1.61024 + 0.586079i 0.981487 0.191526i \(-0.0613437\pi\)
0.628752 + 0.777606i \(0.283566\pi\)
\(272\) −3.23026 + 3.84967i −0.195863 + 0.233421i
\(273\) −12.4995 7.21657i −0.756502 0.436766i
\(274\) −1.24883 2.16303i −0.0754445 0.130674i
\(275\) 0 0
\(276\) 0.197705 1.12124i 0.0119004 0.0674907i
\(277\) 7.28486 4.20592i 0.437705 0.252709i −0.264919 0.964271i \(-0.585345\pi\)
0.702624 + 0.711562i \(0.252012\pi\)
\(278\) −10.2469 5.91604i −0.614567 0.354821i
\(279\) 2.75518 + 2.31187i 0.164948 + 0.138408i
\(280\) 0 0
\(281\) −20.9967 + 7.64218i −1.25256 + 0.455894i −0.881266 0.472621i \(-0.843308\pi\)
−0.371294 + 0.928515i \(0.621086\pi\)
\(282\) 1.27647 + 1.52123i 0.0760125 + 0.0905882i
\(283\) 12.5725 2.21687i 0.747357 0.131779i 0.213016 0.977049i \(-0.431671\pi\)
0.534340 + 0.845269i \(0.320560\pi\)
\(284\) 15.5981 0.925579
\(285\) 0 0
\(286\) −11.6453 −0.688600
\(287\) −10.4560 + 1.84368i −0.617198 + 0.108829i
\(288\) −1.13756 1.35570i −0.0670316 0.0798851i
\(289\) 7.75671 2.82321i 0.456277 0.166071i
\(290\) 0 0
\(291\) −10.1175 8.48962i −0.593100 0.497670i
\(292\) 10.9226 + 6.30614i 0.639194 + 0.369039i
\(293\) 25.0376 14.4554i 1.46271 0.844496i 0.463575 0.886058i \(-0.346567\pi\)
0.999136 + 0.0415616i \(0.0132333\pi\)
\(294\) −3.33137 + 18.8931i −0.194289 + 1.10187i
\(295\) 0 0
\(296\) 1.00054 + 1.73298i 0.0581551 + 0.100728i
\(297\) −20.2108 11.6687i −1.17275 0.677086i
\(298\) 12.9472 15.4299i 0.750011 0.893829i
\(299\) −2.54639 0.926810i −0.147261 0.0535988i
\(300\) 0 0
\(301\) 5.70307 4.78544i 0.328719 0.275828i
\(302\) −7.56206 + 1.33339i −0.435147 + 0.0767282i
\(303\) 1.60187i 0.0920251i
\(304\) 2.50999 3.56370i 0.143958 0.204392i
\(305\) 0 0
\(306\) 1.54436 + 8.75849i 0.0882851 + 0.500690i
\(307\) 15.0835 + 17.9758i 0.860860 + 1.02593i 0.999367 + 0.0355713i \(0.0113251\pi\)
−0.138507 + 0.990361i \(0.544230\pi\)
\(308\) 7.43671 + 20.4322i 0.423746 + 1.16423i
\(309\) 4.64999 + 1.69246i 0.264528 + 0.0962805i
\(310\) 0 0
\(311\) −2.12258 + 3.67642i −0.120360 + 0.208470i −0.919910 0.392130i \(-0.871738\pi\)
0.799549 + 0.600600i \(0.205072\pi\)
\(312\) 2.53584 1.46407i 0.143563 0.0828864i
\(313\) 11.4384 + 2.01689i 0.646534 + 0.114001i 0.487293 0.873238i \(-0.337984\pi\)
0.159241 + 0.987240i \(0.449095\pi\)
\(314\) −1.00728 + 5.71258i −0.0568442 + 0.322379i
\(315\) 0 0
\(316\) 1.41730 2.45484i 0.0797295 0.138096i
\(317\) 1.43742 1.71306i 0.0807338 0.0962148i −0.724165 0.689626i \(-0.757775\pi\)
0.804899 + 0.593411i \(0.202219\pi\)
\(318\) −2.13341 + 5.86150i −0.119636 + 0.328697i
\(319\) 11.0450 4.02005i 0.618401 0.225080i
\(320\) 0 0
\(321\) 1.51445 + 8.58887i 0.0845283 + 0.479384i
\(322\) 5.05962i 0.281962i
\(323\) −19.8783 + 9.20277i −1.10606 + 0.512056i
\(324\) 0.558833 0.0310463
\(325\) 0 0
\(326\) 8.21542 6.89356i 0.455010 0.381799i
\(327\) −0.956860 2.62895i −0.0529145 0.145381i
\(328\) 0.736709 2.02409i 0.0406779 0.111762i
\(329\) −6.76032 5.67258i −0.372708 0.312739i
\(330\) 0 0
\(331\) 0.254634 + 0.441039i 0.0139959 + 0.0242417i 0.872939 0.487830i \(-0.162211\pi\)
−0.858943 + 0.512072i \(0.828878\pi\)
\(332\) −7.17241 1.26469i −0.393637 0.0694089i
\(333\) 3.48757 + 0.614953i 0.191118 + 0.0336992i
\(334\) −4.94659 8.56775i −0.270666 0.468806i
\(335\) 0 0
\(336\) −4.18816 3.51429i −0.228483 0.191720i
\(337\) −5.15806 + 14.1717i −0.280977 + 0.771979i 0.716269 + 0.697824i \(0.245848\pi\)
−0.997247 + 0.0741552i \(0.976374\pi\)
\(338\) 2.06266 + 5.66711i 0.112194 + 0.308250i
\(339\) 2.20758 1.85238i 0.119899 0.100607i
\(340\) 0 0
\(341\) 8.96493 0.485478
\(342\) −1.97601 7.45672i −0.106850 0.403213i
\(343\) 50.7518i 2.74034i
\(344\) 0.262274 + 1.48743i 0.0141409 + 0.0801968i
\(345\) 0 0
\(346\) −14.7550 + 5.37038i −0.793234 + 0.288714i
\(347\) 11.5530 31.7415i 0.620196 1.70398i −0.0863093 0.996268i \(-0.527507\pi\)
0.706506 0.707707i \(-0.250270\pi\)
\(348\) −1.89971 + 2.26399i −0.101835 + 0.121363i
\(349\) −0.0164139 + 0.0284297i −0.000878615 + 0.00152181i −0.866464 0.499239i \(-0.833613\pi\)
0.865586 + 0.500761i \(0.166946\pi\)
\(350\) 0 0
\(351\) 2.42524 13.7542i 0.129450 0.734146i
\(352\) −4.34420 0.766000i −0.231547 0.0408280i
\(353\) 0.243332 0.140488i 0.0129512 0.00747740i −0.493510 0.869740i \(-0.664287\pi\)
0.506462 + 0.862262i \(0.330953\pi\)
\(354\) 7.79401 13.4996i 0.414247 0.717497i
\(355\) 0 0
\(356\) −9.48219 3.45123i −0.502555 0.182915i
\(357\) 9.39703 + 25.8181i 0.497344 + 1.36644i
\(358\) 6.50041 + 7.74689i 0.343557 + 0.409436i
\(359\) −2.29364 13.0079i −0.121054 0.686530i −0.983574 0.180507i \(-0.942226\pi\)
0.862520 0.506023i \(-0.168885\pi\)
\(360\) 0 0
\(361\) 16.5066 9.40916i 0.868768 0.495219i
\(362\) 2.67870i 0.140789i
\(363\) −9.23981 + 1.62923i −0.484964 + 0.0855122i
\(364\) −9.96816 + 8.36428i −0.522474 + 0.438408i
\(365\) 0 0
\(366\) 15.1246 + 5.50492i 0.790577 + 0.287747i
\(367\) −6.62354 + 7.89363i −0.345746 + 0.412044i −0.910693 0.413083i \(-0.864452\pi\)
0.564948 + 0.825127i \(0.308896\pi\)
\(368\) −0.888952 0.513237i −0.0463398 0.0267543i
\(369\) −1.90600 3.30128i −0.0992222 0.171858i
\(370\) 0 0
\(371\) 4.81354 27.2989i 0.249906 1.41729i
\(372\) −1.95217 + 1.12709i −0.101215 + 0.0584368i
\(373\) 24.5861 + 14.1948i 1.27302 + 0.734977i 0.975555 0.219756i \(-0.0705261\pi\)
0.297463 + 0.954733i \(0.403859\pi\)
\(374\) 16.9817 + 14.2494i 0.878105 + 0.736818i
\(375\) 0 0
\(376\) 1.68240 0.612343i 0.0867631 0.0315792i
\(377\) 4.52147 + 5.38848i 0.232867 + 0.277521i
\(378\) −25.6812 + 4.52829i −1.32090 + 0.232910i
\(379\) −19.1984 −0.986157 −0.493079 0.869985i \(-0.664129\pi\)
−0.493079 + 0.869985i \(0.664129\pi\)
\(380\) 0 0
\(381\) 22.9860 1.17761
\(382\) 3.69402 0.651355i 0.189002 0.0333262i
\(383\) −13.4201 15.9934i −0.685734 0.817226i 0.305099 0.952321i \(-0.401311\pi\)
−0.990833 + 0.135095i \(0.956866\pi\)
\(384\) 1.04228 0.379360i 0.0531887 0.0193591i
\(385\) 0 0
\(386\) 11.0559 + 9.27700i 0.562731 + 0.472187i
\(387\) 2.31485 + 1.33648i 0.117671 + 0.0679371i
\(388\) −10.3122 + 5.95376i −0.523523 + 0.302256i
\(389\) −2.69629 + 15.2914i −0.136707 + 0.775304i 0.836949 + 0.547281i \(0.184337\pi\)
−0.973656 + 0.228023i \(0.926774\pi\)
\(390\) 0 0
\(391\) 2.57921 + 4.46733i 0.130436 + 0.225923i
\(392\) 14.9790 + 8.64815i 0.756556 + 0.436798i
\(393\) 1.23846 1.47594i 0.0624722 0.0744515i
\(394\) 18.6059 + 6.77199i 0.937351 + 0.341168i
\(395\) 0 0
\(396\) −5.98027 + 5.01804i −0.300520 + 0.252166i
\(397\) −4.74331 + 0.836373i −0.238060 + 0.0419764i −0.291405 0.956600i \(-0.594123\pi\)
0.0533453 + 0.998576i \(0.483012\pi\)
\(398\) 19.9801i 1.00151i
\(399\) −10.0119 21.6261i −0.501224 1.08266i
\(400\) 0 0
\(401\) −2.15856 12.2418i −0.107793 0.611326i −0.990068 0.140591i \(-0.955100\pi\)
0.882275 0.470735i \(-0.156011\pi\)
\(402\) −9.72636 11.5914i −0.485107 0.578128i
\(403\) 1.83498 + 5.04156i 0.0914068 + 0.251138i
\(404\) −1.35711 0.493947i −0.0675186 0.0245748i
\(405\) 0 0
\(406\) 6.56691 11.3742i 0.325910 0.564493i
\(407\) 7.64456 4.41359i 0.378927 0.218774i
\(408\) −5.48934 0.967919i −0.271763 0.0479191i
\(409\) 2.99828 17.0041i 0.148255 0.840797i −0.816440 0.577430i \(-0.804056\pi\)
0.964696 0.263367i \(-0.0848332\pi\)
\(410\) 0 0
\(411\) 1.38517 2.39918i 0.0683253 0.118343i
\(412\) 2.86770 3.41759i 0.141282 0.168373i
\(413\) −23.6926 + 65.0950i −1.16584 + 3.20312i
\(414\) −1.70703 + 0.621309i −0.0838961 + 0.0305357i
\(415\) 0 0
\(416\) −0.458418 2.59982i −0.0224758 0.127466i
\(417\) 13.1238i 0.642677i
\(418\) −15.7203 11.0721i −0.768903 0.541556i
\(419\) −18.2962 −0.893827 −0.446914 0.894577i \(-0.647477\pi\)
−0.446914 + 0.894577i \(0.647477\pi\)
\(420\) 0 0
\(421\) 21.4711 18.0164i 1.04644 0.878067i 0.0537246 0.998556i \(-0.482891\pi\)
0.992715 + 0.120489i \(0.0384462\pi\)
\(422\) 4.66941 + 12.8291i 0.227303 + 0.624510i
\(423\) 1.08368 2.97740i 0.0526905 0.144766i
\(424\) 4.30802 + 3.61486i 0.209216 + 0.175553i
\(425\) 0 0
\(426\) 8.65052 + 14.9831i 0.419119 + 0.725935i
\(427\) −70.4403 12.4205i −3.40885 0.601072i
\(428\) 7.74349 + 1.36539i 0.374296 + 0.0659984i
\(429\) −6.45831 11.1861i −0.311810 0.540071i
\(430\) 0 0
\(431\) 11.8489 + 9.94239i 0.570740 + 0.478908i 0.881892 0.471452i \(-0.156270\pi\)
−0.311151 + 0.950360i \(0.600715\pi\)
\(432\) 1.80944 4.97141i 0.0870569 0.239187i
\(433\) 4.81630 + 13.2327i 0.231457 + 0.635922i 0.999992 0.00388467i \(-0.00123653\pi\)
−0.768536 + 0.639807i \(0.779014\pi\)
\(434\) 7.67383 6.43911i 0.368356 0.309087i
\(435\) 0 0
\(436\) −2.52230 −0.120796
\(437\) −2.55624 3.67219i −0.122282 0.175665i
\(438\) 13.9892i 0.668430i
\(439\) −1.61433 9.15534i −0.0770479 0.436961i −0.998791 0.0491593i \(-0.984346\pi\)
0.921743 0.387801i \(-0.126765\pi\)
\(440\) 0 0
\(441\) 28.7639 10.4692i 1.36971 0.498533i
\(442\) −4.53746 + 12.4666i −0.215825 + 0.592974i
\(443\) −7.64795 + 9.11448i −0.363365 + 0.433042i −0.916491 0.400056i \(-0.868991\pi\)
0.553125 + 0.833098i \(0.313435\pi\)
\(444\) −1.10977 + 1.92218i −0.0526673 + 0.0912225i
\(445\) 0 0
\(446\) 4.02533 22.8288i 0.190605 1.08097i
\(447\) 22.0019 + 3.87952i 1.04065 + 0.183495i
\(448\) −4.26875 + 2.46456i −0.201680 + 0.116440i
\(449\) −9.95157 + 17.2366i −0.469644 + 0.813446i −0.999398 0.0347048i \(-0.988951\pi\)
0.529754 + 0.848151i \(0.322284\pi\)
\(450\) 0 0
\(451\) −8.92871 3.24978i −0.420436 0.153026i
\(452\) −0.888617 2.44146i −0.0417970 0.114836i
\(453\) −5.47464 6.52442i −0.257221 0.306544i
\(454\) −1.28134 7.26682i −0.0601361 0.341049i
\(455\) 0 0
\(456\) 4.81520 + 0.434651i 0.225492 + 0.0203544i
\(457\) 36.8095i 1.72188i −0.508708 0.860939i \(-0.669877\pi\)
0.508708 0.860939i \(-0.330123\pi\)
\(458\) 13.0428 2.29980i 0.609449 0.107462i
\(459\) −20.3665 + 17.0896i −0.950628 + 0.797672i
\(460\) 0 0
\(461\) −28.6287 10.4200i −1.33337 0.485308i −0.425653 0.904886i \(-0.639956\pi\)
−0.907719 + 0.419578i \(0.862178\pi\)
\(462\) −15.5023 + 18.4749i −0.721232 + 0.859530i
\(463\) −19.3969 11.1988i −0.901452 0.520454i −0.0237813 0.999717i \(-0.507571\pi\)
−0.877671 + 0.479263i \(0.840904\pi\)
\(464\) 1.33227 + 2.30755i 0.0618489 + 0.107125i
\(465\) 0 0
\(466\) −2.62905 + 14.9101i −0.121789 + 0.690697i
\(467\) −12.8027 + 7.39165i −0.592439 + 0.342045i −0.766061 0.642768i \(-0.777786\pi\)
0.173623 + 0.984812i \(0.444453\pi\)
\(468\) −4.04604 2.33598i −0.187028 0.107981i
\(469\) 51.5119 + 43.2236i 2.37860 + 1.99588i
\(470\) 0 0
\(471\) −6.04597 + 2.20055i −0.278583 + 0.101396i
\(472\) −9.03357 10.7658i −0.415804 0.495535i
\(473\) 6.56137 1.15695i 0.301692 0.0531965i
\(474\) 3.14407 0.144412
\(475\) 0 0
\(476\) 24.7708 1.13537
\(477\) 9.80130 1.72823i 0.448770 0.0791303i
\(478\) 7.51186 + 8.95228i 0.343584 + 0.409468i
\(479\) −25.2882 + 9.20416i −1.15545 + 0.420549i −0.847469 0.530844i \(-0.821875\pi\)
−0.307979 + 0.951393i \(0.599653\pi\)
\(480\) 0 0
\(481\) 4.04677 + 3.39564i 0.184517 + 0.154828i
\(482\) 11.0485 + 6.37885i 0.503245 + 0.290549i
\(483\) −4.86013 + 2.80600i −0.221144 + 0.127677i
\(484\) −1.46887 + 8.33035i −0.0667667 + 0.378652i
\(485\) 0 0
\(486\) −7.62577 13.2082i −0.345912 0.599137i
\(487\) 12.2827 + 7.09140i 0.556581 + 0.321342i 0.751772 0.659423i \(-0.229199\pi\)
−0.195191 + 0.980765i \(0.562533\pi\)
\(488\) 9.32754 11.1161i 0.422238 0.503204i
\(489\) 11.1779 + 4.06843i 0.505483 + 0.183981i
\(490\) 0 0
\(491\) 7.44701 6.24878i 0.336079 0.282004i −0.459092 0.888389i \(-0.651825\pi\)
0.795171 + 0.606385i \(0.207381\pi\)
\(492\) 2.35285 0.414871i 0.106075 0.0187039i
\(493\) 13.3903i 0.603069i
\(494\) 3.00889 11.1068i 0.135376 0.499719i
\(495\) 0 0
\(496\) 0.352906 + 2.00143i 0.0158459 + 0.0898667i
\(497\) −49.4209 58.8975i −2.21683 2.64191i
\(498\) −2.76290 7.59100i −0.123808 0.340161i
\(499\) −11.5577 4.20666i −0.517394 0.188316i 0.0701069 0.997539i \(-0.477666\pi\)
−0.587501 + 0.809223i \(0.699888\pi\)
\(500\) 0 0
\(501\) 5.48663 9.50312i 0.245124 0.424568i
\(502\) −23.2583 + 13.4282i −1.03807 + 0.599329i
\(503\) 24.5454 + 4.32801i 1.09442 + 0.192976i 0.691586 0.722295i \(-0.256913\pi\)
0.402839 + 0.915271i \(0.368024\pi\)
\(504\) −1.51478 + 8.59073i −0.0674735 + 0.382661i
\(505\) 0 0
\(506\) −2.26400 + 3.92136i −0.100647 + 0.174326i
\(507\) −4.29974 + 5.12424i −0.190958 + 0.227575i
\(508\) 7.08788 19.4738i 0.314474 0.864010i
\(509\) −12.5923 + 4.58321i −0.558142 + 0.203147i −0.605660 0.795723i \(-0.707091\pi\)
0.0475184 + 0.998870i \(0.484869\pi\)
\(510\) 0 0
\(511\) −10.7953 61.2231i −0.477555 2.70835i
\(512\) 1.00000i 0.0441942i
\(513\) 16.3512 16.2613i 0.721922 0.717954i
\(514\) −0.159696 −0.00704389
\(515\) 0 0
\(516\) −1.28333 + 1.07684i −0.0564954 + 0.0474053i
\(517\) −2.70118 7.42143i −0.118798 0.326394i
\(518\) 3.37353 9.26871i 0.148225 0.407244i
\(519\) −13.3416 11.1949i −0.585630 0.491402i
\(520\) 0 0
\(521\) −0.583692 1.01098i −0.0255720 0.0442920i 0.852956 0.521983i \(-0.174807\pi\)
−0.878528 + 0.477690i \(0.841474\pi\)
\(522\) 4.64388 + 0.818841i 0.203257 + 0.0358397i
\(523\) 9.28028 + 1.63636i 0.405798 + 0.0715532i 0.372822 0.927903i \(-0.378390\pi\)
0.0329765 + 0.999456i \(0.489501\pi\)
\(524\) −0.868533 1.50434i −0.0379420 0.0657175i
\(525\) 0 0
\(526\) −7.09280 5.95157i −0.309261 0.259501i
\(527\) 3.49309 9.59718i 0.152161 0.418060i
\(528\) −1.67344 4.59773i −0.0728271 0.200091i
\(529\) 16.8119 14.1068i 0.730951 0.613341i
\(530\) 0 0
\(531\) −24.8714 −1.07933
\(532\) −21.4089 + 1.81359i −0.928193 + 0.0786293i
\(533\) 5.68637i 0.246304i
\(534\) −1.94353 11.0223i −0.0841050 0.476983i
\(535\) 0 0
\(536\) −12.8194 + 4.66590i −0.553716 + 0.201536i
\(537\) −3.83640 + 10.5404i −0.165553 + 0.454853i
\(538\) −8.02092 + 9.55896i −0.345807 + 0.412116i
\(539\) 38.1489 66.0759i 1.64319 2.84609i
\(540\) 0 0
\(541\) −7.26524 + 41.2032i −0.312357 + 1.77147i 0.274314 + 0.961640i \(0.411549\pi\)
−0.586671 + 0.809825i \(0.699562\pi\)
\(542\) 27.7806 + 4.89846i 1.19328 + 0.210407i
\(543\) 2.57308 1.48557i 0.110422 0.0637520i
\(544\) −2.51269 + 4.35211i −0.107731 + 0.186595i
\(545\) 0 0
\(546\) −13.5627 4.93642i −0.580430 0.211259i
\(547\) −9.61418 26.4147i −0.411073 1.12941i −0.956622 0.291334i \(-0.905901\pi\)
0.545549 0.838079i \(-0.316321\pi\)
\(548\) −1.60546 1.91332i −0.0685820 0.0817328i
\(549\) −4.45942 25.2906i −0.190323 1.07938i
\(550\) 0 0
\(551\) 0.980372 + 11.5730i 0.0417653 + 0.493025i
\(552\) 1.13854i 0.0484594i
\(553\) −13.7599 + 2.42623i −0.585129 + 0.103174i
\(554\) 6.44384 5.40702i 0.273772 0.229722i
\(555\) 0 0
\(556\) −11.1185 4.04681i −0.471530 0.171623i
\(557\) −7.93117 + 9.45200i −0.336055 + 0.400494i −0.907436 0.420190i \(-0.861963\pi\)
0.571381 + 0.820685i \(0.306408\pi\)
\(558\) 3.11478 + 1.79832i 0.131859 + 0.0761289i
\(559\) 1.99364 + 3.45308i 0.0843218 + 0.146050i
\(560\) 0 0
\(561\) −4.26971 + 24.2147i −0.180267 + 1.02235i
\(562\) −19.3507 + 11.1721i −0.816259 + 0.471268i
\(563\) −12.5114 7.22347i −0.527293 0.304433i 0.212620 0.977135i \(-0.431800\pi\)
−0.739914 + 0.672702i \(0.765134\pi\)
\(564\) 1.52123 + 1.27647i 0.0640555 + 0.0537490i
\(565\) 0 0
\(566\) 11.9965 4.36638i 0.504252 0.183533i
\(567\) −1.77060 2.11012i −0.0743581 0.0886166i
\(568\) 15.3612 2.70859i 0.644540 0.113650i
\(569\) −31.8303 −1.33439 −0.667197 0.744881i \(-0.732506\pi\)
−0.667197 + 0.744881i \(0.732506\pi\)
\(570\) 0 0
\(571\) −9.10909 −0.381204 −0.190602 0.981667i \(-0.561044\pi\)
−0.190602 + 0.981667i \(0.561044\pi\)
\(572\) −11.4684 + 2.02218i −0.479516 + 0.0845516i
\(573\) 2.67432 + 3.18714i 0.111722 + 0.133145i
\(574\) −9.97700 + 3.63133i −0.416432 + 0.151569i
\(575\) 0 0
\(576\) −1.35570 1.13756i −0.0564873 0.0473985i
\(577\) −10.1300 5.84857i −0.421718 0.243479i 0.274094 0.961703i \(-0.411622\pi\)
−0.695812 + 0.718224i \(0.744955\pi\)
\(578\) 7.14863 4.12726i 0.297344 0.171671i
\(579\) −2.77978 + 15.7649i −0.115524 + 0.655167i
\(580\) 0 0
\(581\) 17.9496 + 31.0896i 0.744674 + 1.28981i
\(582\) −11.4380 6.60375i −0.474122 0.273734i
\(583\) 15.9459 19.0036i 0.660413 0.787050i
\(584\) 11.8517 + 4.31365i 0.490425 + 0.178500i
\(585\) 0 0
\(586\) 22.1470 18.5836i 0.914885 0.767680i
\(587\) 30.2839 5.33986i 1.24995 0.220400i 0.490774 0.871287i \(-0.336714\pi\)
0.759175 + 0.650887i \(0.225603\pi\)
\(588\) 19.1846i 0.791160i
\(589\) −2.31635 + 8.55040i −0.0954435 + 0.352313i
\(590\) 0 0
\(591\) 3.81359 + 21.6280i 0.156870 + 0.889655i
\(592\) 1.28627 + 1.53291i 0.0528652 + 0.0630023i
\(593\) 2.12039 + 5.82573i 0.0870741 + 0.239234i 0.975585 0.219621i \(-0.0704820\pi\)
−0.888511 + 0.458855i \(0.848260\pi\)
\(594\) −21.9300 7.98186i −0.899798 0.327500i
\(595\) 0 0
\(596\) 10.0711 17.4437i 0.412530 0.714523i
\(597\) −19.1924 + 11.0807i −0.785491 + 0.453503i
\(598\) −2.66864 0.470554i −0.109129 0.0192424i
\(599\) 5.09116 28.8734i 0.208019 1.17973i −0.684599 0.728920i \(-0.740022\pi\)
0.892618 0.450815i \(-0.148866\pi\)
\(600\) 0 0
\(601\) 23.1718 40.1348i 0.945199 1.63713i 0.189846 0.981814i \(-0.439201\pi\)
0.755353 0.655318i \(-0.227466\pi\)
\(602\) 4.78544 5.70307i 0.195040 0.232440i
\(603\) −8.25740 + 22.6870i −0.336267 + 0.923887i
\(604\) −7.21563 + 2.62627i −0.293600 + 0.106862i
\(605\) 0 0
\(606\) −0.278162 1.57754i −0.0112996 0.0640830i
\(607\) 25.4409i 1.03262i 0.856403 + 0.516308i \(0.172694\pi\)
−0.856403 + 0.516308i \(0.827306\pi\)
\(608\) 1.85303 3.94541i 0.0751503 0.160008i
\(609\) 14.5677 0.590312
\(610\) 0 0
\(611\) 3.62066 3.03810i 0.146476 0.122908i
\(612\) 3.04179 + 8.35725i 0.122957 + 0.337822i
\(613\) 10.4412 28.6870i 0.421717 1.15866i −0.529006 0.848618i \(-0.677435\pi\)
0.950723 0.310041i \(-0.100343\pi\)
\(614\) 17.9758 + 15.0835i 0.725444 + 0.608720i
\(615\) 0 0
\(616\) 10.8717 + 18.8304i 0.438035 + 0.758698i
\(617\) 6.00494 + 1.05883i 0.241750 + 0.0426270i 0.293210 0.956048i \(-0.405276\pi\)
−0.0514603 + 0.998675i \(0.516388\pi\)
\(618\) 4.87323 + 0.859283i 0.196030 + 0.0345654i
\(619\) 9.07568 + 15.7195i 0.364782 + 0.631821i 0.988741 0.149636i \(-0.0478101\pi\)
−0.623959 + 0.781457i \(0.714477\pi\)
\(620\) 0 0
\(621\) −4.16002 3.49067i −0.166936 0.140076i
\(622\) −1.45193 + 3.98914i −0.0582171 + 0.159950i
\(623\) 17.0116 + 46.7389i 0.681554 + 1.87255i
\(624\) 2.24308 1.88217i 0.0897950 0.0753469i
\(625\) 0 0
\(626\) 11.6148 0.464221
\(627\) 1.91734 21.2409i 0.0765712 0.848279i
\(628\) 5.80070i 0.231473i
\(629\) −1.74624 9.90340i −0.0696270 0.394874i
\(630\) 0 0
\(631\) −14.9306 + 5.43428i −0.594376 + 0.216335i −0.621653 0.783293i \(-0.713539\pi\)
0.0272768 + 0.999628i \(0.491316\pi\)
\(632\) 0.969492 2.66366i 0.0385643 0.105955i
\(633\) −9.73368 + 11.6001i −0.386879 + 0.461064i
\(634\) 1.11812 1.93664i 0.0444061 0.0769137i
\(635\) 0 0
\(636\) −1.08316 + 6.14292i −0.0429502 + 0.243582i
\(637\) 44.9672 + 7.92893i 1.78167 + 0.314156i
\(638\) 10.1791 5.87692i 0.402995 0.232669i
\(639\) 13.8023 23.9063i 0.546010 0.945717i
\(640\) 0 0
\(641\) 33.1458 + 12.0641i 1.30918 + 0.476503i 0.899976 0.435940i \(-0.143584\pi\)
0.409205 + 0.912443i \(0.365806\pi\)
\(642\) 2.98288 + 8.19540i 0.117725 + 0.323447i
\(643\) 5.36891 + 6.39841i 0.211729 + 0.252329i 0.861448 0.507846i \(-0.169558\pi\)
−0.649719 + 0.760174i \(0.725113\pi\)
\(644\) 0.878594 + 4.98275i 0.0346215 + 0.196348i
\(645\) 0 0
\(646\) −17.9782 + 12.5148i −0.707343 + 0.492387i
\(647\) 12.0057i 0.471991i −0.971754 0.235995i \(-0.924165\pi\)
0.971754 0.235995i \(-0.0758350\pi\)
\(648\) 0.550344 0.0970404i 0.0216195 0.00381211i
\(649\) −47.4903 + 39.8491i −1.86416 + 1.56421i
\(650\) 0 0
\(651\) 10.4410 + 3.80023i 0.409216 + 0.148943i
\(652\) 6.89356 8.21542i 0.269973 0.321741i
\(653\) −33.8062 19.5180i −1.32294 0.763798i −0.338741 0.940880i \(-0.610001\pi\)
−0.984196 + 0.177081i \(0.943334\pi\)
\(654\) −1.39884 2.42285i −0.0546988 0.0947411i
\(655\) 0 0
\(656\) 0.374037 2.12127i 0.0146037 0.0828216i
\(657\) 19.3300 11.1602i 0.754136 0.435401i
\(658\) −7.64265 4.41248i −0.297941 0.172017i
\(659\) 3.38617 + 2.84133i 0.131906 + 0.110683i 0.706354 0.707859i \(-0.250339\pi\)
−0.574448 + 0.818541i \(0.694783\pi\)
\(660\) 0 0
\(661\) 5.32012 1.93636i 0.206929 0.0753159i −0.236476 0.971637i \(-0.575993\pi\)
0.443405 + 0.896321i \(0.353770\pi\)
\(662\) 0.327351 + 0.390122i 0.0127229 + 0.0151625i
\(663\) −14.4914 + 2.55523i −0.562801 + 0.0992370i
\(664\) −7.28306 −0.282638
\(665\) 0 0
\(666\) 3.54137 0.137225
\(667\) 2.69352 0.474940i 0.104294 0.0183898i
\(668\) −6.35922 7.57862i −0.246046 0.293226i
\(669\) 24.1611 8.79392i 0.934122 0.339992i
\(670\) 0 0
\(671\) −49.0357 41.1458i −1.89300 1.58842i
\(672\) −4.73478 2.73363i −0.182648 0.105452i
\(673\) −14.1761 + 8.18457i −0.546448 + 0.315492i −0.747688 0.664050i \(-0.768836\pi\)
0.201240 + 0.979542i \(0.435503\pi\)
\(674\) −2.61882 + 14.8520i −0.100873 + 0.572079i
\(675\) 0 0
\(676\) 3.01541 + 5.22284i 0.115977 + 0.200878i
\(677\) 16.2304 + 9.37064i 0.623786 + 0.360143i 0.778341 0.627841i \(-0.216061\pi\)
−0.154556 + 0.987984i \(0.549395\pi\)
\(678\) 1.85238 2.20758i 0.0711402 0.0847816i
\(679\) 55.1540 + 20.0744i 2.11662 + 0.770386i
\(680\) 0 0
\(681\) 6.26969 5.26089i 0.240255 0.201598i
\(682\) 8.82873 1.55674i 0.338070 0.0596108i
\(683\) 11.1202i 0.425501i −0.977107 0.212751i \(-0.931758\pi\)
0.977107 0.212751i \(-0.0682422\pi\)
\(684\) −3.24084 7.00030i −0.123917 0.267663i
\(685\) 0 0
\(686\) −8.81296 49.9808i −0.336480 1.90828i
\(687\) 9.44247 + 11.2531i 0.360253 + 0.429333i
\(688\) 0.516578 + 1.41929i 0.0196944 + 0.0541098i
\(689\) 13.9509 + 5.07769i 0.531485 + 0.193445i
\(690\) 0 0
\(691\) −5.97792 + 10.3541i −0.227411 + 0.393887i −0.957040 0.289956i \(-0.906359\pi\)
0.729629 + 0.683843i \(0.239693\pi\)
\(692\) −13.5983 + 7.85098i −0.516929 + 0.298449i
\(693\) 37.8956 + 6.68201i 1.43953 + 0.253829i
\(694\) 5.86560 33.2655i 0.222655 1.26274i
\(695\) 0 0
\(696\) −1.47771 + 2.55947i −0.0560126 + 0.0970166i
\(697\) −6.95795 + 8.29216i −0.263551 + 0.314088i
\(698\) −0.0112278 + 0.0308480i −0.000424977 + 0.00116761i
\(699\) −15.7803 + 5.74355i −0.596865 + 0.217241i
\(700\) 0 0
\(701\) 3.45791 + 19.6108i 0.130603 + 0.740689i 0.977821 + 0.209443i \(0.0671650\pi\)
−0.847217 + 0.531246i \(0.821724\pi\)
\(702\) 13.9664i 0.527128i
\(703\) 2.23432 + 8.43146i 0.0842688 + 0.317999i
\(704\) −4.41122 −0.166254
\(705\) 0 0
\(706\) 0.215239 0.180607i 0.00810064 0.00679725i
\(707\) 2.43473 + 6.68935i 0.0915673 + 0.251579i
\(708\) 5.33142 14.6480i 0.200367 0.550504i
\(709\) 9.27123 + 7.77949i 0.348188 + 0.292165i 0.800062 0.599917i \(-0.204800\pi\)
−0.451874 + 0.892082i \(0.649244\pi\)
\(710\) 0 0
\(711\) −2.50825 4.34442i −0.0940667 0.162928i
\(712\) −9.93743 1.75224i −0.372421 0.0656679i
\(713\) 2.05441 + 0.362248i 0.0769383 + 0.0135663i
\(714\) 13.7375 + 23.7941i 0.514115 + 0.890473i
\(715\) 0 0
\(716\) 7.74689 + 6.50041i 0.289515 + 0.242932i
\(717\) −4.43334 + 12.1805i −0.165566 + 0.454889i
\(718\) −4.51759 12.4120i −0.168595 0.463211i
\(719\) −22.9902 + 19.2911i −0.857389 + 0.719435i −0.961404 0.275141i \(-0.911275\pi\)
0.104015 + 0.994576i \(0.466831\pi\)
\(720\) 0 0
\(721\) −21.9906 −0.818972
\(722\) 14.6219 12.1326i 0.544172 0.451527i
\(723\) 14.1505i 0.526263i
\(724\) −0.465151 2.63800i −0.0172872 0.0980407i
\(725\) 0 0
\(726\) −8.81652 + 3.20895i −0.327212 + 0.119095i
\(727\) −14.4115 + 39.5954i −0.534494 + 1.46851i 0.319175 + 0.947696i \(0.396594\pi\)
−0.853669 + 0.520815i \(0.825628\pi\)
\(728\) −8.36428 + 9.96816i −0.310001 + 0.369445i
\(729\) 9.29655 16.1021i 0.344317 0.596374i
\(730\) 0 0
\(731\) 1.31803 7.47490i 0.0487490 0.276469i
\(732\) 15.8508 + 2.79492i 0.585862 + 0.103303i
\(733\) 7.24116 4.18069i 0.267458 0.154417i −0.360274 0.932847i \(-0.617317\pi\)
0.627732 + 0.778429i \(0.283983\pi\)
\(734\) −5.15220 + 8.92387i −0.190171 + 0.329386i
\(735\) 0 0
\(736\) −0.964570 0.351075i −0.0355545 0.0129408i
\(737\) 20.5823 + 56.5494i 0.758159 + 2.08302i
\(738\) −2.45030 2.92016i −0.0901969 0.107492i
\(739\) 3.03167 + 17.1935i 0.111522 + 0.632472i 0.988414 + 0.151784i \(0.0485019\pi\)
−0.876892 + 0.480688i \(0.840387\pi\)
\(740\) 0 0
\(741\) 12.3376 3.26943i 0.453232 0.120105i
\(742\) 27.7200i 1.01763i
\(743\) −15.4396 + 2.72242i −0.566424 + 0.0998758i −0.449524 0.893268i \(-0.648407\pi\)
−0.116899 + 0.993144i \(0.537295\pi\)
\(744\) −1.72680 + 1.44896i −0.0633075 + 0.0531213i
\(745\) 0 0
\(746\) 26.6774 + 9.70980i 0.976731 + 0.355501i
\(747\) −8.28494 + 9.87361i −0.303130 + 0.361257i
\(748\) 19.1981 + 11.0840i 0.701953 + 0.405273i
\(749\) −19.3787 33.5649i −0.708083 1.22644i
\(750\) 0 0
\(751\) −0.425213 + 2.41150i −0.0155162 + 0.0879970i −0.991583 0.129476i \(-0.958670\pi\)
0.976066 + 0.217473i \(0.0697815\pi\)
\(752\) 1.55051 0.895185i 0.0565412 0.0326441i
\(753\) −25.7975 14.8942i −0.940111 0.542774i
\(754\) 5.38848 + 4.52147i 0.196237 + 0.164662i
\(755\) 0 0
\(756\) −24.5047 + 8.91898i −0.891228 + 0.324380i
\(757\) 17.7921 + 21.2038i 0.646664 + 0.770664i 0.985407 0.170215i \(-0.0544461\pi\)
−0.338743 + 0.940879i \(0.610002\pi\)
\(758\) −18.9068 + 3.33377i −0.686725 + 0.121088i
\(759\) −5.02234 −0.182299
\(760\) 0 0
\(761\) −34.7738 −1.26055 −0.630275 0.776372i \(-0.717058\pi\)
−0.630275 + 0.776372i \(0.717058\pi\)
\(762\) 22.6368 3.99148i 0.820046 0.144596i
\(763\) 7.99162 + 9.52404i 0.289316 + 0.344793i
\(764\) 3.52479 1.28292i 0.127522 0.0464143i
\(765\) 0 0
\(766\) −15.9934 13.4201i −0.577866 0.484887i
\(767\) −32.1302 18.5504i −1.16015 0.669815i
\(768\) 0.960572 0.554587i 0.0346617 0.0200119i
\(769\) 1.17313 6.65313i 0.0423040 0.239918i −0.956322 0.292314i \(-0.905575\pi\)
0.998626 + 0.0523962i \(0.0166859\pi\)
\(770\) 0 0
\(771\) −0.0885653 0.153400i −0.00318960 0.00552455i
\(772\) 12.4989 + 7.21623i 0.449844 + 0.259718i
\(773\) 7.77917 9.27086i 0.279797 0.333450i −0.607782 0.794104i \(-0.707941\pi\)
0.887580 + 0.460654i \(0.152385\pi\)
\(774\) 2.51176 + 0.914207i 0.0902834 + 0.0328605i
\(775\) 0 0
\(776\) −9.12169 + 7.65401i −0.327450 + 0.274763i
\(777\) 10.7742 1.89978i 0.386522 0.0681542i
\(778\) 15.5273i 0.556680i
\(779\) 5.40650 7.67617i 0.193708 0.275027i
\(780\) 0 0
\(781\) −11.9482 67.7615i −0.427540 2.42470i
\(782\) 3.31577 + 3.95159i 0.118572 + 0.141308i
\(783\) 4