Properties

Label 950.2.u.h.99.8
Level $950$
Weight $2$
Character 950.99
Analytic conductor $7.586$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [950,2,Mod(99,950)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(950, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("950.99");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
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

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 99.8
Character \(\chi\) \(=\) 950.99
Dual form 950.2.u.h.499.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.342020 - 0.939693i) q^{2} +(2.84564 - 0.501764i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.501764 - 2.84564i) q^{6} +(3.49580 + 2.01830i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(5.02684 - 1.82962i) q^{9} +O(q^{10})\) \(q+(0.342020 - 0.939693i) q^{2} +(2.84564 - 0.501764i) q^{3} +(-0.766044 - 0.642788i) q^{4} +(0.501764 - 2.84564i) q^{6} +(3.49580 + 2.01830i) q^{7} +(-0.866025 + 0.500000i) q^{8} +(5.02684 - 1.82962i) q^{9} +(2.11161 + 3.65741i) q^{11} +(-2.50242 - 1.44477i) q^{12} +(-5.44192 - 0.959556i) q^{13} +(3.09222 - 2.59468i) q^{14} +(0.173648 + 0.984808i) q^{16} +(-0.523948 + 1.43954i) q^{17} -5.34945i q^{18} +(0.805977 - 4.28374i) q^{19} +(10.9605 + 3.98930i) q^{21} +(4.15905 - 0.733353i) q^{22} +(3.83470 - 4.57002i) q^{23} +(-2.21352 + 1.85736i) q^{24} +(-2.76293 + 4.78554i) q^{26} +(5.87931 - 3.39442i) q^{27} +(-1.38060 - 3.79317i) q^{28} +(-4.97373 + 1.81029i) q^{29} +(-1.35962 + 2.35493i) q^{31} +(0.984808 + 0.173648i) q^{32} +(7.84404 + 9.34816i) q^{33} +(1.17352 + 0.984700i) q^{34} +(-5.02684 - 1.82962i) q^{36} +8.71589i q^{37} +(-3.74974 - 2.22249i) q^{38} -15.9672 q^{39} +(-0.560056 - 3.17623i) q^{41} +(7.49743 - 8.93509i) q^{42} +(-1.46718 - 1.74851i) q^{43} +(0.733353 - 4.15905i) q^{44} +(-2.98287 - 5.16648i) q^{46} +(-3.61462 - 9.93108i) q^{47} +(0.988282 + 2.71528i) q^{48} +(4.64708 + 8.04898i) q^{49} +(-0.768663 + 4.35930i) q^{51} +(3.55196 + 4.23306i) q^{52} +(1.66137 - 1.97995i) q^{53} +(-1.17887 - 6.68570i) q^{54} -4.03660 q^{56} +(0.144099 - 12.5944i) q^{57} +5.29293i q^{58} +(-9.90460 - 3.60498i) q^{59} +(-3.45129 - 2.89597i) q^{61} +(1.74789 + 2.08306i) q^{62} +(21.2656 + 3.74969i) q^{63} +(0.500000 - 0.866025i) q^{64} +(11.4672 - 4.17372i) q^{66} +(-3.76316 - 10.3392i) q^{67} +(1.32668 - 0.765961i) q^{68} +(8.61912 - 14.9288i) q^{69} +(-5.73392 + 4.81133i) q^{71} +(-3.43856 + 4.09792i) q^{72} +(1.94167 - 0.342370i) q^{73} +(8.19026 + 2.98101i) q^{74} +(-3.37095 + 2.76346i) q^{76} +17.0474i q^{77} +(-5.46111 + 15.0043i) q^{78} +(-2.15982 - 12.2490i) q^{79} +(2.73346 - 2.29365i) q^{81} +(-3.17623 - 0.560056i) q^{82} +(3.32355 + 1.91885i) q^{83} +(-5.83197 - 10.1013i) q^{84} +(-2.14487 + 0.780669i) q^{86} +(-13.2451 + 7.64707i) q^{87} +(-3.65741 - 2.11161i) q^{88} +(-1.96650 + 11.1526i) q^{89} +(-17.0872 - 14.3378i) q^{91} +(-5.87510 + 1.03594i) q^{92} +(-2.68737 + 7.38349i) q^{93} -10.5684 q^{94} +2.88954 q^{96} +(4.66803 - 12.8253i) q^{97} +(9.15296 - 1.61391i) q^{98} +(17.3064 + 14.5218i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 12 q^{11} + 30 q^{14} + 30 q^{19} - 36 q^{21} - 18 q^{26} + 24 q^{29} + 18 q^{31} + 18 q^{34} - 132 q^{39} + 36 q^{41} - 6 q^{46} + 54 q^{49} - 6 q^{51} - 54 q^{54} - 12 q^{56} - 72 q^{59} + 24 q^{61} + 24 q^{64} + 96 q^{66} - 42 q^{69} - 78 q^{71} - 36 q^{74} + 12 q^{76} + 84 q^{79} - 72 q^{81} - 18 q^{84} - 78 q^{86} + 72 q^{89} + 24 q^{91} - 24 q^{94} + 12 q^{96} - 102 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.342020 0.939693i 0.241845 0.664463i
\(3\) 2.84564 0.501764i 1.64293 0.289693i 0.725690 0.688022i \(-0.241521\pi\)
0.917243 + 0.398328i \(0.130410\pi\)
\(4\) −0.766044 0.642788i −0.383022 0.321394i
\(5\) 0 0
\(6\) 0.501764 2.84564i 0.204844 1.16173i
\(7\) 3.49580 + 2.01830i 1.32129 + 0.762846i 0.983934 0.178531i \(-0.0571346\pi\)
0.337354 + 0.941378i \(0.390468\pi\)
\(8\) −0.866025 + 0.500000i −0.306186 + 0.176777i
\(9\) 5.02684 1.82962i 1.67561 0.609873i
\(10\) 0 0
\(11\) 2.11161 + 3.65741i 0.636674 + 1.10275i 0.986158 + 0.165809i \(0.0530234\pi\)
−0.349484 + 0.936942i \(0.613643\pi\)
\(12\) −2.50242 1.44477i −0.722385 0.417069i
\(13\) −5.44192 0.959556i −1.50932 0.266133i −0.643092 0.765789i \(-0.722349\pi\)
−0.866224 + 0.499656i \(0.833460\pi\)
\(14\) 3.09222 2.59468i 0.826430 0.693457i
\(15\) 0 0
\(16\) 0.173648 + 0.984808i 0.0434120 + 0.246202i
\(17\) −0.523948 + 1.43954i −0.127076 + 0.349139i −0.986873 0.161497i \(-0.948368\pi\)
0.859797 + 0.510636i \(0.170590\pi\)
\(18\) 5.34945i 1.26088i
\(19\) 0.805977 4.28374i 0.184904 0.982757i
\(20\) 0 0
\(21\) 10.9605 + 3.98930i 2.39178 + 0.870537i
\(22\) 4.15905 0.733353i 0.886713 0.156351i
\(23\) 3.83470 4.57002i 0.799591 0.952915i −0.200048 0.979786i \(-0.564110\pi\)
0.999639 + 0.0268711i \(0.00855436\pi\)
\(24\) −2.21352 + 1.85736i −0.451832 + 0.379132i
\(25\) 0 0
\(26\) −2.76293 + 4.78554i −0.541856 + 0.938522i
\(27\) 5.87931 3.39442i 1.13147 0.653257i
\(28\) −1.38060 3.79317i −0.260909 0.716841i
\(29\) −4.97373 + 1.81029i −0.923598 + 0.336162i −0.759669 0.650310i \(-0.774639\pi\)
−0.163929 + 0.986472i \(0.552417\pi\)
\(30\) 0 0
\(31\) −1.35962 + 2.35493i −0.244195 + 0.422958i −0.961905 0.273384i \(-0.911857\pi\)
0.717710 + 0.696342i \(0.245190\pi\)
\(32\) 0.984808 + 0.173648i 0.174091 + 0.0306970i
\(33\) 7.84404 + 9.34816i 1.36547 + 1.62731i
\(34\) 1.17352 + 0.984700i 0.201257 + 0.168875i
\(35\) 0 0
\(36\) −5.02684 1.82962i −0.837807 0.304937i
\(37\) 8.71589i 1.43288i 0.697647 + 0.716442i \(0.254231\pi\)
−0.697647 + 0.716442i \(0.745769\pi\)
\(38\) −3.74974 2.22249i −0.608287 0.360536i
\(39\) −15.9672 −2.55680
\(40\) 0 0
\(41\) −0.560056 3.17623i −0.0874660 0.496044i −0.996797 0.0799712i \(-0.974517\pi\)
0.909331 0.416073i \(-0.136594\pi\)
\(42\) 7.49743 8.93509i 1.15688 1.37871i
\(43\) −1.46718 1.74851i −0.223743 0.266646i 0.642482 0.766301i \(-0.277905\pi\)
−0.866225 + 0.499655i \(0.833460\pi\)
\(44\) 0.733353 4.15905i 0.110557 0.627001i
\(45\) 0 0
\(46\) −2.98287 5.16648i −0.439800 0.761756i
\(47\) −3.61462 9.93108i −0.527246 1.44860i −0.862300 0.506398i \(-0.830977\pi\)
0.335053 0.942199i \(-0.391246\pi\)
\(48\) 0.988282 + 2.71528i 0.142646 + 0.391917i
\(49\) 4.64708 + 8.04898i 0.663869 + 1.14985i
\(50\) 0 0
\(51\) −0.768663 + 4.35930i −0.107634 + 0.610424i
\(52\) 3.55196 + 4.23306i 0.492568 + 0.587020i
\(53\) 1.66137 1.97995i 0.228207 0.271966i −0.639775 0.768562i \(-0.720972\pi\)
0.867982 + 0.496596i \(0.165417\pi\)
\(54\) −1.17887 6.68570i −0.160424 0.909809i
\(55\) 0 0
\(56\) −4.03660 −0.539414
\(57\) 0.144099 12.5944i 0.0190864 1.66817i
\(58\) 5.29293i 0.694996i
\(59\) −9.90460 3.60498i −1.28947 0.469328i −0.395916 0.918287i \(-0.629573\pi\)
−0.893553 + 0.448958i \(0.851795\pi\)
\(60\) 0 0
\(61\) −3.45129 2.89597i −0.441892 0.370792i 0.394525 0.918885i \(-0.370909\pi\)
−0.836417 + 0.548094i \(0.815354\pi\)
\(62\) 1.74789 + 2.08306i 0.221982 + 0.264548i
\(63\) 21.2656 + 3.74969i 2.67921 + 0.472417i
\(64\) 0.500000 0.866025i 0.0625000 0.108253i
\(65\) 0 0
\(66\) 11.4672 4.17372i 1.41152 0.513750i
\(67\) −3.76316 10.3392i −0.459743 1.26313i −0.925677 0.378314i \(-0.876504\pi\)
0.465934 0.884819i \(-0.345718\pi\)
\(68\) 1.32668 0.765961i 0.160884 0.0928864i
\(69\) 8.61912 14.9288i 1.03762 1.79721i
\(70\) 0 0
\(71\) −5.73392 + 4.81133i −0.680491 + 0.570999i −0.916150 0.400836i \(-0.868720\pi\)
0.235659 + 0.971836i \(0.424275\pi\)
\(72\) −3.43856 + 4.09792i −0.405238 + 0.482944i
\(73\) 1.94167 0.342370i 0.227256 0.0400713i −0.0588605 0.998266i \(-0.518747\pi\)
0.286116 + 0.958195i \(0.407636\pi\)
\(74\) 8.19026 + 2.98101i 0.952099 + 0.346536i
\(75\) 0 0
\(76\) −3.37095 + 2.76346i −0.386674 + 0.316991i
\(77\) 17.0474i 1.94274i
\(78\) −5.46111 + 15.0043i −0.618349 + 1.69890i
\(79\) −2.15982 12.2490i −0.242999 1.37812i −0.825094 0.564995i \(-0.808878\pi\)
0.582095 0.813120i \(-0.302233\pi\)
\(80\) 0 0
\(81\) 2.73346 2.29365i 0.303718 0.254850i
\(82\) −3.17623 0.560056i −0.350756 0.0618478i
\(83\) 3.32355 + 1.91885i 0.364807 + 0.210621i 0.671187 0.741288i \(-0.265785\pi\)
−0.306381 + 0.951909i \(0.599118\pi\)
\(84\) −5.83197 10.1013i −0.636320 1.10214i
\(85\) 0 0
\(86\) −2.14487 + 0.780669i −0.231287 + 0.0841817i
\(87\) −13.2451 + 7.64707i −1.42003 + 0.819852i
\(88\) −3.65741 2.11161i −0.389881 0.225098i
\(89\) −1.96650 + 11.1526i −0.208448 + 1.18217i 0.683472 + 0.729976i \(0.260469\pi\)
−0.891921 + 0.452192i \(0.850642\pi\)
\(90\) 0 0
\(91\) −17.0872 14.3378i −1.79122 1.50301i
\(92\) −5.87510 + 1.03594i −0.612522 + 0.108004i
\(93\) −2.68737 + 7.38349i −0.278667 + 0.765632i
\(94\) −10.5684 −1.09005
\(95\) 0 0
\(96\) 2.88954 0.294913
\(97\) 4.66803 12.8253i 0.473967 1.30221i −0.440573 0.897717i \(-0.645225\pi\)
0.914540 0.404496i \(-0.132553\pi\)
\(98\) 9.15296 1.61391i 0.924589 0.163030i
\(99\) 17.3064 + 14.5218i 1.73936 + 1.45949i
\(100\) 0 0
\(101\) −2.46911 + 14.0030i −0.245686 + 1.39335i 0.573209 + 0.819409i \(0.305698\pi\)
−0.818895 + 0.573944i \(0.805413\pi\)
\(102\) 3.83351 + 2.21328i 0.379574 + 0.219147i
\(103\) −6.93582 + 4.00440i −0.683406 + 0.394565i −0.801137 0.598481i \(-0.795771\pi\)
0.117731 + 0.993046i \(0.462438\pi\)
\(104\) 5.19261 1.88996i 0.509178 0.185326i
\(105\) 0 0
\(106\) −1.29232 2.23836i −0.125521 0.217409i
\(107\) 15.1979 + 8.77452i 1.46924 + 0.848265i 0.999405 0.0344902i \(-0.0109807\pi\)
0.469833 + 0.882755i \(0.344314\pi\)
\(108\) −6.68570 1.17887i −0.643332 0.113437i
\(109\) −6.11656 + 5.13241i −0.585861 + 0.491595i −0.886866 0.462027i \(-0.847122\pi\)
0.301005 + 0.953622i \(0.402678\pi\)
\(110\) 0 0
\(111\) 4.37332 + 24.8023i 0.415097 + 2.35413i
\(112\) −1.38060 + 3.79317i −0.130454 + 0.358421i
\(113\) 7.86032i 0.739436i −0.929144 0.369718i \(-0.879454\pi\)
0.929144 0.369718i \(-0.120546\pi\)
\(114\) −11.7856 4.44295i −1.10382 0.416120i
\(115\) 0 0
\(116\) 4.97373 + 1.81029i 0.461799 + 0.168081i
\(117\) −29.1113 + 5.13310i −2.69134 + 0.474555i
\(118\) −6.77514 + 8.07430i −0.623703 + 0.743300i
\(119\) −4.73703 + 3.97484i −0.434243 + 0.364373i
\(120\) 0 0
\(121\) −3.41777 + 5.91975i −0.310706 + 0.538159i
\(122\) −3.90174 + 2.25267i −0.353247 + 0.203947i
\(123\) −3.18744 8.75741i −0.287402 0.789629i
\(124\) 2.55525 0.930034i 0.229468 0.0835195i
\(125\) 0 0
\(126\) 10.7968 18.7006i 0.961856 1.66598i
\(127\) 18.2700 + 3.22150i 1.62120 + 0.285862i 0.909214 0.416328i \(-0.136683\pi\)
0.711989 + 0.702190i \(0.247794\pi\)
\(128\) −0.642788 0.766044i −0.0568149 0.0677094i
\(129\) −5.05241 4.23947i −0.444840 0.373265i
\(130\) 0 0
\(131\) 9.22255 + 3.35673i 0.805778 + 0.293279i 0.711878 0.702303i \(-0.247845\pi\)
0.0938991 + 0.995582i \(0.470067\pi\)
\(132\) 12.2032i 1.06215i
\(133\) 11.4634 13.3484i 0.994003 1.15745i
\(134\) −11.0027 −0.950492
\(135\) 0 0
\(136\) −0.266015 1.50865i −0.0228106 0.129366i
\(137\) −2.10023 + 2.50295i −0.179434 + 0.213842i −0.848263 0.529575i \(-0.822351\pi\)
0.668829 + 0.743417i \(0.266796\pi\)
\(138\) −11.0805 13.2053i −0.943237 1.12411i
\(139\) −0.274807 + 1.55851i −0.0233089 + 0.132191i −0.994242 0.107161i \(-0.965824\pi\)
0.970933 + 0.239352i \(0.0769351\pi\)
\(140\) 0 0
\(141\) −15.2690 26.4466i −1.28588 2.22721i
\(142\) 2.56005 + 7.03369i 0.214835 + 0.590254i
\(143\) −7.98169 21.9295i −0.667463 1.83384i
\(144\) 2.67473 + 4.63276i 0.222894 + 0.386063i
\(145\) 0 0
\(146\) 0.342370 1.94167i 0.0283347 0.160694i
\(147\) 17.2626 + 20.5728i 1.42380 + 1.69682i
\(148\) 5.60247 6.67676i 0.460520 0.548827i
\(149\) 2.09553 + 11.8843i 0.171672 + 0.973603i 0.941915 + 0.335852i \(0.109024\pi\)
−0.770242 + 0.637751i \(0.779865\pi\)
\(150\) 0 0
\(151\) 4.98455 0.405637 0.202818 0.979216i \(-0.434990\pi\)
0.202818 + 0.979216i \(0.434990\pi\)
\(152\) 1.44387 + 4.11281i 0.117113 + 0.333593i
\(153\) 8.19494i 0.662522i
\(154\) 16.0194 + 5.83057i 1.29088 + 0.469841i
\(155\) 0 0
\(156\) 12.2316 + 10.2635i 0.979312 + 0.821740i
\(157\) −10.0731 12.0046i −0.803919 0.958073i 0.195827 0.980639i \(-0.437261\pi\)
−0.999745 + 0.0225655i \(0.992817\pi\)
\(158\) −12.2490 2.15982i −0.974475 0.171826i
\(159\) 3.73421 6.46783i 0.296142 0.512933i
\(160\) 0 0
\(161\) 22.6290 8.23629i 1.78342 0.649111i
\(162\) −1.22042 3.35309i −0.0958856 0.263444i
\(163\) 7.28558 4.20633i 0.570651 0.329465i −0.186758 0.982406i \(-0.559798\pi\)
0.757409 + 0.652940i \(0.226465\pi\)
\(164\) −1.61262 + 2.79313i −0.125924 + 0.218107i
\(165\) 0 0
\(166\) 2.93985 2.46683i 0.228177 0.191463i
\(167\) 2.05862 2.45336i 0.159300 0.189847i −0.680490 0.732757i \(-0.738233\pi\)
0.839791 + 0.542910i \(0.182678\pi\)
\(168\) −11.4867 + 2.02542i −0.886221 + 0.156265i
\(169\) 16.4777 + 5.99739i 1.26751 + 0.461338i
\(170\) 0 0
\(171\) −3.78609 23.0083i −0.289530 1.75949i
\(172\) 2.28252i 0.174041i
\(173\) −4.83471 + 13.2833i −0.367576 + 1.00991i 0.608704 + 0.793397i \(0.291690\pi\)
−0.976280 + 0.216510i \(0.930533\pi\)
\(174\) 2.65580 + 15.0618i 0.201336 + 1.14183i
\(175\) 0 0
\(176\) −3.23517 + 2.71463i −0.243860 + 0.204623i
\(177\) −29.9938 5.28872i −2.25447 0.397524i
\(178\) 9.80739 + 5.66230i 0.735095 + 0.424407i
\(179\) 8.50106 + 14.7243i 0.635399 + 1.10054i 0.986430 + 0.164180i \(0.0524978\pi\)
−0.351031 + 0.936364i \(0.614169\pi\)
\(180\) 0 0
\(181\) −18.7494 + 6.82423i −1.39363 + 0.507241i −0.926282 0.376830i \(-0.877014\pi\)
−0.467352 + 0.884072i \(0.654792\pi\)
\(182\) −19.3173 + 11.1529i −1.43190 + 0.826705i
\(183\) −11.2742 6.50918i −0.833415 0.481172i
\(184\) −1.03594 + 5.87510i −0.0763705 + 0.433118i
\(185\) 0 0
\(186\) 6.01908 + 5.05061i 0.441340 + 0.370328i
\(187\) −6.37135 + 1.12344i −0.465919 + 0.0821541i
\(188\) −3.61462 + 9.93108i −0.263623 + 0.724299i
\(189\) 27.4039 1.99334
\(190\) 0 0
\(191\) 10.0735 0.728896 0.364448 0.931224i \(-0.381258\pi\)
0.364448 + 0.931224i \(0.381258\pi\)
\(192\) 0.988282 2.71528i 0.0713231 0.195959i
\(193\) 4.53351 0.799380i 0.326329 0.0575407i −0.00808358 0.999967i \(-0.502573\pi\)
0.334413 + 0.942427i \(0.391462\pi\)
\(194\) −10.4553 8.77303i −0.750646 0.629867i
\(195\) 0 0
\(196\) 1.61391 9.15296i 0.115280 0.653783i
\(197\) 0.940940 + 0.543252i 0.0670392 + 0.0387051i 0.533145 0.846024i \(-0.321010\pi\)
−0.466106 + 0.884729i \(0.654343\pi\)
\(198\) 19.5651 11.2959i 1.39043 0.802768i
\(199\) −1.22137 + 0.444543i −0.0865808 + 0.0315128i −0.384947 0.922939i \(-0.625780\pi\)
0.298367 + 0.954451i \(0.403558\pi\)
\(200\) 0 0
\(201\) −15.8964 27.5334i −1.12125 1.94206i
\(202\) 12.3141 + 7.10952i 0.866414 + 0.500224i
\(203\) −21.0409 3.71007i −1.47678 0.260396i
\(204\) 3.39094 2.84533i 0.237413 0.199213i
\(205\) 0 0
\(206\) 1.39071 + 7.88712i 0.0968955 + 0.549522i
\(207\) 10.9150 29.9888i 0.758647 2.08437i
\(208\) 5.52587i 0.383150i
\(209\) 17.3693 6.09778i 1.20146 0.421792i
\(210\) 0 0
\(211\) −4.86776 1.77172i −0.335111 0.121970i 0.168984 0.985619i \(-0.445951\pi\)
−0.504094 + 0.863649i \(0.668174\pi\)
\(212\) −2.54537 + 0.448817i −0.174817 + 0.0308249i
\(213\) −13.9025 + 16.5684i −0.952586 + 1.13525i
\(214\) 13.4433 11.2803i 0.918968 0.771106i
\(215\) 0 0
\(216\) −3.39442 + 5.87931i −0.230961 + 0.400036i
\(217\) −9.50591 + 5.48824i −0.645303 + 0.372566i
\(218\) 2.73090 + 7.50308i 0.184960 + 0.508172i
\(219\) 5.35352 1.94852i 0.361758 0.131669i
\(220\) 0 0
\(221\) 4.23260 7.33107i 0.284715 0.493141i
\(222\) 24.8023 + 4.37332i 1.66462 + 0.293518i
\(223\) −5.19927 6.19625i −0.348169 0.414932i 0.563331 0.826231i \(-0.309520\pi\)
−0.911500 + 0.411299i \(0.865075\pi\)
\(224\) 3.09222 + 2.59468i 0.206607 + 0.173364i
\(225\) 0 0
\(226\) −7.38628 2.68839i −0.491328 0.178829i
\(227\) 6.53426i 0.433694i 0.976206 + 0.216847i \(0.0695773\pi\)
−0.976206 + 0.216847i \(0.930423\pi\)
\(228\) −8.20591 + 9.55524i −0.543450 + 0.632811i
\(229\) −25.8896 −1.71084 −0.855418 0.517939i \(-0.826699\pi\)
−0.855418 + 0.517939i \(0.826699\pi\)
\(230\) 0 0
\(231\) 8.55379 + 48.5109i 0.562798 + 3.19179i
\(232\) 3.40223 4.05462i 0.223367 0.266199i
\(233\) 14.5918 + 17.3898i 0.955937 + 1.13924i 0.990176 + 0.139828i \(0.0446550\pi\)
−0.0342384 + 0.999414i \(0.510901\pi\)
\(234\) −5.13310 + 29.1113i −0.335561 + 1.90306i
\(235\) 0 0
\(236\) 5.27013 + 9.12813i 0.343056 + 0.594190i
\(237\) −12.2922 33.7724i −0.798462 2.19376i
\(238\) 2.11497 + 5.81083i 0.137093 + 0.376660i
\(239\) −4.47880 7.75751i −0.289710 0.501792i 0.684031 0.729453i \(-0.260225\pi\)
−0.973740 + 0.227661i \(0.926892\pi\)
\(240\) 0 0
\(241\) 0.582502 3.30353i 0.0375223 0.212799i −0.960282 0.279031i \(-0.909987\pi\)
0.997804 + 0.0662321i \(0.0210978\pi\)
\(242\) 4.39380 + 5.23633i 0.282444 + 0.336604i
\(243\) −6.46376 + 7.70320i −0.414650 + 0.494161i
\(244\) 0.782343 + 4.43689i 0.0500844 + 0.284043i
\(245\) 0 0
\(246\) −9.31944 −0.594186
\(247\) −8.49655 + 22.5384i −0.540622 + 1.43408i
\(248\) 2.71924i 0.172672i
\(249\) 10.4204 + 3.79273i 0.660369 + 0.240354i
\(250\) 0 0
\(251\) 17.0959 + 14.3452i 1.07909 + 0.905460i 0.995845 0.0910693i \(-0.0290285\pi\)
0.0832408 + 0.996529i \(0.473473\pi\)
\(252\) −13.8801 16.5417i −0.874365 1.04203i
\(253\) 24.8118 + 4.37499i 1.55991 + 0.275054i
\(254\) 9.27594 16.0664i 0.582024 1.00810i
\(255\) 0 0
\(256\) −0.939693 + 0.342020i −0.0587308 + 0.0213763i
\(257\) 0.319330 + 0.877351i 0.0199192 + 0.0547277i 0.949254 0.314511i \(-0.101841\pi\)
−0.929334 + 0.369239i \(0.879618\pi\)
\(258\) −5.71183 + 3.29772i −0.355603 + 0.205307i
\(259\) −17.5913 + 30.4690i −1.09307 + 1.89325i
\(260\) 0 0
\(261\) −21.6900 + 18.2001i −1.34258 + 1.12656i
\(262\) 6.30859 7.51829i 0.389746 0.464481i
\(263\) 14.6030 2.57491i 0.900462 0.158776i 0.295793 0.955252i \(-0.404416\pi\)
0.604670 + 0.796476i \(0.293305\pi\)
\(264\) −11.4672 4.17372i −0.705758 0.256875i
\(265\) 0 0
\(266\) −8.62266 15.3375i −0.528689 0.940402i
\(267\) 32.7229i 2.00261i
\(268\) −3.76316 + 10.3392i −0.229872 + 0.631567i
\(269\) 0.487261 + 2.76340i 0.0297088 + 0.168487i 0.996052 0.0887681i \(-0.0282930\pi\)
−0.966343 + 0.257255i \(0.917182\pi\)
\(270\) 0 0
\(271\) 6.28912 5.27720i 0.382037 0.320567i −0.431464 0.902130i \(-0.642003\pi\)
0.813502 + 0.581563i \(0.197559\pi\)
\(272\) −1.50865 0.266015i −0.0914752 0.0161296i
\(273\) −55.8182 32.2267i −3.37827 1.95045i
\(274\) 1.63369 + 2.82963i 0.0986946 + 0.170944i
\(275\) 0 0
\(276\) −16.1987 + 5.89583i −0.975044 + 0.354887i
\(277\) 17.4575 10.0791i 1.04892 0.605595i 0.126574 0.991957i \(-0.459602\pi\)
0.922347 + 0.386362i \(0.126268\pi\)
\(278\) 1.37053 + 0.791276i 0.0821990 + 0.0474576i
\(279\) −2.52596 + 14.3254i −0.151225 + 0.857641i
\(280\) 0 0
\(281\) 3.80083 + 3.18928i 0.226739 + 0.190256i 0.749079 0.662481i \(-0.230496\pi\)
−0.522340 + 0.852737i \(0.674941\pi\)
\(282\) −30.0740 + 5.30286i −1.79088 + 0.315781i
\(283\) −5.16552 + 14.1921i −0.307058 + 0.843635i 0.686168 + 0.727443i \(0.259291\pi\)
−0.993227 + 0.116193i \(0.962931\pi\)
\(284\) 7.48509 0.444159
\(285\) 0 0
\(286\) −23.3369 −1.37994
\(287\) 4.45275 12.2338i 0.262838 0.722141i
\(288\) 5.26818 0.928923i 0.310431 0.0547373i
\(289\) 11.2250 + 9.41891i 0.660295 + 0.554053i
\(290\) 0 0
\(291\) 6.84828 38.8385i 0.401453 2.27675i
\(292\) −1.70748 0.985814i −0.0999227 0.0576904i
\(293\) −2.35283 + 1.35841i −0.137454 + 0.0793589i −0.567150 0.823615i \(-0.691954\pi\)
0.429696 + 0.902974i \(0.358621\pi\)
\(294\) 25.2363 9.18525i 1.47181 0.535695i
\(295\) 0 0
\(296\) −4.35795 7.54819i −0.253301 0.438729i
\(297\) 24.8296 + 14.3354i 1.44076 + 0.831822i
\(298\) 11.8843 + 2.09553i 0.688441 + 0.121391i
\(299\) −25.2533 + 21.1900i −1.46044 + 1.22545i
\(300\) 0 0
\(301\) −1.59993 9.07367i −0.0922186 0.522997i
\(302\) 1.70482 4.68394i 0.0981011 0.269531i
\(303\) 41.0865i 2.36036i
\(304\) 4.35861 + 0.0498692i 0.249984 + 0.00286019i
\(305\) 0 0
\(306\) 7.70073 + 2.80284i 0.440221 + 0.160227i
\(307\) 24.9663 4.40223i 1.42490 0.251248i 0.592566 0.805522i \(-0.298115\pi\)
0.832335 + 0.554273i \(0.187004\pi\)
\(308\) 10.9579 13.0591i 0.624383 0.744111i
\(309\) −17.7276 + 14.8752i −1.00849 + 0.846222i
\(310\) 0 0
\(311\) −1.87719 + 3.25139i −0.106446 + 0.184370i −0.914328 0.404974i \(-0.867280\pi\)
0.807882 + 0.589344i \(0.200614\pi\)
\(312\) 13.8280 7.98361i 0.782857 0.451983i
\(313\) −7.30618 20.0736i −0.412970 1.13463i −0.955604 0.294656i \(-0.904795\pi\)
0.542634 0.839969i \(-0.317427\pi\)
\(314\) −14.7258 + 5.35977i −0.831028 + 0.302469i
\(315\) 0 0
\(316\) −6.21896 + 10.7716i −0.349844 + 0.605947i
\(317\) 20.2025 + 3.56224i 1.13468 + 0.200075i 0.709279 0.704928i \(-0.249021\pi\)
0.425404 + 0.905003i \(0.360132\pi\)
\(318\) −4.80060 5.72114i −0.269204 0.320825i
\(319\) −17.1235 14.3683i −0.958733 0.804473i
\(320\) 0 0
\(321\) 47.6506 + 17.3434i 2.65960 + 0.968014i
\(322\) 24.0813i 1.34200i
\(323\) 5.74430 + 3.40469i 0.319621 + 0.189442i
\(324\) −3.56828 −0.198238
\(325\) 0 0
\(326\) −1.46084 8.28486i −0.0809087 0.458856i
\(327\) −14.8303 + 17.6741i −0.820118 + 0.977378i
\(328\) 2.07314 + 2.47067i 0.114470 + 0.136420i
\(329\) 7.40793 42.0125i 0.408413 2.31622i
\(330\) 0 0
\(331\) −16.3737 28.3601i −0.899982 1.55881i −0.827515 0.561443i \(-0.810246\pi\)
−0.0724661 0.997371i \(-0.523087\pi\)
\(332\) −1.31257 3.60626i −0.0720367 0.197919i
\(333\) 15.9468 + 43.8134i 0.873878 + 2.40096i
\(334\) −1.60132 2.77357i −0.0876203 0.151763i
\(335\) 0 0
\(336\) −2.02542 + 11.4867i −0.110496 + 0.626653i
\(337\) −15.3643 18.3105i −0.836948 0.997435i −0.999942 0.0108083i \(-0.996560\pi\)
0.162994 0.986627i \(-0.447885\pi\)
\(338\) 11.2714 13.4327i 0.613083 0.730644i
\(339\) −3.94402 22.3677i −0.214210 1.21484i
\(340\) 0 0
\(341\) −11.4839 −0.621889
\(342\) −22.9156 4.31153i −1.23914 0.233141i
\(343\) 9.26063i 0.500027i
\(344\) 2.14487 + 0.780669i 0.115644 + 0.0420909i
\(345\) 0 0
\(346\) 10.8286 + 9.08628i 0.582150 + 0.488482i
\(347\) −8.78538 10.4700i −0.471624 0.562059i 0.476822 0.879000i \(-0.341789\pi\)
−0.948445 + 0.316941i \(0.897344\pi\)
\(348\) 15.0618 + 2.65580i 0.807397 + 0.142366i
\(349\) −12.6829 + 21.9674i −0.678899 + 1.17589i 0.296414 + 0.955060i \(0.404209\pi\)
−0.975313 + 0.220828i \(0.929124\pi\)
\(350\) 0 0
\(351\) −35.2518 + 12.8306i −1.88160 + 0.684848i
\(352\) 1.44442 + 3.96852i 0.0769881 + 0.211523i
\(353\) −15.6173 + 9.01663i −0.831223 + 0.479907i −0.854271 0.519828i \(-0.825996\pi\)
0.0230484 + 0.999734i \(0.492663\pi\)
\(354\) −15.2283 + 26.3761i −0.809372 + 1.40187i
\(355\) 0 0
\(356\) 8.67515 7.27931i 0.459782 0.385803i
\(357\) −11.4855 + 13.6879i −0.607876 + 0.724438i
\(358\) 16.7438 2.95239i 0.884939 0.156039i
\(359\) −15.1395 5.51032i −0.799031 0.290824i −0.0899463 0.995947i \(-0.528670\pi\)
−0.709085 + 0.705123i \(0.750892\pi\)
\(360\) 0 0
\(361\) −17.7008 6.90519i −0.931621 0.363431i
\(362\) 19.9527i 1.04869i
\(363\) −6.75544 + 18.5604i −0.354569 + 0.974169i
\(364\) 3.87335 + 21.9669i 0.203019 + 1.15138i
\(365\) 0 0
\(366\) −9.97264 + 8.36804i −0.521278 + 0.437404i
\(367\) 9.75596 + 1.72024i 0.509257 + 0.0897957i 0.422372 0.906423i \(-0.361198\pi\)
0.0868849 + 0.996218i \(0.472309\pi\)
\(368\) 5.16648 + 2.98287i 0.269321 + 0.155493i
\(369\) −8.62661 14.9417i −0.449084 0.777835i
\(370\) 0 0
\(371\) 9.80395 3.56835i 0.508996 0.185259i
\(372\) 6.80466 3.92867i 0.352805 0.203692i
\(373\) 7.58731 + 4.38054i 0.392856 + 0.226816i 0.683397 0.730047i \(-0.260502\pi\)
−0.290541 + 0.956863i \(0.593835\pi\)
\(374\) −1.12344 + 6.37135i −0.0580917 + 0.329454i
\(375\) 0 0
\(376\) 8.09589 + 6.79326i 0.417514 + 0.350336i
\(377\) 28.8037 5.07886i 1.48346 0.261575i
\(378\) 9.37267 25.7512i 0.482078 1.32450i
\(379\) −9.49485 −0.487718 −0.243859 0.969811i \(-0.578413\pi\)
−0.243859 + 0.969811i \(0.578413\pi\)
\(380\) 0 0
\(381\) 53.6064 2.74634
\(382\) 3.44536 9.46604i 0.176280 0.484325i
\(383\) −28.8836 + 5.09296i −1.47588 + 0.260238i −0.852932 0.522022i \(-0.825178\pi\)
−0.622952 + 0.782260i \(0.714067\pi\)
\(384\) −2.21352 1.85736i −0.112958 0.0947831i
\(385\) 0 0
\(386\) 0.799380 4.53351i 0.0406874 0.230750i
\(387\) −10.5744 6.10513i −0.537526 0.310341i
\(388\) −11.8199 + 6.82421i −0.600063 + 0.346447i
\(389\) 11.3431 4.12854i 0.575117 0.209325i −0.0380542 0.999276i \(-0.512116\pi\)
0.613171 + 0.789950i \(0.289894\pi\)
\(390\) 0 0
\(391\) 4.56952 + 7.91464i 0.231091 + 0.400261i
\(392\) −8.04898 4.64708i −0.406535 0.234713i
\(393\) 27.9284 + 4.92452i 1.40880 + 0.248409i
\(394\) 0.832311 0.698392i 0.0419312 0.0351845i
\(395\) 0 0
\(396\) −3.92304 22.2487i −0.197140 1.11804i
\(397\) −3.91763 + 10.7636i −0.196620 + 0.540210i −0.998347 0.0574815i \(-0.981693\pi\)
0.801726 + 0.597691i \(0.203915\pi\)
\(398\) 1.29976i 0.0651509i
\(399\) 25.9230 43.7367i 1.29777 2.18957i
\(400\) 0 0
\(401\) 4.66865 + 1.69925i 0.233141 + 0.0848564i 0.455949 0.890006i \(-0.349300\pi\)
−0.222808 + 0.974862i \(0.571522\pi\)
\(402\) −31.3099 + 5.52078i −1.56159 + 0.275351i
\(403\) 9.65861 11.5107i 0.481130 0.573388i
\(404\) 10.8924 9.13983i 0.541918 0.454723i
\(405\) 0 0
\(406\) −10.6827 + 18.5030i −0.530175 + 0.918290i
\(407\) −31.8776 + 18.4045i −1.58011 + 0.912280i
\(408\) −1.51397 4.15960i −0.0749527 0.205931i
\(409\) 1.22014 0.444093i 0.0603318 0.0219590i −0.311678 0.950188i \(-0.600891\pi\)
0.372010 + 0.928229i \(0.378669\pi\)
\(410\) 0 0
\(411\) −4.72061 + 8.17633i −0.232850 + 0.403309i
\(412\) 7.88712 + 1.39071i 0.388571 + 0.0685155i
\(413\) −27.3486 32.5928i −1.34573 1.60378i
\(414\) −24.4471 20.5136i −1.20151 1.00819i
\(415\) 0 0
\(416\) −5.19261 1.88996i −0.254589 0.0926628i
\(417\) 4.57285i 0.223934i
\(418\) 0.210608 18.4074i 0.0103012 0.900333i
\(419\) 36.1438 1.76574 0.882870 0.469617i \(-0.155608\pi\)
0.882870 + 0.469617i \(0.155608\pi\)
\(420\) 0 0
\(421\) −5.28902 29.9955i −0.257771 1.46189i −0.788859 0.614574i \(-0.789328\pi\)
0.531088 0.847317i \(-0.321783\pi\)
\(422\) −3.32975 + 3.96824i −0.162089 + 0.193171i
\(423\) −36.3402 43.3086i −1.76692 2.10574i
\(424\) −0.448817 + 2.54537i −0.0217965 + 0.123614i
\(425\) 0 0
\(426\) 10.8142 + 18.7308i 0.523952 + 0.907511i
\(427\) −6.22007 17.0895i −0.301010 0.827018i
\(428\) −6.00213 16.4907i −0.290124 0.797108i
\(429\) −33.7165 58.3987i −1.62785 2.81952i
\(430\) 0 0
\(431\) −6.25630 + 35.4813i −0.301355 + 1.70907i 0.338827 + 0.940849i \(0.389970\pi\)
−0.640182 + 0.768223i \(0.721141\pi\)
\(432\) 4.36378 + 5.20055i 0.209953 + 0.250212i
\(433\) 18.7188 22.3082i 0.899568 1.07206i −0.0974763 0.995238i \(-0.531077\pi\)
0.997045 0.0768258i \(-0.0244785\pi\)
\(434\) 1.90605 + 10.8097i 0.0914931 + 0.518883i
\(435\) 0 0
\(436\) 7.98461 0.382393
\(437\) −16.4861 20.1102i −0.788636 0.962001i
\(438\) 5.69710i 0.272218i
\(439\) 3.06643 + 1.11609i 0.146353 + 0.0532681i 0.414158 0.910205i \(-0.364076\pi\)
−0.267805 + 0.963473i \(0.586298\pi\)
\(440\) 0 0
\(441\) 38.0867 + 31.9586i 1.81365 + 1.52184i
\(442\) −5.44132 6.48471i −0.258817 0.308446i
\(443\) 33.5612 + 5.91774i 1.59454 + 0.281160i 0.899206 0.437526i \(-0.144145\pi\)
0.695334 + 0.718687i \(0.255256\pi\)
\(444\) 12.5925 21.8108i 0.597612 1.03509i
\(445\) 0 0
\(446\) −7.60083 + 2.76648i −0.359910 + 0.130996i
\(447\) 11.9263 + 32.7671i 0.564093 + 1.54983i
\(448\) 3.49580 2.01830i 0.165161 0.0953558i
\(449\) 16.0584 27.8139i 0.757841 1.31262i −0.186109 0.982529i \(-0.559588\pi\)
0.943950 0.330089i \(-0.107079\pi\)
\(450\) 0 0
\(451\) 10.4342 8.75531i 0.491326 0.412272i
\(452\) −5.05251 + 6.02135i −0.237650 + 0.283221i
\(453\) 14.1842 2.50106i 0.666434 0.117510i
\(454\) 6.14020 + 2.23485i 0.288174 + 0.104887i
\(455\) 0 0
\(456\) 6.17240 + 10.9791i 0.289049 + 0.514144i
\(457\) 8.66519i 0.405341i 0.979247 + 0.202670i \(0.0649620\pi\)
−0.979247 + 0.202670i \(0.935038\pi\)
\(458\) −8.85478 + 24.3283i −0.413756 + 1.13679i
\(459\) 1.80594 + 10.2420i 0.0842939 + 0.478054i
\(460\) 0 0
\(461\) −13.5892 + 11.4027i −0.632911 + 0.531076i −0.901832 0.432087i \(-0.857777\pi\)
0.268921 + 0.963162i \(0.413333\pi\)
\(462\) 48.5109 + 8.55379i 2.25693 + 0.397958i
\(463\) −22.9510 13.2507i −1.06662 0.615814i −0.139365 0.990241i \(-0.544506\pi\)
−0.927257 + 0.374427i \(0.877840\pi\)
\(464\) −2.64646 4.58381i −0.122859 0.212798i
\(465\) 0 0
\(466\) 21.3317 7.76411i 0.988173 0.359665i
\(467\) 13.6094 7.85739i 0.629768 0.363597i −0.150894 0.988550i \(-0.548215\pi\)
0.780662 + 0.624953i \(0.214882\pi\)
\(468\) 25.6000 + 14.7802i 1.18336 + 0.683214i
\(469\) 7.71236 43.7390i 0.356124 2.01968i
\(470\) 0 0
\(471\) −34.6879 29.1066i −1.59833 1.34116i
\(472\) 10.3801 1.83030i 0.477784 0.0842462i
\(473\) 3.29693 9.05825i 0.151593 0.416499i
\(474\) −35.9399 −1.65077
\(475\) 0 0
\(476\) 6.18376 0.283432
\(477\) 4.72890 12.9926i 0.216522 0.594888i
\(478\) −8.82152 + 1.55547i −0.403487 + 0.0711456i
\(479\) 7.03049 + 5.89928i 0.321231 + 0.269545i 0.789116 0.614245i \(-0.210539\pi\)
−0.467884 + 0.883790i \(0.654984\pi\)
\(480\) 0 0
\(481\) 8.36339 47.4312i 0.381338 2.16267i
\(482\) −2.90508 1.67725i −0.132323 0.0763965i
\(483\) 60.2615 34.7920i 2.74199 1.58309i
\(484\) 6.42331 2.33789i 0.291968 0.106268i
\(485\) 0 0
\(486\) 5.02791 + 8.70859i 0.228071 + 0.395030i
\(487\) 23.0303 + 13.2965i 1.04360 + 0.602524i 0.920852 0.389913i \(-0.127495\pi\)
0.122751 + 0.992438i \(0.460828\pi\)
\(488\) 4.43689 + 0.782343i 0.200849 + 0.0354150i
\(489\) 18.6216 15.6254i 0.842097 0.706603i
\(490\) 0 0
\(491\) −5.89000 33.4038i −0.265812 1.50749i −0.766713 0.641990i \(-0.778109\pi\)
0.500901 0.865504i \(-0.333002\pi\)
\(492\) −3.18744 + 8.75741i −0.143701 + 0.394815i
\(493\) 8.10835i 0.365182i
\(494\) 18.2731 + 15.6927i 0.822147 + 0.706048i
\(495\) 0 0
\(496\) −2.55525 0.930034i −0.114734 0.0417597i
\(497\) −29.7553 + 5.24667i −1.33471 + 0.235345i
\(498\) 7.12800 8.49482i 0.319413 0.380662i
\(499\) 21.1761 17.7689i 0.947973 0.795444i −0.0309820 0.999520i \(-0.509863\pi\)
0.978955 + 0.204076i \(0.0654190\pi\)
\(500\) 0 0
\(501\) 4.62708 8.01433i 0.206723 0.358054i
\(502\) 19.3272 11.1586i 0.862616 0.498032i
\(503\) −7.38317 20.2851i −0.329199 0.904468i −0.988315 0.152426i \(-0.951291\pi\)
0.659116 0.752042i \(-0.270931\pi\)
\(504\) −20.2914 + 7.38545i −0.903849 + 0.328974i
\(505\) 0 0
\(506\) 12.5973 21.8192i 0.560018 0.969980i
\(507\) 49.8989 + 8.79852i 2.21609 + 0.390756i
\(508\) −11.9249 14.2116i −0.529083 0.630536i
\(509\) 1.78133 + 1.49471i 0.0789560 + 0.0662520i 0.681411 0.731901i \(-0.261366\pi\)
−0.602455 + 0.798152i \(0.705811\pi\)
\(510\) 0 0
\(511\) 7.47871 + 2.72203i 0.330839 + 0.120415i
\(512\) 1.00000i 0.0441942i
\(513\) −9.80222 27.9212i −0.432778 1.23275i
\(514\) 0.933658 0.0411819
\(515\) 0 0
\(516\) 1.14529 + 6.49525i 0.0504185 + 0.285937i
\(517\) 28.6894 34.1907i 1.26176 1.50371i
\(518\) 22.6149 + 26.9514i 0.993644 + 1.18418i
\(519\) −7.09280 + 40.2253i −0.311340 + 1.76569i
\(520\) 0 0
\(521\) 2.81228 + 4.87102i 0.123208 + 0.213403i 0.921031 0.389489i \(-0.127348\pi\)
−0.797823 + 0.602892i \(0.794015\pi\)
\(522\) 9.68405 + 26.6067i 0.423859 + 1.16454i
\(523\) 14.2976 + 39.2824i 0.625192 + 1.71770i 0.693908 + 0.720064i \(0.255887\pi\)
−0.0687164 + 0.997636i \(0.521890\pi\)
\(524\) −4.90721 8.49954i −0.214373 0.371304i
\(525\) 0 0
\(526\) 2.57491 14.6030i 0.112271 0.636723i
\(527\) −2.67763 3.19108i −0.116640 0.139006i
\(528\) −7.84404 + 9.34816i −0.341368 + 0.406826i
\(529\) −2.18623 12.3987i −0.0950536 0.539076i
\(530\) 0 0
\(531\) −56.3846 −2.44688
\(532\) −17.3617 + 2.85692i −0.752723 + 0.123863i
\(533\) 17.8222i 0.771965i
\(534\) 30.7495 + 11.1919i 1.33066 + 0.484321i
\(535\) 0 0
\(536\) 8.42859 + 7.07243i 0.364060 + 0.305482i
\(537\) 31.5791 + 37.6345i 1.36274 + 1.62405i
\(538\) 2.76340 + 0.487261i 0.119138 + 0.0210073i
\(539\) −19.6256 + 33.9926i −0.845335 + 1.46416i
\(540\) 0 0
\(541\) 19.0797 6.94444i 0.820300 0.298565i 0.102428 0.994740i \(-0.467339\pi\)
0.717871 + 0.696176i \(0.245117\pi\)
\(542\) −2.80794 7.71475i −0.120611 0.331377i
\(543\) −49.9300 + 28.8271i −2.14270 + 1.23709i
\(544\) −0.765961 + 1.32668i −0.0328403 + 0.0568811i
\(545\) 0 0
\(546\) −49.3741 + 41.4298i −2.11302 + 1.77303i
\(547\) −23.7651 + 28.3221i −1.01612 + 1.21097i −0.0387920 + 0.999247i \(0.512351\pi\)
−0.977330 + 0.211720i \(0.932093\pi\)
\(548\) 3.21773 0.567373i 0.137455 0.0242370i
\(549\) −22.6476 8.24306i −0.966576 0.351805i
\(550\) 0 0
\(551\) 3.74609 + 22.7652i 0.159589 + 0.969829i
\(552\) 17.2382i 0.733708i
\(553\) 17.1718 47.1791i 0.730219 2.00626i
\(554\) −3.50044 19.8520i −0.148719 0.843430i
\(555\) 0 0
\(556\) 1.21231 1.01725i 0.0514132 0.0431408i
\(557\) 12.2041 + 2.15190i 0.517102 + 0.0911791i 0.426108 0.904672i \(-0.359884\pi\)
0.0909943 + 0.995851i \(0.470995\pi\)
\(558\) 12.5976 + 7.27321i 0.533298 + 0.307900i
\(559\) 6.30646 + 10.9231i 0.266735 + 0.461998i
\(560\) 0 0
\(561\) −17.5669 + 6.39382i −0.741674 + 0.269947i
\(562\) 4.29690 2.48082i 0.181254 0.104647i
\(563\) 8.54424 + 4.93302i 0.360097 + 0.207902i 0.669123 0.743152i \(-0.266670\pi\)
−0.309027 + 0.951053i \(0.600003\pi\)
\(564\) −5.30286 + 30.0740i −0.223291 + 1.26634i
\(565\) 0 0
\(566\) 11.5695 + 9.70800i 0.486304 + 0.408058i
\(567\) 14.1849 2.50118i 0.595711 0.105040i
\(568\) 2.56005 7.03369i 0.107417 0.295127i
\(569\) −15.2083 −0.637565 −0.318782 0.947828i \(-0.603274\pi\)
−0.318782 + 0.947828i \(0.603274\pi\)
\(570\) 0 0
\(571\) −26.6461 −1.11511 −0.557553 0.830141i \(-0.688260\pi\)
−0.557553 + 0.830141i \(0.688260\pi\)
\(572\) −7.98169 + 21.9295i −0.333731 + 0.916920i
\(573\) 28.6657 5.05454i 1.19753 0.211156i
\(574\) −9.97312 8.36844i −0.416270 0.349292i
\(575\) 0 0
\(576\) 0.928923 5.26818i 0.0387051 0.219508i
\(577\) −29.6874 17.1401i −1.23590 0.713550i −0.267650 0.963516i \(-0.586247\pi\)
−0.968254 + 0.249967i \(0.919580\pi\)
\(578\) 12.6901 7.32661i 0.527837 0.304747i
\(579\) 12.4997 4.54950i 0.519468 0.189071i
\(580\) 0 0
\(581\) 7.74564 + 13.4158i 0.321343 + 0.556583i
\(582\) −34.1540 19.7188i −1.41573 0.817372i
\(583\) 10.7496 + 1.89545i 0.445205 + 0.0785016i
\(584\) −1.51035 + 1.26734i −0.0624989 + 0.0524428i
\(585\) 0 0
\(586\) 0.471769 + 2.67554i 0.0194886 + 0.110525i
\(587\) 10.9423 30.0636i 0.451636 1.24086i −0.479937 0.877303i \(-0.659340\pi\)
0.931572 0.363556i \(-0.118437\pi\)
\(588\) 26.8559i 1.10752i
\(589\) 8.99207 + 7.72226i 0.370512 + 0.318190i
\(590\) 0 0
\(591\) 2.95016 + 1.07377i 0.121354 + 0.0441691i
\(592\) −8.58348 + 1.51350i −0.352779 + 0.0622044i
\(593\) −10.8774 + 12.9632i −0.446683 + 0.532336i −0.941658 0.336571i \(-0.890733\pi\)
0.494975 + 0.868907i \(0.335177\pi\)
\(594\) 21.9631 18.4292i 0.901155 0.756159i
\(595\) 0 0
\(596\) 6.03384 10.4509i 0.247156 0.428086i
\(597\) −3.25253 + 1.87785i −0.133117 + 0.0768554i
\(598\) 11.2750 + 30.9778i 0.461069 + 1.26678i
\(599\) −16.3401 + 5.94730i −0.667637 + 0.243000i −0.653530 0.756901i \(-0.726713\pi\)
−0.0141069 + 0.999900i \(0.504491\pi\)
\(600\) 0 0
\(601\) 2.18870 3.79093i 0.0892787 0.154635i −0.817928 0.575321i \(-0.804877\pi\)
0.907206 + 0.420686i \(0.138210\pi\)
\(602\) −9.07367 1.59993i −0.369815 0.0652084i
\(603\) −37.8336 45.0883i −1.54070 1.83614i
\(604\) −3.81838 3.20400i −0.155368 0.130369i
\(605\) 0 0
\(606\) 38.6087 + 14.0524i 1.56837 + 0.570841i
\(607\) 36.1181i 1.46599i −0.680234 0.732995i \(-0.738122\pi\)
0.680234 0.732995i \(-0.261878\pi\)
\(608\) 1.53760 4.07870i 0.0623577 0.165413i
\(609\) −61.7364 −2.50168
\(610\) 0 0
\(611\) 10.1410 + 57.5126i 0.410262 + 2.32671i
\(612\) 5.26761 6.27769i 0.212930 0.253761i
\(613\) −8.07763 9.62654i −0.326252 0.388812i 0.577840 0.816150i \(-0.303896\pi\)
−0.904092 + 0.427338i \(0.859451\pi\)
\(614\) 4.40223 24.9663i 0.177660 1.00756i
\(615\) 0 0
\(616\) −8.52372 14.7635i −0.343430 0.594839i
\(617\) −8.14855 22.3880i −0.328048 0.901305i −0.988605 0.150530i \(-0.951902\pi\)
0.660557 0.750776i \(-0.270320\pi\)
\(618\) 7.91494 + 21.7461i 0.318386 + 0.874757i
\(619\) −0.743546 1.28786i −0.0298856 0.0517635i 0.850696 0.525658i \(-0.176181\pi\)
−0.880581 + 0.473895i \(0.842848\pi\)
\(620\) 0 0
\(621\) 7.03283 39.8851i 0.282218 1.60054i
\(622\) 2.41327 + 2.87603i 0.0967634 + 0.115318i
\(623\) −29.3837 + 35.0181i −1.17723 + 1.40297i
\(624\) −2.77268 15.7246i −0.110996 0.629489i
\(625\) 0 0
\(626\) −21.3618 −0.853791
\(627\) 46.3672 26.0674i 1.85173 1.04103i
\(628\) 15.6709i 0.625338i
\(629\) −12.5468 4.56668i −0.500275 0.182085i
\(630\) 0 0
\(631\) 20.1333 + 16.8939i 0.801495 + 0.672534i 0.948562 0.316592i \(-0.102539\pi\)
−0.147067 + 0.989127i \(0.546983\pi\)
\(632\) 7.99494 + 9.52800i 0.318022 + 0.379003i
\(633\) −14.7409 2.59922i −0.585898 0.103310i
\(634\) 10.2571 17.7657i 0.407360 0.705568i
\(635\) 0 0
\(636\) −7.01801 + 2.55435i −0.278282 + 0.101286i
\(637\) −17.5656 48.2610i −0.695973 1.91217i
\(638\) −19.3584 + 11.1766i −0.766407 + 0.442485i
\(639\) −20.0206 + 34.6767i −0.792002 + 1.37179i
\(640\) 0 0
\(641\) −3.77655 + 3.16890i −0.149165 + 0.125164i −0.714316 0.699823i \(-0.753262\pi\)
0.565151 + 0.824987i \(0.308818\pi\)
\(642\) 32.5949 38.8451i 1.28642 1.53309i
\(643\) −7.58704 + 1.33780i −0.299204 + 0.0527577i −0.321235 0.947000i \(-0.604098\pi\)
0.0220310 + 0.999757i \(0.492987\pi\)
\(644\) −22.6290 8.23629i −0.891709 0.324555i
\(645\) 0 0
\(646\) 5.16403 4.23341i 0.203176 0.166561i
\(647\) 33.7875i 1.32832i −0.747590 0.664161i \(-0.768789\pi\)
0.747590 0.664161i \(-0.231211\pi\)
\(648\) −1.22042 + 3.35309i −0.0479428 + 0.131722i
\(649\) −7.72973 43.8375i −0.303418 1.72077i
\(650\) 0 0
\(651\) −24.2966 + 20.3873i −0.952260 + 0.799041i
\(652\) −8.28486 1.46084i −0.324460 0.0572111i
\(653\) 10.7184 + 6.18826i 0.419442 + 0.242165i 0.694839 0.719166i \(-0.255476\pi\)
−0.275396 + 0.961331i \(0.588809\pi\)
\(654\) 11.5359 + 19.9808i 0.451091 + 0.781312i
\(655\) 0 0
\(656\) 3.03073 1.10309i 0.118330 0.0430686i
\(657\) 9.13408 5.27357i 0.356355 0.205741i
\(658\) −36.9452 21.3303i −1.44027 0.831542i
\(659\) −1.69829 + 9.63145i −0.0661558 + 0.375188i 0.933698 + 0.358063i \(0.116563\pi\)
−0.999853 + 0.0171255i \(0.994549\pi\)
\(660\) 0 0
\(661\) 13.0726 + 10.9692i 0.508466 + 0.426654i 0.860589 0.509300i \(-0.170096\pi\)
−0.352123 + 0.935954i \(0.614540\pi\)
\(662\) −32.2500 + 5.68654i −1.25343 + 0.221014i
\(663\) 8.36599 22.9854i 0.324908 0.892678i
\(664\) −3.83770 −0.148932
\(665\) 0 0
\(666\) 46.6253 1.80669
\(667\) −10.7997 + 29.6719i −0.418166 + 1.14890i
\(668\) −3.15398 + 0.556132i −0.122031 + 0.0215174i
\(669\) −17.9043 15.0235i −0.692221 0.580843i
\(670\) 0 0
\(671\) 3.30400 18.7379i 0.127550 0.723370i
\(672\) 10.1013 + 5.83197i 0.389665 + 0.224973i
\(673\) −21.1903 + 12.2342i −0.816826 + 0.471595i −0.849321 0.527877i \(-0.822988\pi\)
0.0324944 + 0.999472i \(0.489655\pi\)
\(674\) −22.4611 + 8.17518i −0.865170 + 0.314896i
\(675\) 0 0
\(676\) −8.76759 15.1859i −0.337215 0.584074i
\(677\) 2.20353 + 1.27221i 0.0846884 + 0.0488949i 0.541746 0.840542i \(-0.317763\pi\)
−0.457058 + 0.889437i \(0.651097\pi\)
\(678\) −22.3677 3.94402i −0.859025 0.151469i
\(679\) 42.2039 35.4132i 1.61964 1.35904i
\(680\) 0 0
\(681\) 3.27866 + 18.5942i 0.125638 + 0.712531i
\(682\) −3.92773 + 10.7914i −0.150401 + 0.413222i
\(683\) 13.2825i 0.508240i 0.967173 + 0.254120i \(0.0817857\pi\)
−0.967173 + 0.254120i \(0.918214\pi\)
\(684\) −11.8891 + 20.0590i −0.454592 + 0.766976i
\(685\) 0 0
\(686\) 8.70214 + 3.16732i 0.332249 + 0.120929i
\(687\) −73.6727 + 12.9905i −2.81079 + 0.495618i
\(688\) 1.46718 1.74851i 0.0559356 0.0666615i
\(689\) −10.9409 + 9.18052i −0.416816 + 0.349750i
\(690\) 0 0
\(691\) 3.25288 5.63415i 0.123745 0.214333i −0.797497 0.603324i \(-0.793843\pi\)
0.921242 + 0.388990i \(0.127176\pi\)
\(692\) 12.2419 7.06787i 0.465368 0.268680i
\(693\) 31.1903 + 85.6948i 1.18482 + 3.25528i
\(694\) −12.8434 + 4.67460i −0.487527 + 0.177445i
\(695\) 0 0
\(696\) 7.64707 13.2451i 0.289861 0.502055i
\(697\) 4.86574 + 0.857961i 0.184303 + 0.0324976i
\(698\) 16.3048 + 19.4313i 0.617145 + 0.735485i
\(699\) 50.2485 + 42.1635i 1.90057 + 1.59477i
\(700\) 0 0
\(701\) −5.89524 2.14569i −0.222660 0.0810417i 0.228281 0.973595i \(-0.426689\pi\)
−0.450941 + 0.892554i \(0.648912\pi\)
\(702\) 37.5142i 1.41588i
\(703\) 37.3366 + 7.02481i 1.40818 + 0.264946i
\(704\) 4.22321 0.159168
\(705\) 0 0
\(706\) 3.13144 + 17.7593i 0.117853 + 0.668380i
\(707\) −36.8939 + 43.9684i −1.38754 + 1.65360i
\(708\) 19.5771 + 23.3310i 0.735751 + 0.876834i
\(709\) −1.34174 + 7.60941i −0.0503903 + 0.285777i −0.999582 0.0289219i \(-0.990793\pi\)
0.949191 + 0.314699i \(0.101904\pi\)
\(710\) 0 0
\(711\) −33.2680 57.6219i −1.24765 2.16099i
\(712\) −3.87324 10.6416i −0.145156 0.398812i
\(713\) 5.54834 + 15.2439i 0.207787 + 0.570890i
\(714\) 8.93412 + 15.4743i 0.334351 + 0.579113i
\(715\) 0 0
\(716\) 2.95239 16.7438i 0.110336 0.625746i
\(717\) −16.6375 19.8278i −0.621339 0.740483i
\(718\) −10.3560 + 12.3418i −0.386483 + 0.460593i
\(719\) 1.92572 + 10.9213i 0.0718173 + 0.407296i 0.999430 + 0.0337534i \(0.0107461\pi\)
−0.927613 + 0.373543i \(0.878143\pi\)
\(720\) 0 0
\(721\) −32.3283 −1.20397
\(722\) −12.5428 + 14.2716i −0.466794 + 0.531134i
\(723\) 9.69296i 0.360485i
\(724\) 18.7494 + 6.82423i 0.696817 + 0.253621i
\(725\) 0 0
\(726\) 15.1306 + 12.6961i 0.561549 + 0.471195i
\(727\) −19.0466 22.6989i −0.706401 0.841855i 0.286834 0.957980i \(-0.407397\pi\)
−0.993235 + 0.116125i \(0.962953\pi\)
\(728\) 21.9669 + 3.87335i 0.814146 + 0.143556i
\(729\) −19.8808 + 34.4345i −0.736325 + 1.27535i
\(730\) 0 0
\(731\) 3.28577 1.19592i 0.121529 0.0442328i
\(732\) 4.45254 + 12.2333i 0.164571 + 0.452154i
\(733\) 22.9943 13.2758i 0.849314 0.490352i −0.0111055 0.999938i \(-0.503535\pi\)
0.860419 + 0.509587i \(0.170202\pi\)
\(734\) 4.95323 8.57924i 0.182827 0.316666i
\(735\) 0 0
\(736\) 4.57002 3.83470i 0.168453 0.141349i
\(737\) 29.8684 35.5957i 1.10022 1.31119i
\(738\) −16.9911 + 2.99599i −0.625451 + 0.110284i
\(739\) 16.6006 + 6.04212i 0.610663 + 0.222263i 0.628793 0.777573i \(-0.283549\pi\)
−0.0181306 + 0.999836i \(0.505771\pi\)
\(740\) 0 0
\(741\) −12.8692 + 68.3994i −0.472762 + 2.51271i
\(742\) 10.4331i 0.383013i
\(743\) −2.83848 + 7.79867i −0.104134 + 0.286105i −0.980807 0.194981i \(-0.937535\pi\)
0.876673 + 0.481086i \(0.159758\pi\)
\(744\) −1.36441 7.73798i −0.0500219 0.283688i
\(745\) 0 0
\(746\) 6.71137 5.63151i 0.245721 0.206184i
\(747\) 20.2177 + 3.56493i 0.739727 + 0.130434i
\(748\) 5.60287 + 3.23482i 0.204861 + 0.118277i
\(749\) 35.4193 + 61.3480i 1.29419 + 2.24161i
\(750\) 0 0
\(751\) −3.43969 + 1.25195i −0.125516 + 0.0456841i −0.404015 0.914753i \(-0.632386\pi\)
0.278498 + 0.960437i \(0.410163\pi\)
\(752\) 9.15254 5.28422i 0.333759 0.192696i
\(753\) 55.8468 + 32.2432i 2.03517 + 1.17501i
\(754\) 5.07886 28.8037i 0.184961 1.04897i
\(755\) 0 0
\(756\) −20.9926 17.6149i −0.763492 0.640646i
\(757\) 39.8461 7.02594i 1.44823 0.255362i 0.606424 0.795141i \(-0.292603\pi\)
0.841807 + 0.539779i \(0.181492\pi\)
\(758\) −3.24743 + 8.92224i −0.117952 + 0.324070i
\(759\) 72.8008 2.64250
\(760\) 0 0
\(761\) −16.2575 −0.589335 −0.294667 0.955600i \(-0.595209\pi\)
−0.294667 + 0.955600i \(0.595209\pi\)
\(762\) 18.3345 50.3736i 0.664188 1.82484i
\(763\) −31.7410 + 5.59680i −1.14910 + 0.202618i
\(764\) −7.71678 6.47515i −0.279183 0.234263i
\(765\) 0 0
\(766\) −5.09296 + 28.8836i −0.184016 + 1.04361i
\(767\) 50.4408 + 29.1220i 1.82131 + 1.05153i
\(768\) −2.50242 + 1.44477i −0.0902982 + 0.0521337i
\(769\) −4.84451 + 1.76326i −0.174697 + 0.0635846i −0.427888 0.903832i \(-0.640742\pi\)
0.253191 + 0.967416i \(0.418520\pi\)
\(770\) 0 0
\(771\) 1.34892 + 2.33640i 0.0485802 + 0.0841434i
\(772\) −3.98670 2.30172i −0.143485 0.0828409i
\(773\) −34.6179 6.10407i −1.24512 0.219548i −0.488012 0.872837i \(-0.662278\pi\)
−0.757109 + 0.653289i \(0.773389\pi\)
\(774\) −9.35359 + 7.84860i −0.336208 + 0.282112i
\(775\) 0 0
\(776\) 2.37002 + 13.4411i 0.0850788 + 0.482506i
\(777\) −34.7703 + 95.5307i −1.24738 + 3.42714i
\(778\) 12.0710i 0.432768i
\(779\) −14.0575 0.160840i −0.503664 0.00576268i
\(780\) 0 0
\(781\) −29.7048 10.8117i −1.06292 0.386871i
\(782\) 9.00020 1.58698i 0.321846 0.0567502i
\(783\) −23.0972 + 27.5262i −0.825426 + 0.983705i
\(784\) −7.11974 + 5.97417i −0.254277 + 0.213363i
\(785\) 0 0
\(786\) 14.1796 24.5598i 0.505770 0.876019i
\(787\) 23.3860 13.5019i 0.833622 0.481292i −0.0214692 0.999770i \(-0.506834\pi\)
0.855091 + 0.518478i \(0.173501\pi\)
\(788\) −0.371606 1.02098i −0.0132379 0.0363709i
\(789\) 40.2631 14.6546i 1.43340 0.521716i
\(790\) 0 0
\(791\) 15.8645 27.4781i 0.564076 0.977009i
\(792\) −22.2487 3.92304i −0.790572 0.139399i
\(793\) 16.0028 + 19.0714i 0.568275 + 0.677244i
\(794\) 8.77457 + 7.36274i 0.311398 + 0.261294i
\(795\) 0 0
\(796\) 1.22137 + 0.444543i 0.0432904 + 0.0157564i
\(797\) 19.8667i 0.703715i −0.936054 0.351857i \(-0.885550\pi\)
0.936054 0.351857i \(-0.114450\pi\)
\(798\) −32.2328 39.3185i −1.14103 1.39186i
\(799\) 16.1900 0.572762
\(800\) 0 0
\(801\) 10.5197 + 59.6601i 0.371695 + 2.10798i
\(802\) 3.19354 3.80592i 0.112768 0.134392i
\(803\) 5.35224 + 6.37855i 0.188876 + 0.225094i
\(804\) −5.52078 + 31.3099i −0.194703 + 1.10421i
\(805\) 0 0
\(806\) −7.51307 13.0130i −0.264637 0.458364i
\(807\) 2.77314 + 7.61915i 0.0976193 + 0.268207i
\(808\) −4.86320 13.3615i −0.171087 0.470057i
\(809\) −9.17170 15.8859i −0.322460 0.558517i 0.658535 0.752550i \(-0.271176\pi\)
−0.980995 + 0.194033i \(0.937843\pi\)
\(810\) 0 0
\(811\) 7.96210 45.1553i 0.279587 1.58562i −0.444416 0.895820i \(-0.646589\pi\)
0.724003 0.689796i \(-0.242300\pi\)
\(812\) 13.7334 + 16.3669i 0.481950 + 0.574365i
\(813\) 15.2487 18.1727i 0.534795 0.637344i
\(814\) 6.39183 + 36.2499i 0.224034 + 1.27056i
\(815\) 0 0
\(816\) −4.42655 −0.154960
\(817\) −8.67269 + 4.87574i −0.303419 + 0.170581i
\(818\) 1.29844i 0.0453989i
\(819\) −112.127 40.8110i −3.91805 1.42605i
\(820\) 0 0
\(821\) −12.8300 10.7656i −0.447769 0.375723i 0.390838 0.920459i \(-0.372185\pi\)
−0.838607 + 0.544737i \(0.816630\pi\)
\(822\) 6.06869 + 7.23239i 0.211670 + 0.252258i
\(823\) −14.3394 2.52843i −0.499841 0.0881355i −0.0819572 0.996636i \(-0.526117\pi\)
−0.417884 + 0.908500i \(0.637228\pi\)
\(824\) 4.00440 6.93582i 0.139500 0.241621i
\(825\) 0 0
\(826\) −39.9809 + 14.5519i −1.39111 + 0.506324i
\(827\) −1.27214 3.49518i −0.0442367 0.121539i 0.915607 0.402074i \(-0.131710\pi\)
−0.959844 + 0.280535i \(0.909488\pi\)
\(828\) −27.6378 + 15.9567i −0.960481 + 0.554534i
\(829\) −9.26652 + 16.0501i −0.321840 + 0.557442i −0.980868 0.194676i \(-0.937634\pi\)
0.659028 + 0.752118i \(0.270968\pi\)
\(830\) 0 0
\(831\) 44.6206 37.4411i 1.54787 1.29882i
\(832\) −3.55196 + 4.23306i −0.123142 + 0.146755i
\(833\) −14.0216 + 2.47239i −0.485820 + 0.0856633i
\(834\) 4.29708 + 1.56401i 0.148796 + 0.0541572i
\(835\) 0 0
\(836\) −17.2252 6.49360i −0.595747 0.224586i
\(837\) 18.4605i 0.638087i
\(838\) 12.3619 33.9641i 0.427035 1.17327i
\(839\) −4.49001 25.4641i −0.155013 0.879120i −0.958774 0.284168i \(-0.908282\pi\)
0.803762 0.594951i \(-0.202829\pi\)
\(840\) 0 0
\(841\) −0.754479 + 0.633083i −0.0260165 + 0.0218305i
\(842\) −29.9955 5.28902i −1.03371 0.182272i
\(843\) 12.4161 + 7.16843i 0.427633 + 0.246894i
\(844\) 2.59008 + 4.48615i 0.0891543 + 0.154420i
\(845\) 0 0
\(846\) −53.1259 + 19.3362i −1.82650 + 0.664793i
\(847\) −23.8957 + 13.7962i −0.821066 + 0.474042i
\(848\) 2.23836 + 1.29232i 0.0768656 + 0.0443784i
\(849\) −7.57812 + 42.9777i −0.260080 + 1.47499i
\(850\) 0 0
\(851\) 39.8318 + 33.4229i 1.36542 + 1.14572i
\(852\) 21.2999 3.75575i 0.729723 0.128670i
\(853\) −10.7040 + 29.4089i −0.366497 + 1.00694i 0.610186 + 0.792258i \(0.291095\pi\)
−0.976683 + 0.214685i \(0.931128\pi\)
\(854\) −18.1863 −0.622321
\(855\) 0 0
\(856\) −17.5490 −0.599814
\(857\) −1.15540 + 3.17443i −0.0394677 + 0.108437i −0.957861 0.287232i \(-0.907265\pi\)
0.918393 + 0.395669i \(0.129487\pi\)
\(858\) −66.4085 + 11.7096i −2.26715 + 0.399760i
\(859\) 39.0805 + 32.7924i 1.33341 + 1.11886i 0.983268 + 0.182167i \(0.0583112\pi\)
0.350142 + 0.936697i \(0.386133\pi\)
\(860\) 0 0
\(861\) 6.53245 37.0474i 0.222625 1.26257i
\(862\) 31.2017 + 18.0143i 1.06273 + 0.613570i
\(863\) 21.3865 12.3475i 0.728006 0.420315i −0.0896861 0.995970i \(-0.528586\pi\)
0.817692 + 0.575656i \(0.195253\pi\)
\(864\) 6.37942 2.32192i 0.217032 0.0789933i
\(865\) 0 0
\(866\) −14.5606 25.2198i −0.494791 0.857003i
\(867\) 36.6685 + 21.1705i 1.24533 + 0.718989i
\(868\) 10.8097 + 1.90605i 0.366906 + 0.0646954i
\(869\) 40.2388 33.7643i 1.36501 1.14538i
\(870\) 0 0
\(871\) 10.5578 + 59.8760i 0.357736 + 2.02882i
\(872\) 2.73090 7.50308i 0.0924798 0.254086i
\(873\) 73.0115i 2.47107i
\(874\) −24.5360 + 8.61376i −0.829941 + 0.291365i
\(875\) 0 0
\(876\) −5.35352 1.94852i −0.180879 0.0658345i
\(877\) −6.87335 + 1.21196i −0.232096 + 0.0409249i −0.288487 0.957484i \(-0.593152\pi\)
0.0563901 + 0.998409i \(0.482041\pi\)
\(878\) 2.09756 2.49978i 0.0707894 0.0843635i
\(879\) −6.01371 + 5.04610i −0.202837 + 0.170201i
\(880\) 0 0
\(881\) −0.780822 + 1.35242i −0.0263065 + 0.0455643i −0.878879 0.477045i \(-0.841708\pi\)
0.852572 + 0.522609i \(0.175041\pi\)
\(882\) 43.0576 24.8593i 1.44983 0.837058i
\(883\) −18.4078 50.5749i −0.619471 1.70198i −0.708278 0.705933i \(-0.750528\pi\)
0.0888076 0.996049i \(-0.471694\pi\)
\(884\) −7.95468 + 2.89527i −0.267545 + 0.0973783i
\(885\) 0 0
\(886\) 17.0395 29.5132i 0.572452 0.991516i
\(887\) −49.2169 8.67826i −1.65254 0.291388i −0.731787 0.681533i \(-0.761314\pi\)
−0.920753 + 0.390145i \(0.872425\pi\)
\(888\) −16.1886 19.2928i −0.543253 0.647424i
\(889\) 57.3665 + 48.1362i 1.92401 + 1.61444i
\(890\) 0 0
\(891\) 14.1608 + 5.15412i 0.474405 + 0.172669i
\(892\) 8.08863i 0.270827i
\(893\) −45.4555 + 7.47985i −1.52111 + 0.250304i
\(894\) 34.8700 1.16623
\(895\) 0 0
\(896\) −0.700949 3.97528i −0.0234171 0.132805i
\(897\) −61.2295 + 72.9705i −2.04439 + 2.43641i
\(898\) −20.6442 24.6028i −0.688907 0.821007i
\(899\) 2.49927 14.1741i 0.0833553 0.472732i
\(900\) 0 0
\(901\) 1.97973 + 3.42899i 0.0659543 + 0.114236i
\(902\) −4.65860 12.7994i −0.155115 0.426174i
\(903\) −9.10567 25.0176i −0.303018 0.832535i
\(904\) 3.93016 + 6.80723i 0.130715 + 0.226405i
\(905\) 0 0
\(906\) 2.50106 14.1842i 0.0830923 0.471240i
\(907\) −32.7593 39.0410i −1.08776 1.29634i −0.952169 0.305571i \(-0.901153\pi\)
−0.135586 0.990766i \(-0.543292\pi\)
\(908\) 4.20014 5.00554i 0.139387 0.166115i
\(909\) 13.2084 + 74.9085i 0.438095 + 2.48456i
\(910\) 0 0
\(911\) −36.8444 −1.22071 −0.610355 0.792128i \(-0.708973\pi\)
−0.610355 + 0.792128i \(0.708973\pi\)
\(912\) 12.4281 2.04508i 0.411535 0.0677195i
\(913\) 16.2074i 0.536388i
\(914\) 8.14262 + 2.96367i 0.269334 + 0.0980295i
\(915\) 0 0
\(916\) 19.8326 + 16.6415i 0.655288 + 0.549852i
\(917\) 25.4653 + 30.3483i 0.840938 + 1.00219i
\(918\) 10.2420 + 1.80594i 0.338035 + 0.0596048i
\(919\) −7.33804 + 12.7099i −0.242060 + 0.419260i −0.961301 0.275501i \(-0.911156\pi\)
0.719241 + 0.694761i \(0.244490\pi\)
\(920\) 0 0
\(921\) 68.8363 25.0543i 2.26823 0.825569i
\(922\) 6.06724 + 16.6696i 0.199814 + 0.548984i
\(923\) 35.8202 20.6808i 1.17904 0.680717i
\(924\) 24.6296 42.6598i 0.810256 1.40340i
\(925\) 0 0
\(926\) −20.3013 + 17.0348i −0.667143 + 0.559799i
\(927\) −27.5387 + 32.8194i −0.904490 + 1.07793i
\(928\) −5.21252 + 0.919107i −0.171109 + 0.0301712i
\(929\) 35.9586 + 13.0879i 1.17976 + 0.429399i 0.856119 0.516780i \(-0.172869\pi\)
0.323645 + 0.946178i \(0.395092\pi\)
\(930\) 0 0
\(931\) 38.2252 13.4196i 1.25278 0.439809i
\(932\) 22.7007i 0.743587i
\(933\) −3.71039 + 10.1942i −0.121473 + 0.333744i
\(934\) −2.72884 15.4760i −0.0892905 0.506392i
\(935\) 0 0
\(936\) 22.6445 19.0010i 0.740160 0.621068i
\(937\) 9.32123 + 1.64359i 0.304511 + 0.0536936i 0.323816 0.946120i \(-0.395034\pi\)
−0.0193046 + 0.999814i \(0.506145\pi\)
\(938\) −38.4634 22.2069i −1.25587 0.725079i
\(939\) −30.8630 53.4562i −1.00717 1.74448i
\(940\) 0 0
\(941\) −21.1763 + 7.70755i −0.690328 + 0.251259i −0.663276 0.748375i \(-0.730834\pi\)
−0.0270523 + 0.999634i \(0.508612\pi\)
\(942\) −39.2152 + 22.6409i −1.27770 + 0.737680i
\(943\) −16.6631 9.62044i −0.542625 0.313285i
\(944\) 1.83030 10.3801i 0.0595710 0.337844i
\(945\) 0 0
\(946\) −7.38435 6.19621i −0.240086 0.201456i
\(947\) −40.7294 + 7.18168i −1.32353 + 0.233373i −0.790363 0.612639i \(-0.790108\pi\)
−0.533163 + 0.846012i \(0.678997\pi\)
\(948\) −12.2922 + 33.7724i −0.399231 + 1.09688i
\(949\) −10.8950 −0.353665
\(950\) 0 0
\(951\) 59.2764 1.92217
\(952\) 2.11497 5.81083i 0.0685466 0.188330i
\(953\) −1.63331 + 0.287997i −0.0529083 + 0.00932915i −0.200040 0.979788i \(-0.564107\pi\)
0.147131 + 0.989117i \(0.452996\pi\)
\(954\) −10.5916 8.88743i −0.342916 0.287741i
\(955\) 0 0
\(956\) −1.55547 + 8.82152i −0.0503076 + 0.285308i
\(957\) −55.9370 32.2952i −1.80819 1.04396i
\(958\) 7.94808 4.58883i 0.256791 0.148258i
\(959\) −12.3937 + 4.51093i −0.400213 + 0.145666i
\(960\) 0 0
\(961\) 11.8029 + 20.4432i 0.380738 + 0.659457i
\(962\) −41.7103 24.0814i −1.34479 0.776416i
\(963\) 92.4516 + 16.3017i 2.97921 + 0.525315i
\(964\) −2.56969 + 2.15623i −0.0827642 + 0.0694474i
\(965\) 0 0
\(966\) −12.0831 68.5268i −0.388768 2.20481i
\(967\) −13.8597 + 38.0792i −0.445697 + 1.22454i 0.489994 + 0.871726i \(0.336999\pi\)
−0.935692 + 0.352818i \(0.885223\pi\)
\(968\) 6.83554i 0.219703i
\(969\) 18.0546 + 6.80625i 0.579997 + 0.218648i
\(970\) 0 0
\(971\) 28.2395 + 10.2783i 0.906248 + 0.329847i 0.752754 0.658302i \(-0.228725\pi\)
0.153494 + 0.988150i \(0.450947\pi\)
\(972\) 9.90305 1.74617i 0.317640 0.0560086i
\(973\) −4.10622 + 4.89360i −0.131639 + 0.156882i
\(974\) 20.3715 17.0937i 0.652745 0.547718i
\(975\) 0 0
\(976\) 2.25267 3.90174i 0.0721061 0.124892i
\(977\) 26.0144 15.0194i 0.832273 0.480513i −0.0223570 0.999750i \(-0.507117\pi\)
0.854630 + 0.519237i \(0.173784\pi\)
\(978\) −8.31408 22.8427i −0.265855 0.730431i
\(979\) −44.9419 + 16.3575i −1.43635 + 0.522789i
\(980\) 0 0
\(981\) −21.3566 + 36.9908i −0.681865 + 1.18102i
\(982\) −33.4038 5.89000i −1.06596 0.187957i
\(983\) 12.4389 + 14.8241i 0.396740 + 0.472816i 0.927023 0.375004i \(-0.122359\pi\)
−0.530283 + 0.847821i \(0.677914\pi\)
\(984\) 7.13911 + 5.99042i 0.227586 + 0.190968i
\(985\) 0 0
\(986\) −7.61936 2.77322i −0.242650 0.0883173i
\(987\) 123.270i 3.92371i
\(988\) 20.9961 11.8039i 0.667975 0.375532i
\(989\) −13.6169 −0.432993
\(990\) 0 0
\(991\) 3.11302 + 17.6548i 0.0988885 + 0.560824i 0.993486 + 0.113952i \(0.0363510\pi\)
−0.894598 + 0.446872i \(0.852538\pi\)
\(992\) −1.74789 + 2.08306i −0.0554956 + 0.0661371i
\(993\) −60.8239 72.4871i −1.93019 2.30031i
\(994\) −5.24667 + 29.7553i −0.166414 + 0.943782i
\(995\) 0 0
\(996\) −5.54460 9.60353i −0.175687 0.304299i
\(997\) 14.1528 + 38.8845i 0.448224 + 1.23149i 0.933959 + 0.357380i \(0.116330\pi\)
−0.485735 + 0.874106i \(0.661448\pi\)
\(998\) −9.45462 25.9763i −0.299281 0.822267i
\(999\) 29.5854 + 51.2434i 0.936041 + 1.62127i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 950.2.u.h.99.8 48
5.2 odd 4 950.2.l.j.251.1 24
5.3 odd 4 950.2.l.k.251.4 yes 24
5.4 even 2 inner 950.2.u.h.99.1 48
19.5 even 9 inner 950.2.u.h.499.1 48
95.24 even 18 inner 950.2.u.h.499.8 48
95.43 odd 36 950.2.l.k.651.4 yes 24
95.62 odd 36 950.2.l.j.651.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.l.j.251.1 24 5.2 odd 4
950.2.l.j.651.1 yes 24 95.62 odd 36
950.2.l.k.251.4 yes 24 5.3 odd 4
950.2.l.k.651.4 yes 24 95.43 odd 36
950.2.u.h.99.1 48 5.4 even 2 inner
950.2.u.h.99.8 48 1.1 even 1 trivial
950.2.u.h.499.1 48 19.5 even 9 inner
950.2.u.h.499.8 48 95.24 even 18 inner