Properties

Label 950.2.u.g.549.2
Level $950$
Weight $2$
Character 950.549
Analytic conductor $7.586$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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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 549.2
Character \(\chi\) \(=\) 950.549
Dual form 950.2.u.g.199.2

$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).

\(n\) \(77\) \(401\)
\(\chi(n)\) \(-1\) \(e\left(\frac{5}{9}\right)\)

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 \(-0.881525\pi\)
0.519900 + 0.854227i \(0.325969\pi\)
\(4\) 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 0.624870 0.780729i \(-0.285152\pi\)
0.988566 0.150789i \(-0.0481814\pi\)
\(8\) −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 0.314264 + 0.949336i \(0.398242\pi\)
−0.979281 + 0.202507i \(0.935091\pi\)
\(12\) −0.960572 + 0.554587i −0.277293 + 0.160095i
\(13\) −1.69691 2.02230i −0.470638 0.560884i 0.477546 0.878607i \(-0.341526\pi\)
−0.948184 + 0.317722i \(0.897082\pi\)
\(14\) −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 \(-0.235848\pi\)
0.462483 + 0.886628i \(0.346959\pi\)
\(18\) 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 \(-0.854759\pi\)
0.970898 + 0.239493i \(0.0769811\pi\)
\(24\) 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 −0.997154 0.0753868i \(-0.975981\pi\)
0.911235 0.411887i \(-0.135130\pi\)
\(30\) 0 0
\(31\) −1.01615 1.76003i −0.182506 0.316110i 0.760227 0.649657i \(-0.225088\pi\)
−0.942733 + 0.333547i \(0.891754\pi\)
\(32\) −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 0.762477 0.647015i \(-0.223983\pi\)
−0.504782 + 0.863247i \(0.668427\pi\)
\(42\) 1.86991 5.13754i 0.288534 0.792740i
\(43\) 0.516578 + 1.41929i 0.0787775 + 0.216439i 0.972829 0.231525i \(-0.0743714\pi\)
−0.894052 + 0.447964i \(0.852149\pi\)
\(44\) −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 \(-0.597238\pi\)
0.0435690 + 0.999050i \(0.486127\pi\)
\(48\) −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 0.734670 + 0.678425i \(0.237337\pi\)
−0.998873 + 0.0474667i \(0.984885\pi\)
\(54\) 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 0.238869 + 0.971052i \(0.423223\pi\)
−0.556583 + 0.830792i \(0.687888\pi\)
\(60\) 0 0
\(61\) 13.6360 + 4.96308i 1.74590 + 0.635457i 0.999547 0.0300876i \(-0.00957861\pi\)
0.746358 + 0.665545i \(0.231801\pi\)
\(62\) 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 \(-0.241988\pi\)
0.916657 + 0.399674i \(0.130877\pi\)
\(68\) 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 0.740287 0.672291i \(-0.234690\pi\)
0.999233 + 0.0391574i \(0.0124674\pi\)
\(72\) 0.605285 1.66301i 0.0713335 0.195987i
\(73\) −8.10702 + 9.66157i −0.948855 + 1.13080i 0.0424348 + 0.999099i \(0.486489\pi\)
−0.991289 + 0.131702i \(0.957956\pi\)
\(74\) 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 0.756716 0.653744i \(-0.226803\pi\)
−0.512410 + 0.858741i \(0.671247\pi\)
\(80\) 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 \(-0.535778\pi\)
0.804480 + 0.593980i \(0.202444\pi\)
\(84\) −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 −0.952825 0.303520i \(-0.901838\pi\)
0.133452 + 0.991055i \(0.457394\pi\)
\(90\) 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 \(-0.237812\pi\)
0.457002 + 0.889466i \(0.348923\pi\)
\(98\) −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 −0.696168 0.717879i \(-0.745113\pi\)
0.586085 + 0.810250i \(0.300669\pi\)
\(102\) 4.82725 2.78701i 0.477969 0.275955i
\(103\) −3.86364 2.23068i −0.380696 0.219795i 0.297425 0.954745i \(-0.403872\pi\)
−0.678121 + 0.734950i \(0.737206\pi\)
\(104\) 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 \(-0.790767\pi\)
0.133329 + 0.991072i \(0.457433\pi\)
\(108\) −3.40064 4.05273i −0.327227 0.389974i
\(109\) −2.37019 + 0.862678i −0.227023 + 0.0826296i −0.453027 0.891497i \(-0.649656\pi\)
0.226004 + 0.974126i \(0.427434\pi\)
\(110\) 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 −0.892213 0.451614i \(-0.850848\pi\)
−0.289822 0.957080i \(-0.593596\pi\)
\(128\) −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 −0.995145 0.0984163i \(-0.968622\pi\)
0.968791 + 0.247879i \(0.0797334\pi\)
\(132\) 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 \(-0.854862\pi\)
0.970820 + 0.239808i \(0.0770844\pi\)
\(138\) −0.389403 1.06988i −0.0331482 0.0910738i
\(139\) −9.06390 + 7.60552i −0.768790 + 0.645092i −0.940399 0.340074i \(-0.889548\pi\)
0.171609 + 0.985165i \(0.445104\pi\)
\(140\) 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 0.995237 + 0.0974880i \(0.0310808\pi\)
0.268828 + 0.963188i \(0.413364\pi\)
\(150\) 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 \(-0.0367565\pi\)
−0.835003 + 0.550245i \(0.814534\pi\)
\(158\) −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 \(-0.471304\pi\)
−0.817495 + 0.575936i \(0.804638\pi\)
\(164\) 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 −0.737208 0.675666i \(-0.763856\pi\)
0.999044 0.0437226i \(-0.0139218\pi\)
\(168\) 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 \(-0.240844\pi\)
0.448510 + 0.893778i \(0.351955\pi\)
\(174\) −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 −0.612827 0.790217i \(-0.709968\pi\)
0.990762 + 0.135615i \(0.0433010\pi\)
\(180\) 0 0
\(181\) 0.465151 + 2.63800i 0.0345744 + 0.196081i 0.997203 0.0747449i \(-0.0238142\pi\)
−0.962628 + 0.270826i \(0.912703\pi\)
\(182\) 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 \(-0.951635\pi\)
0.320706 + 0.947179i \(0.396080\pi\)
\(194\) −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 \(-0.915875\pi\)
−0.256415 + 0.966567i \(0.582541\pi\)
\(198\) 6.76079 + 3.90335i 0.480469 + 0.277399i
\(199\) −3.46951 19.6766i −0.245947 1.39484i −0.818282 0.574817i \(-0.805073\pi\)
0.572335 0.820020i \(-0.306038\pi\)
\(200\) 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 −0.787687 0.616076i \(-0.788721\pi\)
0.950894 0.309518i \(-0.100168\pi\)
\(212\) −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 −0.857976 0.513690i \(-0.828278\pi\)
0.327054 0.945006i \(-0.393944\pi\)
\(224\) −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 0.985612 + 0.169025i \(0.0540620\pi\)
−0.646375 + 0.763020i \(0.723716\pi\)
\(234\) −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 −0.612802 0.790237i \(-0.709958\pi\)
0.990766 + 0.135583i \(0.0432909\pi\)
\(240\) 0 0
\(241\) 9.77297 8.20049i 0.629532 0.528240i −0.271251 0.962509i \(-0.587437\pi\)
0.900784 + 0.434268i \(0.142993\pi\)
\(242\) 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 −0.614964 0.788556i \(-0.710829\pi\)
−0.977963 + 0.208778i \(0.933051\pi\)
\(252\) 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 \(-0.553970\pi\)
0.178551 + 0.983931i \(0.442859\pi\)
\(258\) 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 \(-0.685629\pi\)
0.917663 + 0.397360i \(0.130073\pi\)
\(264\) −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 0.303052 0.952974i \(-0.401995\pi\)
−0.885872 + 0.463930i \(0.846439\pi\)
\(270\) 0 0
\(271\) 26.5079 9.64808i 1.61024 0.586079i 0.628752 0.777606i \(-0.283566\pi\)
0.981487 + 0.191526i \(0.0613437\pi\)
\(272\) 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 \(-0.414655\pi\)
−0.702624 + 0.711562i \(0.747988\pi\)
\(278\) 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 −0.371294 0.928515i \(-0.621086\pi\)
−0.881266 + 0.472621i \(0.843308\pi\)
\(282\) −1.27647 + 1.52123i −0.0760125 + 0.0905882i
\(283\) −12.5725 2.21687i −0.747357 0.131779i −0.213016 0.977049i \(-0.568329\pi\)
−0.534340 + 0.845269i \(0.679440\pi\)
\(284\) 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 \(-0.653433\pi\)
−0.999136 + 0.0415616i \(0.986767\pi\)
\(294\) −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 0.138507 + 0.990361i \(0.455770\pi\)
−0.999367 + 0.0355713i \(0.988675\pi\)
\(308\) −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 0.799549 0.600600i \(-0.205072\pi\)
−0.919910 + 0.392130i \(0.871738\pi\)
\(312\) −2.53584 1.46407i −0.143563 0.0828864i
\(313\) −11.4384 + 2.01689i −0.646534 + 0.114001i −0.487293 0.873238i \(-0.662016\pi\)
−0.159241 + 0.987240i \(0.550905\pi\)
\(314\) −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 \(-0.242225\pi\)
−0.804899 + 0.593411i \(0.797781\pi\)
\(318\) 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 −0.858943 0.512072i \(-0.828878\pi\)
0.872939 + 0.487830i \(0.162211\pi\)
\(332\) 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 0.997247 + 0.0741552i \(0.0236260\pi\)
−0.716269 + 0.697824i \(0.754152\pi\)
\(338\) −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 −0.706506 0.707707i \(-0.749730\pi\)
0.0863093 0.996268i \(-0.472493\pi\)
\(348\) 1.89971 + 2.26399i 0.101835 + 0.121363i
\(349\) −0.0164139 0.0284297i −0.000878615 0.00152181i 0.865586 0.500761i \(-0.166946\pi\)
−0.866464 + 0.499239i \(0.833613\pi\)
\(350\) 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 \(-0.335713\pi\)
−0.506462 + 0.862262i \(0.669047\pi\)
\(354\) 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 0.862520 + 0.506023i \(0.168885\pi\)
−0.983574 + 0.180507i \(0.942226\pi\)
\(360\) 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 \(-0.135548\pi\)
−0.564948 + 0.825127i \(0.691104\pi\)
\(368\) 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 \(-0.929474\pi\)
−0.297463 + 0.954733i \(0.596141\pi\)
\(374\) 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 \(-0.598689\pi\)
0.990833 + 0.135095i \(0.0431339\pi\)
\(384\) 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 −0.973656 0.228023i \(-0.926774\pi\)
0.836949 0.547281i \(-0.184337\pi\)
\(390\) 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 \(-0.405877\pi\)
−0.0533453 + 0.998576i \(0.516988\pi\)
\(398\) 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 0.882275 + 0.470735i \(0.156011\pi\)
−0.990068 + 0.140591i \(0.955100\pi\)
\(402\) 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 0.964696 + 0.263367i \(0.0848332\pi\)
−0.816440 + 0.577430i \(0.804056\pi\)
\(410\) 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 0.992715 0.120489i \(-0.0384462\pi\)
0.0537246 + 0.998556i \(0.482891\pi\)
\(422\) −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 −0.311151 0.950360i \(-0.600715\pi\)
0.881892 + 0.471452i \(0.156270\pi\)
\(432\) −1.80944 4.97141i −0.0870569 0.239187i
\(433\) −4.81630 + 13.2327i −0.231457 + 0.635922i −0.999992 0.00388467i \(-0.998763\pi\)
0.768536 + 0.639807i \(0.220986\pi\)
\(434\) 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 0.921743 + 0.387801i \(0.126765\pi\)
−0.998791 + 0.0491593i \(0.984346\pi\)
\(440\) 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 \(-0.131009\pi\)
−0.553125 + 0.833098i \(0.686565\pi\)
\(444\) −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 0.529754 0.848151i \(-0.322284\pi\)
−0.999398 + 0.0347048i \(0.988951\pi\)
\(450\) 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 −0.907719 0.419578i \(-0.862178\pi\)
−0.425653 + 0.904886i \(0.639956\pi\)
\(462\) 15.5023 + 18.4749i 0.721232 + 0.859530i
\(463\) 19.3969 11.1988i 0.901452 0.520454i 0.0237813 0.999717i \(-0.492429\pi\)
0.877671 + 0.479263i \(0.159096\pi\)
\(464\) 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 \(-0.222214\pi\)
−0.173623 + 0.984812i \(0.555547\pi\)
\(468\) 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 −0.307979 0.951393i \(-0.599653\pi\)
−0.847469 + 0.530844i \(0.821875\pi\)
\(480\) 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 \(-0.770801\pi\)
0.195191 + 0.980765i \(0.437467\pi\)
\(488\) −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 0.795171 0.606385i \(-0.207381\pi\)
−0.459092 + 0.888389i \(0.651825\pi\)
\(492\) −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 −0.587501 0.809223i \(-0.699888\pi\)
0.0701069 + 0.997539i \(0.477666\pi\)
\(500\) 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 \(-0.743087\pi\)
−0.402839 + 0.915271i \(0.631976\pi\)
\(504\) −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 0.0475184 0.998870i \(-0.484869\pi\)
−0.605660 + 0.795723i \(0.707091\pi\)
\(510\) 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 −0.878528 0.477690i \(-0.841474\pi\)
0.852956 + 0.521983i \(0.174807\pi\)
\(522\) −4.64388 + 0.818841i −0.203257 + 0.0358397i
\(523\) −9.28028 + 1.63636i −0.405798 + 0.0715532i −0.372822 0.927903i \(-0.621610\pi\)
−0.0329765 + 0.999456i \(0.510499\pi\)
\(524\) −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 −0.586671 0.809825i \(-0.699562\pi\)
0.274314 0.961640i \(-0.411549\pi\)
\(542\) −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 −0.545549 0.838079i \(-0.683679\pi\)
0.956622 0.291334i \(-0.0940990\pi\)
\(548\) 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 \(-0.138037\pi\)
−0.571381 + 0.820685i \(0.693592\pi\)
\(558\) −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 \(-0.568200\pi\)
0.739914 + 0.672702i \(0.234866\pi\)
\(564\) 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 \(-0.588378\pi\)
0.695812 + 0.718224i \(0.255045\pi\)
\(578\) −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 \(-0.663286\pi\)
−0.759175 + 0.650887i \(0.774397\pi\)
\(588\) 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 \(-0.929518\pi\)
0.888511 + 0.458855i \(0.151740\pi\)
\(594\) −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 0.892618 + 0.450815i \(0.148866\pi\)
−0.684599 + 0.728920i \(0.740022\pi\)
\(600\) 0 0
\(601\) 23.1718 + 40.1348i 0.945199 + 1.63713i 0.755353 + 0.655318i \(0.227466\pi\)
0.189846 + 0.981814i \(0.439201\pi\)
\(602\) −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 −0.950723 0.310041i \(-0.899657\pi\)
0.529006 0.848618i \(-0.322565\pi\)
\(614\) 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 \(-0.594724\pi\)
0.0514603 + 0.998675i \(0.483612\pi\)
\(618\) −4.87323 + 0.859283i −0.196030 + 0.0345654i
\(619\) 9.07568 15.7195i 0.364782 0.631821i −0.623959 0.781457i \(-0.714477\pi\)
0.988741 + 0.149636i \(0.0478101\pi\)
\(620\) 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 0.0272768 0.999628i \(-0.491316\pi\)
−0.621653 + 0.783293i \(0.713539\pi\)
\(632\) −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 0.409205 0.912443i \(-0.365806\pi\)
0.899976 + 0.435940i \(0.143584\pi\)
\(642\) −2.98288 + 8.19540i −0.117725 + 0.323447i
\(643\) −5.36891 + 6.39841i −0.211729 + 0.252329i −0.861448 0.507846i \(-0.830442\pi\)
0.649719 + 0.760174i \(0.274887\pi\)
\(644\) 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 \(-0.389999\pi\)
0.984196 + 0.177081i \(0.0566655\pi\)
\(654\) −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 −0.574448 0.818541i \(-0.694783\pi\)
0.706354 + 0.707859i \(0.250339\pi\)
\(660\) 0 0
\(661\) 5.32012 + 1.93636i 0.206929 + 0.0753159i 0.443405 0.896321i \(-0.353770\pi\)
−0.236476 + 0.971637i \(0.575993\pi\)
\(662\) −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 \(-0.231164\pi\)
−0.201240 + 0.979542i \(0.564497\pi\)
\(674\) −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 \(-0.783939\pi\)
0.154556 + 0.987984i \(0.450605\pi\)
\(678\) −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 0.729629 0.683843i \(-0.239693\pi\)
−0.957040 + 0.289956i \(0.906359\pi\)
\(692\) 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 −0.847217 0.531246i \(-0.821724\pi\)
0.977821 0.209443i \(-0.0671650\pi\)
\(702\) 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 −0.451874 0.892082i \(-0.649244\pi\)
0.800062 + 0.599917i \(0.204800\pi\)
\(710\) 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 0.104015 0.994576i \(-0.466831\pi\)
−0.961404 + 0.275141i \(0.911275\pi\)
\(720\) 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 0.853669 + 0.520815i \(0.174372\pi\)
−0.319175 + 0.947696i \(0.603406\pi\)
\(728\) 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 \(-0.382683\pi\)
−0.627732 + 0.778429i \(0.716017\pi\)
\(734\) −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 −0.876892 0.480688i \(-0.840387\pi\)
0.988414 0.151784i \(-0.0485019\pi\)
\(740\) 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 \(-0.351593\pi\)
0.116899 + 0.993144i \(0.462705\pi\)
\(744\) −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 0.976066 0.217473i \(-0.0697815\pi\)
−0.991583 + 0.129476i \(0.958670\pi\)
\(752\) −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 \(-0.945554\pi\)
0.338743 + 0.940879i \(0.389998\pi\)
\(758\) 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 0.998626 0.0523962i \(-0.0166859\pi\)
−0.956322 + 0.292314i \(0.905575\pi\)
\(770\) 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 \(-0.292059\pi\)
−0.887580 + 0.460654i \(0.847615\pi\)
\(774\) 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 +