Properties

Label 700.2.t.c.299.13
Level $700$
Weight $2$
Character 700.299
Analytic conductor $5.590$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,2,Mod(199,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.199");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.t (of order \(6\), degree \(2\), 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: \(5.58952814149\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 299.13
Character \(\chi\) \(=\) 700.299
Dual form 700.2.t.c.199.13

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.14053 + 0.836177i) q^{2} +(2.62152 - 1.51353i) q^{3} +(0.601615 + 1.90737i) q^{4} +(4.25550 + 0.465823i) q^{6} +(0.602834 - 2.57616i) q^{7} +(-0.908739 + 2.67847i) q^{8} +(3.08156 - 5.33743i) q^{9} +O(q^{10})\) \(q+(1.14053 + 0.836177i) q^{2} +(2.62152 - 1.51353i) q^{3} +(0.601615 + 1.90737i) q^{4} +(4.25550 + 0.465823i) q^{6} +(0.602834 - 2.57616i) q^{7} +(-0.908739 + 2.67847i) q^{8} +(3.08156 - 5.33743i) q^{9} +(1.03659 - 0.598478i) q^{11} +(4.46401 + 4.08964i) q^{12} -4.83692 q^{13} +(2.84167 - 2.43411i) q^{14} +(-3.27612 + 2.29501i) q^{16} +(1.27265 + 2.20430i) q^{17} +(7.97765 - 3.51076i) q^{18} +(0.711130 - 1.23171i) q^{19} +(-2.31876 - 7.66585i) q^{21} +(1.68270 + 0.184195i) q^{22} +(-2.90326 + 5.02859i) q^{23} +(1.67168 + 8.39706i) q^{24} +(-5.51665 - 4.04452i) q^{26} -9.57500i q^{27} +(5.27636 - 0.400029i) q^{28} -0.774233 q^{29} +(3.31933 + 5.74924i) q^{31} +(-5.65554 - 0.121894i) q^{32} +(1.81163 - 3.13784i) q^{33} +(-0.391687 + 3.57823i) q^{34} +(12.0344 + 2.66661i) q^{36} +(-4.42479 - 2.55465i) q^{37} +(1.84100 - 0.810175i) q^{38} +(-12.6801 + 7.32084i) q^{39} +7.46685i q^{41} +(3.76539 - 10.6820i) q^{42} +1.38202 q^{43} +(1.76515 + 1.61711i) q^{44} +(-7.51604 + 3.30762i) q^{46} +(0.927389 + 0.535428i) q^{47} +(-5.11483 + 10.9749i) q^{48} +(-6.27318 - 3.10599i) q^{49} +(6.67256 + 3.85240i) q^{51} +(-2.90997 - 9.22580i) q^{52} +(-2.91156 + 1.68099i) q^{53} +(8.00640 - 10.9206i) q^{54} +(6.35234 + 3.95573i) q^{56} -4.30528i q^{57} +(-0.883036 - 0.647396i) q^{58} +(4.94206 + 8.55990i) q^{59} +(8.31115 + 4.79845i) q^{61} +(-1.02160 + 9.33272i) q^{62} +(-11.8924 - 11.1562i) q^{63} +(-6.34839 - 4.86806i) q^{64} +(4.69001 - 2.06395i) q^{66} +(-5.27776 - 9.14135i) q^{67} +(-3.43876 + 3.75356i) q^{68} +17.5767i q^{69} -16.3277i q^{71} +(11.4958 + 13.1042i) q^{72} +(-0.0535547 - 0.0927594i) q^{73} +(-2.91046 - 6.61356i) q^{74} +(2.77716 + 0.615371i) q^{76} +(-0.916880 - 3.03121i) q^{77} +(-20.5835 - 2.25315i) q^{78} +(-9.32609 - 5.38442i) q^{79} +(-5.24739 - 9.08874i) q^{81} +(-6.24361 + 8.51617i) q^{82} -15.8027i q^{83} +(13.2266 - 9.03463i) q^{84} +(1.57623 + 1.15561i) q^{86} +(-2.02967 + 1.17183i) q^{87} +(0.661010 + 3.32035i) q^{88} +(3.41325 + 1.97064i) q^{89} +(-2.91586 + 12.4607i) q^{91} +(-11.3380 - 2.51231i) q^{92} +(17.4033 + 10.0478i) q^{93} +(0.610001 + 1.38613i) q^{94} +(-15.0106 + 8.24030i) q^{96} +8.71387 q^{97} +(-4.55759 - 8.78797i) q^{98} -7.37699i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q + 2 q^{4} + 16 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q + 2 q^{4} + 16 q^{9} - 14 q^{12} - 8 q^{13} - 2 q^{14} - 14 q^{16} + 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} + 32 q^{28} + 40 q^{29} + 60 q^{32} - 24 q^{33} + 60 q^{36} - 60 q^{37} - 46 q^{38} + 78 q^{42} + 18 q^{44} + 2 q^{46} - 28 q^{48} + 16 q^{49} - 46 q^{52} - 12 q^{53} - 12 q^{54} - 4 q^{56} + 42 q^{58} + 24 q^{61} + 8 q^{62} - 4 q^{64} + 24 q^{66} - 4 q^{68} + 90 q^{72} - 24 q^{73} - 38 q^{74} + 20 q^{77} - 36 q^{81} + 8 q^{82} + 20 q^{84} + 28 q^{86} - 78 q^{88} + 60 q^{89} + 72 q^{93} - 18 q^{94} - 60 q^{96} - 48 q^{97} - 124 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14053 + 0.836177i 0.806476 + 0.591267i
\(3\) 2.62152 1.51353i 1.51353 0.873839i 0.513659 0.857995i \(-0.328290\pi\)
0.999874 0.0158441i \(-0.00504353\pi\)
\(4\) 0.601615 + 1.90737i 0.300808 + 0.953685i
\(5\) 0 0
\(6\) 4.25550 + 0.465823i 1.73730 + 0.190171i
\(7\) 0.602834 2.57616i 0.227850 0.973696i
\(8\) −0.908739 + 2.67847i −0.321288 + 0.946982i
\(9\) 3.08156 5.33743i 1.02719 1.77914i
\(10\) 0 0
\(11\) 1.03659 0.598478i 0.312545 0.180448i −0.335520 0.942033i \(-0.608912\pi\)
0.648065 + 0.761585i \(0.275579\pi\)
\(12\) 4.46401 + 4.08964i 1.28865 + 1.18058i
\(13\) −4.83692 −1.34152 −0.670760 0.741674i \(-0.734032\pi\)
−0.670760 + 0.741674i \(0.734032\pi\)
\(14\) 2.84167 2.43411i 0.759469 0.650543i
\(15\) 0 0
\(16\) −3.27612 + 2.29501i −0.819030 + 0.573751i
\(17\) 1.27265 + 2.20430i 0.308664 + 0.534621i 0.978070 0.208275i \(-0.0667850\pi\)
−0.669407 + 0.742896i \(0.733452\pi\)
\(18\) 7.97765 3.51076i 1.88035 0.827494i
\(19\) 0.711130 1.23171i 0.163144 0.282575i −0.772850 0.634588i \(-0.781170\pi\)
0.935995 + 0.352014i \(0.114503\pi\)
\(20\) 0 0
\(21\) −2.31876 7.66585i −0.505996 1.67283i
\(22\) 1.68270 + 0.184195i 0.358753 + 0.0392704i
\(23\) −2.90326 + 5.02859i −0.605371 + 1.04853i 0.386622 + 0.922238i \(0.373642\pi\)
−0.991993 + 0.126295i \(0.959691\pi\)
\(24\) 1.67168 + 8.39706i 0.341229 + 1.71404i
\(25\) 0 0
\(26\) −5.51665 4.04452i −1.08190 0.793197i
\(27\) 9.57500i 1.84271i
\(28\) 5.27636 0.400029i 0.997138 0.0755985i
\(29\) −0.774233 −0.143772 −0.0718858 0.997413i \(-0.522902\pi\)
−0.0718858 + 0.997413i \(0.522902\pi\)
\(30\) 0 0
\(31\) 3.31933 + 5.74924i 0.596169 + 1.03259i 0.993381 + 0.114867i \(0.0366443\pi\)
−0.397212 + 0.917727i \(0.630022\pi\)
\(32\) −5.65554 0.121894i −0.999768 0.0215481i
\(33\) 1.81163 3.13784i 0.315365 0.546228i
\(34\) −0.391687 + 3.57823i −0.0671737 + 0.613661i
\(35\) 0 0
\(36\) 12.0344 + 2.66661i 2.00573 + 0.444434i
\(37\) −4.42479 2.55465i −0.727431 0.419982i 0.0900509 0.995937i \(-0.471297\pi\)
−0.817481 + 0.575955i \(0.804630\pi\)
\(38\) 1.84100 0.810175i 0.298649 0.131428i
\(39\) −12.6801 + 7.32084i −2.03044 + 1.17227i
\(40\) 0 0
\(41\) 7.46685i 1.16613i 0.812427 + 0.583063i \(0.198146\pi\)
−0.812427 + 0.583063i \(0.801854\pi\)
\(42\) 3.76539 10.6820i 0.581013 1.64827i
\(43\) 1.38202 0.210756 0.105378 0.994432i \(-0.466395\pi\)
0.105378 + 0.994432i \(0.466395\pi\)
\(44\) 1.76515 + 1.61711i 0.266106 + 0.243789i
\(45\) 0 0
\(46\) −7.51604 + 3.30762i −1.10818 + 0.487681i
\(47\) 0.927389 + 0.535428i 0.135274 + 0.0781002i 0.566110 0.824330i \(-0.308448\pi\)
−0.430836 + 0.902430i \(0.641781\pi\)
\(48\) −5.11483 + 10.9749i −0.738262 + 1.58409i
\(49\) −6.27318 3.10599i −0.896169 0.443713i
\(50\) 0 0
\(51\) 6.67256 + 3.85240i 0.934345 + 0.539444i
\(52\) −2.90997 9.22580i −0.403540 1.27939i
\(53\) −2.91156 + 1.68099i −0.399934 + 0.230902i −0.686456 0.727172i \(-0.740834\pi\)
0.286521 + 0.958074i \(0.407501\pi\)
\(54\) 8.00640 10.9206i 1.08953 1.48610i
\(55\) 0 0
\(56\) 6.35234 + 3.95573i 0.848867 + 0.528606i
\(57\) 4.30528i 0.570248i
\(58\) −0.883036 0.647396i −0.115948 0.0850073i
\(59\) 4.94206 + 8.55990i 0.643402 + 1.11440i 0.984668 + 0.174438i \(0.0558108\pi\)
−0.341267 + 0.939967i \(0.610856\pi\)
\(60\) 0 0
\(61\) 8.31115 + 4.79845i 1.06413 + 0.614378i 0.926573 0.376115i \(-0.122740\pi\)
0.137561 + 0.990493i \(0.456074\pi\)
\(62\) −1.02160 + 9.33272i −0.129743 + 1.18526i
\(63\) −11.8924 11.1562i −1.49830 1.40555i
\(64\) −6.34839 4.86806i −0.793548 0.608507i
\(65\) 0 0
\(66\) 4.69001 2.06395i 0.577300 0.254055i
\(67\) −5.27776 9.14135i −0.644781 1.11679i −0.984352 0.176213i \(-0.943615\pi\)
0.339571 0.940580i \(-0.389718\pi\)
\(68\) −3.43876 + 3.75356i −0.417011 + 0.455186i
\(69\) 17.5767i 2.11599i
\(70\) 0 0
\(71\) 16.3277i 1.93775i −0.247558 0.968873i \(-0.579628\pi\)
0.247558 0.968873i \(-0.420372\pi\)
\(72\) 11.4958 + 13.1042i 1.35479 + 1.54435i
\(73\) −0.0535547 0.0927594i −0.00626810 0.0108567i 0.862874 0.505419i \(-0.168662\pi\)
−0.869142 + 0.494562i \(0.835329\pi\)
\(74\) −2.91046 6.61356i −0.338334 0.768811i
\(75\) 0 0
\(76\) 2.77716 + 0.615371i 0.318562 + 0.0705879i
\(77\) −0.916880 3.03121i −0.104488 0.345439i
\(78\) −20.5835 2.25315i −2.33062 0.255119i
\(79\) −9.32609 5.38442i −1.04927 0.605795i −0.126823 0.991925i \(-0.540478\pi\)
−0.922444 + 0.386130i \(0.873811\pi\)
\(80\) 0 0
\(81\) −5.24739 9.08874i −0.583043 1.00986i
\(82\) −6.24361 + 8.51617i −0.689492 + 0.940453i
\(83\) 15.8027i 1.73457i −0.497808 0.867287i \(-0.665862\pi\)
0.497808 0.867287i \(-0.334138\pi\)
\(84\) 13.2266 9.03463i 1.44314 0.985759i
\(85\) 0 0
\(86\) 1.57623 + 1.15561i 0.169969 + 0.124613i
\(87\) −2.02967 + 1.17183i −0.217603 + 0.125633i
\(88\) 0.661010 + 3.32035i 0.0704639 + 0.353950i
\(89\) 3.41325 + 1.97064i 0.361803 + 0.208887i 0.669872 0.742477i \(-0.266349\pi\)
−0.308068 + 0.951364i \(0.599682\pi\)
\(90\) 0 0
\(91\) −2.91586 + 12.4607i −0.305665 + 1.30623i
\(92\) −11.3380 2.51231i −1.18207 0.261926i
\(93\) 17.4033 + 10.0478i 1.80464 + 1.04191i
\(94\) 0.610001 + 1.38613i 0.0629168 + 0.142969i
\(95\) 0 0
\(96\) −15.0106 + 8.24030i −1.53201 + 0.841022i
\(97\) 8.71387 0.884760 0.442380 0.896828i \(-0.354134\pi\)
0.442380 + 0.896828i \(0.354134\pi\)
\(98\) −4.55759 8.78797i −0.460386 0.887719i
\(99\) 7.37699i 0.741416i
\(100\) 0 0
\(101\) −2.60279 + 1.50272i −0.258987 + 0.149526i −0.623872 0.781526i \(-0.714442\pi\)
0.364885 + 0.931052i \(0.381108\pi\)
\(102\) 4.38896 + 9.97322i 0.434571 + 0.987496i
\(103\) 0.331470 + 0.191374i 0.0326607 + 0.0188567i 0.516241 0.856443i \(-0.327331\pi\)
−0.483581 + 0.875300i \(0.660664\pi\)
\(104\) 4.39550 12.9555i 0.431014 1.27040i
\(105\) 0 0
\(106\) −4.72633 0.517362i −0.459062 0.0502507i
\(107\) 0.421235 0.729600i 0.0407223 0.0705331i −0.844946 0.534852i \(-0.820367\pi\)
0.885668 + 0.464319i \(0.153701\pi\)
\(108\) 18.2631 5.76047i 1.75736 0.554301i
\(109\) 1.97534 + 3.42139i 0.189203 + 0.327710i 0.944985 0.327114i \(-0.106076\pi\)
−0.755781 + 0.654824i \(0.772743\pi\)
\(110\) 0 0
\(111\) −15.4662 −1.46799
\(112\) 3.93734 + 9.82331i 0.372044 + 0.928215i
\(113\) 2.68201i 0.252302i −0.992011 0.126151i \(-0.959738\pi\)
0.992011 0.126151i \(-0.0402625\pi\)
\(114\) 3.59997 4.91030i 0.337169 0.459891i
\(115\) 0 0
\(116\) −0.465791 1.47675i −0.0432476 0.137113i
\(117\) −14.9053 + 25.8167i −1.37799 + 2.38676i
\(118\) −1.52103 + 13.8953i −0.140022 + 1.27916i
\(119\) 6.44582 1.94973i 0.590887 0.178731i
\(120\) 0 0
\(121\) −4.78365 + 8.28552i −0.434877 + 0.753229i
\(122\) 5.46676 + 12.4224i 0.494938 + 1.12467i
\(123\) 11.3013 + 19.5745i 1.01901 + 1.76497i
\(124\) −8.96897 + 9.79001i −0.805437 + 0.879169i
\(125\) 0 0
\(126\) −4.23507 22.6681i −0.377290 2.01943i
\(127\) 2.14034 0.189925 0.0949624 0.995481i \(-0.469727\pi\)
0.0949624 + 0.995481i \(0.469727\pi\)
\(128\) −3.16996 10.8605i −0.280188 0.959945i
\(129\) 3.62298 2.09173i 0.318986 0.184166i
\(130\) 0 0
\(131\) 4.83287 8.37078i 0.422250 0.731359i −0.573909 0.818919i \(-0.694574\pi\)
0.996159 + 0.0875604i \(0.0279071\pi\)
\(132\) 7.07493 + 1.56768i 0.615793 + 0.136449i
\(133\) −2.74440 2.57450i −0.237969 0.223238i
\(134\) 1.62435 14.8391i 0.140322 1.28190i
\(135\) 0 0
\(136\) −7.06065 + 1.40563i −0.605446 + 0.120531i
\(137\) 3.70285 2.13784i 0.316356 0.182648i −0.333411 0.942781i \(-0.608200\pi\)
0.649767 + 0.760133i \(0.274866\pi\)
\(138\) −14.6972 + 20.0467i −1.25111 + 1.70649i
\(139\) −7.53742 −0.639316 −0.319658 0.947533i \(-0.603568\pi\)
−0.319658 + 0.947533i \(0.603568\pi\)
\(140\) 0 0
\(141\) 3.24155 0.272988
\(142\) 13.6529 18.6223i 1.14572 1.56275i
\(143\) −5.01393 + 2.89479i −0.419286 + 0.242075i
\(144\) 2.15385 + 24.5582i 0.179488 + 2.04652i
\(145\) 0 0
\(146\) 0.0164826 0.150576i 0.00136411 0.0124618i
\(147\) −21.1463 + 1.35227i −1.74411 + 0.111533i
\(148\) 2.21065 9.97662i 0.181714 0.820073i
\(149\) −1.42882 + 2.47480i −0.117054 + 0.202743i −0.918599 0.395191i \(-0.870678\pi\)
0.801545 + 0.597934i \(0.204012\pi\)
\(150\) 0 0
\(151\) −5.72359 + 3.30451i −0.465779 + 0.268918i −0.714471 0.699665i \(-0.753333\pi\)
0.248692 + 0.968583i \(0.419999\pi\)
\(152\) 2.65287 + 3.02405i 0.215177 + 0.245283i
\(153\) 15.6870 1.26822
\(154\) 1.48890 4.22386i 0.119979 0.340369i
\(155\) 0 0
\(156\) −21.5921 19.7813i −1.72875 1.58377i
\(157\) −7.79155 13.4954i −0.621834 1.07705i −0.989144 0.146949i \(-0.953055\pi\)
0.367310 0.930098i \(-0.380279\pi\)
\(158\) −6.13435 13.9394i −0.488023 1.10896i
\(159\) −5.08847 + 8.81350i −0.403542 + 0.698956i
\(160\) 0 0
\(161\) 11.2043 + 10.5107i 0.883019 + 0.828355i
\(162\) 1.61500 14.7537i 0.126886 1.15916i
\(163\) −4.82015 + 8.34874i −0.377543 + 0.653924i −0.990704 0.136034i \(-0.956564\pi\)
0.613161 + 0.789958i \(0.289898\pi\)
\(164\) −14.2421 + 4.49217i −1.11212 + 0.350780i
\(165\) 0 0
\(166\) 13.2139 18.0235i 1.02560 1.39889i
\(167\) 4.94876i 0.382947i 0.981498 + 0.191473i \(0.0613265\pi\)
−0.981498 + 0.191473i \(0.938673\pi\)
\(168\) 22.6399 + 0.755525i 1.74671 + 0.0582901i
\(169\) 10.3958 0.799678
\(170\) 0 0
\(171\) −4.38279 7.59121i −0.335160 0.580514i
\(172\) 0.831443 + 2.63602i 0.0633969 + 0.200994i
\(173\) −3.46535 + 6.00216i −0.263465 + 0.456336i −0.967160 0.254167i \(-0.918199\pi\)
0.703695 + 0.710502i \(0.251532\pi\)
\(174\) −3.29475 0.360656i −0.249774 0.0273412i
\(175\) 0 0
\(176\) −2.02250 + 4.33967i −0.152451 + 0.327115i
\(177\) 25.9114 + 14.9599i 1.94762 + 1.12446i
\(178\) 2.24510 + 5.10165i 0.168278 + 0.382385i
\(179\) 18.2838 10.5561i 1.36659 0.789003i 0.376103 0.926578i \(-0.377264\pi\)
0.990491 + 0.137575i \(0.0439307\pi\)
\(180\) 0 0
\(181\) 6.10438i 0.453735i 0.973926 + 0.226868i \(0.0728485\pi\)
−0.973926 + 0.226868i \(0.927152\pi\)
\(182\) −13.7450 + 11.7736i −1.01884 + 0.872717i
\(183\) 29.0504 2.14747
\(184\) −10.8306 12.3460i −0.798443 0.910156i
\(185\) 0 0
\(186\) 11.4473 + 26.0121i 0.839354 + 1.90730i
\(187\) 2.63845 + 1.52331i 0.192942 + 0.111395i
\(188\) −0.463328 + 2.09099i −0.0337917 + 0.152501i
\(189\) −24.6667 5.77213i −1.79424 0.419861i
\(190\) 0 0
\(191\) 3.21572 + 1.85660i 0.232681 + 0.134339i 0.611808 0.791006i \(-0.290442\pi\)
−0.379127 + 0.925345i \(0.623776\pi\)
\(192\) −24.0104 3.15320i −1.73280 0.227563i
\(193\) −13.2769 + 7.66545i −0.955695 + 0.551771i −0.894846 0.446376i \(-0.852714\pi\)
−0.0608498 + 0.998147i \(0.519381\pi\)
\(194\) 9.93843 + 7.28634i 0.713538 + 0.523129i
\(195\) 0 0
\(196\) 2.15023 13.8339i 0.153588 0.988135i
\(197\) 24.4602i 1.74272i −0.490644 0.871360i \(-0.663239\pi\)
0.490644 0.871360i \(-0.336761\pi\)
\(198\) 6.16847 8.41368i 0.438374 0.597934i
\(199\) −6.43311 11.1425i −0.456031 0.789868i 0.542716 0.839916i \(-0.317396\pi\)
−0.998747 + 0.0500478i \(0.984063\pi\)
\(200\) 0 0
\(201\) −27.6715 15.9761i −1.95179 1.12687i
\(202\) −4.22510 0.462495i −0.297277 0.0325410i
\(203\) −0.466734 + 1.99455i −0.0327583 + 0.139990i
\(204\) −3.33364 + 15.0447i −0.233402 + 1.05334i
\(205\) 0 0
\(206\) 0.218029 + 0.495436i 0.0151908 + 0.0345186i
\(207\) 17.8931 + 30.9918i 1.24366 + 2.15408i
\(208\) 15.8463 11.1008i 1.09875 0.769699i
\(209\) 1.70238i 0.117756i
\(210\) 0 0
\(211\) 16.9384i 1.16609i −0.812441 0.583044i \(-0.801862\pi\)
0.812441 0.583044i \(-0.198138\pi\)
\(212\) −4.95791 4.54212i −0.340511 0.311954i
\(213\) −24.7126 42.8034i −1.69328 2.93284i
\(214\) 1.09051 0.479903i 0.0745454 0.0328055i
\(215\) 0 0
\(216\) 25.6463 + 8.70118i 1.74501 + 0.592040i
\(217\) 16.8120 5.08527i 1.14127 0.345211i
\(218\) −0.607955 + 5.55393i −0.0411759 + 0.376160i
\(219\) −0.280789 0.162114i −0.0189740 0.0109546i
\(220\) 0 0
\(221\) −6.15572 10.6620i −0.414079 0.717205i
\(222\) −17.6397 12.9325i −1.18390 0.867972i
\(223\) 18.9687i 1.27024i −0.772414 0.635119i \(-0.780951\pi\)
0.772414 0.635119i \(-0.219049\pi\)
\(224\) −3.72337 + 14.4961i −0.248778 + 0.968561i
\(225\) 0 0
\(226\) 2.24264 3.05891i 0.149178 0.203476i
\(227\) −0.809262 + 0.467228i −0.0537126 + 0.0310110i −0.526616 0.850103i \(-0.676539\pi\)
0.472903 + 0.881114i \(0.343206\pi\)
\(228\) 8.21175 2.59012i 0.543837 0.171535i
\(229\) 11.3283 + 6.54038i 0.748594 + 0.432201i 0.825185 0.564862i \(-0.191071\pi\)
−0.0765920 + 0.997063i \(0.524404\pi\)
\(230\) 0 0
\(231\) −6.99146 6.55865i −0.460004 0.431527i
\(232\) 0.703576 2.07376i 0.0461920 0.136149i
\(233\) −13.5114 7.80080i −0.885160 0.511047i −0.0128037 0.999918i \(-0.504076\pi\)
−0.872356 + 0.488871i \(0.837409\pi\)
\(234\) −38.5873 + 16.9813i −2.52253 + 1.11010i
\(235\) 0 0
\(236\) −13.3537 + 14.5761i −0.869250 + 0.948824i
\(237\) −32.5980 −2.11747
\(238\) 8.98197 + 3.16612i 0.582214 + 0.205229i
\(239\) 14.1327i 0.914167i 0.889424 + 0.457084i \(0.151106\pi\)
−0.889424 + 0.457084i \(0.848894\pi\)
\(240\) 0 0
\(241\) 18.6916 10.7916i 1.20403 0.695146i 0.242580 0.970131i \(-0.422006\pi\)
0.961449 + 0.274985i \(0.0886728\pi\)
\(242\) −12.3841 + 5.44990i −0.796077 + 0.350333i
\(243\) −2.63564 1.52169i −0.169076 0.0976163i
\(244\) −4.15230 + 18.7393i −0.265824 + 1.19966i
\(245\) 0 0
\(246\) −3.47823 + 31.7752i −0.221764 + 2.02591i
\(247\) −3.43968 + 5.95770i −0.218862 + 0.379080i
\(248\) −18.4156 + 3.66615i −1.16939 + 0.232801i
\(249\) −23.9179 41.4271i −1.51574 2.62534i
\(250\) 0 0
\(251\) −1.04460 −0.0659345 −0.0329673 0.999456i \(-0.510496\pi\)
−0.0329673 + 0.999456i \(0.510496\pi\)
\(252\) 14.1243 29.3949i 0.889748 1.85170i
\(253\) 6.95014i 0.436952i
\(254\) 2.44113 + 1.78971i 0.153170 + 0.112296i
\(255\) 0 0
\(256\) 5.46590 15.0374i 0.341619 0.939839i
\(257\) −2.45194 + 4.24688i −0.152948 + 0.264913i −0.932310 0.361661i \(-0.882210\pi\)
0.779362 + 0.626574i \(0.215543\pi\)
\(258\) 5.88117 + 0.643775i 0.366146 + 0.0400797i
\(259\) −9.24860 + 9.85892i −0.574680 + 0.612604i
\(260\) 0 0
\(261\) −2.38585 + 4.13241i −0.147680 + 0.255790i
\(262\) 12.5115 5.50599i 0.772963 0.340161i
\(263\) −3.89819 6.75186i −0.240373 0.416337i 0.720448 0.693509i \(-0.243936\pi\)
−0.960820 + 0.277172i \(0.910603\pi\)
\(264\) 6.75830 + 7.70388i 0.415945 + 0.474141i
\(265\) 0 0
\(266\) −0.977325 5.23110i −0.0599236 0.320739i
\(267\) 11.9305 0.730135
\(268\) 14.2608 15.5662i 0.871114 0.950858i
\(269\) 18.2838 10.5562i 1.11479 0.643622i 0.174721 0.984618i \(-0.444098\pi\)
0.940065 + 0.340996i \(0.110764\pi\)
\(270\) 0 0
\(271\) −10.7604 + 18.6375i −0.653647 + 1.13215i 0.328584 + 0.944475i \(0.393429\pi\)
−0.982231 + 0.187676i \(0.939905\pi\)
\(272\) −9.22824 4.30080i −0.559544 0.260774i
\(273\) 11.2157 + 37.0791i 0.678804 + 2.24413i
\(274\) 6.01082 + 0.657967i 0.363127 + 0.0397492i
\(275\) 0 0
\(276\) −33.5253 + 10.5744i −2.01798 + 0.636505i
\(277\) −4.47513 + 2.58372i −0.268884 + 0.155241i −0.628381 0.777906i \(-0.716282\pi\)
0.359496 + 0.933147i \(0.382949\pi\)
\(278\) −8.59665 6.30262i −0.515593 0.378006i
\(279\) 40.9149 2.44951
\(280\) 0 0
\(281\) 15.6322 0.932539 0.466270 0.884643i \(-0.345598\pi\)
0.466270 + 0.884643i \(0.345598\pi\)
\(282\) 3.69709 + 2.71051i 0.220158 + 0.161409i
\(283\) −24.7424 + 14.2850i −1.47078 + 0.849156i −0.999462 0.0328062i \(-0.989556\pi\)
−0.471320 + 0.881962i \(0.656222\pi\)
\(284\) 31.1430 9.82302i 1.84800 0.582889i
\(285\) 0 0
\(286\) −8.13909 0.890936i −0.481274 0.0526821i
\(287\) 19.2358 + 4.50127i 1.13545 + 0.265702i
\(288\) −18.0785 + 29.8104i −1.06529 + 1.75660i
\(289\) 5.26071 9.11182i 0.309454 0.535990i
\(290\) 0 0
\(291\) 22.8436 13.1887i 1.33911 0.773137i
\(292\) 0.144707 0.157954i 0.00846835 0.00924356i
\(293\) −0.657174 −0.0383925 −0.0191963 0.999816i \(-0.506111\pi\)
−0.0191963 + 0.999816i \(0.506111\pi\)
\(294\) −25.2487 16.1397i −1.47253 0.941288i
\(295\) 0 0
\(296\) 10.8635 9.53014i 0.631430 0.553928i
\(297\) −5.73043 9.92539i −0.332513 0.575930i
\(298\) −3.69898 + 1.62783i −0.214276 + 0.0942975i
\(299\) 14.0428 24.3229i 0.812118 1.40663i
\(300\) 0 0
\(301\) 0.833126 3.56030i 0.0480206 0.205212i
\(302\) −9.29108 1.01704i −0.534642 0.0585239i
\(303\) −4.54883 + 7.87881i −0.261324 + 0.452626i
\(304\) 0.497043 + 5.66729i 0.0285073 + 0.325041i
\(305\) 0 0
\(306\) 17.8915 + 13.1171i 1.02279 + 0.749857i
\(307\) 4.88042i 0.278540i 0.990254 + 0.139270i \(0.0444756\pi\)
−0.990254 + 0.139270i \(0.955524\pi\)
\(308\) 5.23004 3.57245i 0.298009 0.203559i
\(309\) 1.15861 0.0659108
\(310\) 0 0
\(311\) 5.94840 + 10.3029i 0.337303 + 0.584226i 0.983924 0.178585i \(-0.0571520\pi\)
−0.646621 + 0.762811i \(0.723819\pi\)
\(312\) −8.08577 40.6159i −0.457766 2.29942i
\(313\) 13.3037 23.0427i 0.751970 1.30245i −0.194897 0.980824i \(-0.562437\pi\)
0.946867 0.321626i \(-0.104229\pi\)
\(314\) 2.39802 21.9070i 0.135328 1.23628i
\(315\) 0 0
\(316\) 4.65936 21.0277i 0.262110 1.18290i
\(317\) 22.9113 + 13.2278i 1.28683 + 0.742950i 0.978087 0.208197i \(-0.0667595\pi\)
0.308739 + 0.951147i \(0.400093\pi\)
\(318\) −13.1732 + 5.79719i −0.738716 + 0.325090i
\(319\) −0.802566 + 0.463362i −0.0449351 + 0.0259433i
\(320\) 0 0
\(321\) 2.55021i 0.142339i
\(322\) 3.99002 + 21.3565i 0.222355 + 1.19015i
\(323\) 3.62009 0.201427
\(324\) 14.1787 15.4766i 0.787705 0.859813i
\(325\) 0 0
\(326\) −12.4786 + 5.49149i −0.691123 + 0.304145i
\(327\) 10.3568 + 5.97949i 0.572731 + 0.330667i
\(328\) −19.9997 6.78542i −1.10430 0.374662i
\(329\) 1.93841 2.06633i 0.106868 0.113920i
\(330\) 0 0
\(331\) 21.0294 + 12.1414i 1.15588 + 0.667349i 0.950314 0.311294i \(-0.100762\pi\)
0.205569 + 0.978643i \(0.434096\pi\)
\(332\) 30.1416 9.50716i 1.65424 0.521773i
\(333\) −27.2705 + 15.7447i −1.49442 + 0.862802i
\(334\) −4.13804 + 5.64421i −0.226423 + 0.308837i
\(335\) 0 0
\(336\) 25.1897 + 19.7927i 1.37421 + 1.07978i
\(337\) 19.7077i 1.07355i 0.843726 + 0.536774i \(0.180357\pi\)
−0.843726 + 0.536774i \(0.819643\pi\)
\(338\) 11.8567 + 8.69275i 0.644922 + 0.472823i
\(339\) −4.05931 7.03094i −0.220472 0.381868i
\(340\) 0 0
\(341\) 6.88159 + 3.97309i 0.372659 + 0.215155i
\(342\) 1.34890 12.3228i 0.0729401 0.666340i
\(343\) −11.7832 + 14.2883i −0.636233 + 0.771497i
\(344\) −1.25589 + 3.70169i −0.0677132 + 0.199582i
\(345\) 0 0
\(346\) −8.97120 + 3.94799i −0.482295 + 0.212245i
\(347\) −4.21851 7.30667i −0.226461 0.392242i 0.730296 0.683131i \(-0.239382\pi\)
−0.956757 + 0.290889i \(0.906049\pi\)
\(348\) −3.45619 3.16633i −0.185271 0.169733i
\(349\) 23.5784i 1.26212i 0.775732 + 0.631062i \(0.217381\pi\)
−0.775732 + 0.631062i \(0.782619\pi\)
\(350\) 0 0
\(351\) 46.3135i 2.47203i
\(352\) −5.93545 + 3.25836i −0.316361 + 0.173671i
\(353\) 10.3362 + 17.9028i 0.550141 + 0.952872i 0.998264 + 0.0589002i \(0.0187594\pi\)
−0.448123 + 0.893972i \(0.647907\pi\)
\(354\) 17.0435 + 38.7288i 0.905854 + 2.05841i
\(355\) 0 0
\(356\) −1.70528 + 7.69589i −0.0903794 + 0.407881i
\(357\) 13.9468 14.8672i 0.738145 0.786856i
\(358\) 29.6800 + 3.24889i 1.56864 + 0.171709i
\(359\) 23.7741 + 13.7260i 1.25475 + 0.724429i 0.972049 0.234780i \(-0.0754369\pi\)
0.282699 + 0.959209i \(0.408770\pi\)
\(360\) 0 0
\(361\) 8.48859 + 14.7027i 0.446768 + 0.773824i
\(362\) −5.10435 + 6.96223i −0.268278 + 0.365927i
\(363\) 28.9608i 1.52005i
\(364\) −25.5213 + 1.93491i −1.33768 + 0.101417i
\(365\) 0 0
\(366\) 33.1329 + 24.2913i 1.73188 + 1.26973i
\(367\) −17.3574 + 10.0213i −0.906051 + 0.523109i −0.879159 0.476529i \(-0.841895\pi\)
−0.0268927 + 0.999638i \(0.508561\pi\)
\(368\) −2.02922 23.1372i −0.105781 1.20611i
\(369\) 39.8538 + 23.0096i 2.07471 + 1.19783i
\(370\) 0 0
\(371\) 2.57531 + 8.51401i 0.133704 + 0.442025i
\(372\) −8.69480 + 39.2395i −0.450804 + 2.03447i
\(373\) 17.8325 + 10.2956i 0.923331 + 0.533085i 0.884696 0.466168i \(-0.154366\pi\)
0.0386345 + 0.999253i \(0.487699\pi\)
\(374\) 1.73547 + 3.94359i 0.0897391 + 0.203918i
\(375\) 0 0
\(376\) −2.27688 + 1.99742i −0.117421 + 0.103009i
\(377\) 3.74491 0.192873
\(378\) −23.3066 27.2090i −1.19876 1.39948i
\(379\) 3.26339i 0.167629i 0.996481 + 0.0838145i \(0.0267103\pi\)
−0.996481 + 0.0838145i \(0.973290\pi\)
\(380\) 0 0
\(381\) 5.61095 3.23948i 0.287458 0.165964i
\(382\) 2.11518 + 4.80641i 0.108222 + 0.245917i
\(383\) 29.2293 + 16.8755i 1.49355 + 0.862300i 0.999973 0.00740376i \(-0.00235671\pi\)
0.493574 + 0.869704i \(0.335690\pi\)
\(384\) −24.7479 23.6732i −1.26291 1.20807i
\(385\) 0 0
\(386\) −21.5524 2.35921i −1.09699 0.120081i
\(387\) 4.25878 7.37642i 0.216486 0.374964i
\(388\) 5.24240 + 16.6206i 0.266142 + 0.843782i
\(389\) −1.80604 3.12816i −0.0915701 0.158604i 0.816602 0.577201i \(-0.195855\pi\)
−0.908172 + 0.418597i \(0.862522\pi\)
\(390\) 0 0
\(391\) −14.7793 −0.747424
\(392\) 14.0200 13.9800i 0.708116 0.706096i
\(393\) 29.2589i 1.47591i
\(394\) 20.4531 27.8976i 1.03041 1.40546i
\(395\) 0 0
\(396\) 14.0707 4.43811i 0.707077 0.223024i
\(397\) 3.73862 6.47548i 0.187636 0.324995i −0.756826 0.653617i \(-0.773251\pi\)
0.944462 + 0.328622i \(0.106584\pi\)
\(398\) 1.97993 18.0875i 0.0992449 0.906646i
\(399\) −11.0911 2.59537i −0.555248 0.129931i
\(400\) 0 0
\(401\) 4.77337 8.26772i 0.238371 0.412870i −0.721876 0.692022i \(-0.756720\pi\)
0.960247 + 0.279152i \(0.0900533\pi\)
\(402\) −18.2013 41.3595i −0.907796 2.06282i
\(403\) −16.0553 27.8086i −0.799773 1.38525i
\(404\) −4.43212 4.06042i −0.220506 0.202013i
\(405\) 0 0
\(406\) −2.20012 + 1.88457i −0.109190 + 0.0935296i
\(407\) −6.11561 −0.303140
\(408\) −16.3822 + 14.3714i −0.811037 + 0.711490i
\(409\) −18.7682 + 10.8358i −0.928026 + 0.535796i −0.886187 0.463328i \(-0.846655\pi\)
−0.0418392 + 0.999124i \(0.513322\pi\)
\(410\) 0 0
\(411\) 6.47138 11.2088i 0.319210 0.552887i
\(412\) −0.165604 + 0.747370i −0.00815873 + 0.0368203i
\(413\) 25.0309 7.57134i 1.23169 0.372561i
\(414\) −5.50701 + 50.3090i −0.270655 + 2.47255i
\(415\) 0 0
\(416\) 27.3554 + 0.589594i 1.34121 + 0.0289072i
\(417\) −19.7595 + 11.4081i −0.967625 + 0.558659i
\(418\) 1.42349 1.94162i 0.0696254 0.0949677i
\(419\) −13.0327 −0.636690 −0.318345 0.947975i \(-0.603127\pi\)
−0.318345 + 0.947975i \(0.603127\pi\)
\(420\) 0 0
\(421\) −34.2800 −1.67070 −0.835352 0.549715i \(-0.814736\pi\)
−0.835352 + 0.549715i \(0.814736\pi\)
\(422\) 14.1635 19.3187i 0.689469 0.940422i
\(423\) 5.71562 3.29991i 0.277903 0.160447i
\(424\) −1.85663 9.32612i −0.0901660 0.452916i
\(425\) 0 0
\(426\) 7.60584 69.4827i 0.368504 3.36645i
\(427\) 17.3718 18.5182i 0.840681 0.896158i
\(428\) 1.64504 + 0.364512i 0.0795159 + 0.0176194i
\(429\) −8.76273 + 15.1775i −0.423068 + 0.732776i
\(430\) 0 0
\(431\) 2.47034 1.42625i 0.118992 0.0687001i −0.439323 0.898329i \(-0.644781\pi\)
0.558315 + 0.829629i \(0.311448\pi\)
\(432\) 21.9747 + 31.3688i 1.05726 + 1.50923i
\(433\) 34.6179 1.66363 0.831815 0.555053i \(-0.187302\pi\)
0.831815 + 0.555053i \(0.187302\pi\)
\(434\) 23.4267 + 8.25787i 1.12452 + 0.396390i
\(435\) 0 0
\(436\) −5.33746 + 5.82607i −0.255618 + 0.279018i
\(437\) 4.12919 + 7.15196i 0.197526 + 0.342125i
\(438\) −0.184692 0.419685i −0.00882495 0.0200533i
\(439\) 5.46905 9.47267i 0.261023 0.452106i −0.705491 0.708719i \(-0.749273\pi\)
0.966514 + 0.256613i \(0.0826067\pi\)
\(440\) 0 0
\(441\) −35.9092 + 23.9113i −1.70996 + 1.13864i
\(442\) 1.89456 17.3076i 0.0901149 0.823240i
\(443\) 17.6971 30.6522i 0.840813 1.45633i −0.0483948 0.998828i \(-0.515411\pi\)
0.889208 0.457503i \(-0.151256\pi\)
\(444\) −9.30470 29.4998i −0.441582 1.40000i
\(445\) 0 0
\(446\) 15.8612 21.6344i 0.751050 1.02442i
\(447\) 8.65029i 0.409145i
\(448\) −16.3679 + 13.4198i −0.773311 + 0.634027i
\(449\) −28.0029 −1.32154 −0.660768 0.750590i \(-0.729769\pi\)
−0.660768 + 0.750590i \(0.729769\pi\)
\(450\) 0 0
\(451\) 4.46875 + 7.74010i 0.210425 + 0.364467i
\(452\) 5.11559 1.61354i 0.240617 0.0758945i
\(453\) −10.0030 + 17.3257i −0.469981 + 0.814031i
\(454\) −1.31367 0.143800i −0.0616537 0.00674885i
\(455\) 0 0
\(456\) 11.5315 + 3.91237i 0.540014 + 0.183214i
\(457\) −17.4849 10.0949i −0.817908 0.472220i 0.0317863 0.999495i \(-0.489880\pi\)
−0.849695 + 0.527275i \(0.823214\pi\)
\(458\) 7.45131 + 16.9319i 0.348177 + 0.791178i
\(459\) 21.1062 12.1856i 0.985151 0.568777i
\(460\) 0 0
\(461\) 0.127845i 0.00595433i 0.999996 + 0.00297717i \(0.000947663\pi\)
−0.999996 + 0.00297717i \(0.999052\pi\)
\(462\) −2.48977 13.3264i −0.115835 0.620002i
\(463\) −17.8655 −0.830282 −0.415141 0.909757i \(-0.636268\pi\)
−0.415141 + 0.909757i \(0.636268\pi\)
\(464\) 2.53648 1.77687i 0.117753 0.0824891i
\(465\) 0 0
\(466\) −8.88728 20.1950i −0.411695 0.935513i
\(467\) 12.7042 + 7.33477i 0.587880 + 0.339413i 0.764259 0.644910i \(-0.223105\pi\)
−0.176379 + 0.984322i \(0.556438\pi\)
\(468\) −58.2093 12.8982i −2.69072 0.596218i
\(469\) −26.7312 + 8.08563i −1.23433 + 0.373360i
\(470\) 0 0
\(471\) −40.8514 23.5855i −1.88233 1.08676i
\(472\) −27.4185 + 5.45844i −1.26204 + 0.251245i
\(473\) 1.43259 0.827107i 0.0658706 0.0380304i
\(474\) −37.1790 27.2577i −1.70769 1.25199i
\(475\) 0 0
\(476\) 7.59676 + 11.1216i 0.348197 + 0.509756i
\(477\) 20.7203i 0.948719i
\(478\) −11.8174 + 16.1187i −0.540517 + 0.737254i
\(479\) −13.0757 22.6478i −0.597444 1.03480i −0.993197 0.116446i \(-0.962850\pi\)
0.395753 0.918357i \(-0.370483\pi\)
\(480\) 0 0
\(481\) 21.4024 + 12.3567i 0.975863 + 0.563415i
\(482\) 30.3419 + 3.32134i 1.38204 + 0.151283i
\(483\) 45.2804 + 10.5958i 2.06033 + 0.482127i
\(484\) −18.6815 4.13949i −0.849158 0.188159i
\(485\) 0 0
\(486\) −1.73362 3.93939i −0.0786388 0.178694i
\(487\) −8.31227 14.3973i −0.376665 0.652403i 0.613910 0.789376i \(-0.289596\pi\)
−0.990575 + 0.136974i \(0.956262\pi\)
\(488\) −20.4052 + 17.9006i −0.923698 + 0.810323i
\(489\) 29.1818i 1.31965i
\(490\) 0 0
\(491\) 21.9094i 0.988758i −0.869246 0.494379i \(-0.835395\pi\)
0.869246 0.494379i \(-0.164605\pi\)
\(492\) −30.5367 + 33.3321i −1.37670 + 1.50273i
\(493\) −0.985330 1.70664i −0.0443770 0.0768633i
\(494\) −8.90476 + 3.91875i −0.400644 + 0.176313i
\(495\) 0 0
\(496\) −24.0690 11.2173i −1.08073 0.503673i
\(497\) −42.0628 9.84291i −1.88678 0.441515i
\(498\) 7.36127 67.2485i 0.329867 3.01348i
\(499\) 35.2377 + 20.3445i 1.57746 + 0.910745i 0.995213 + 0.0977301i \(0.0311582\pi\)
0.582243 + 0.813015i \(0.302175\pi\)
\(500\) 0 0
\(501\) 7.49011 + 12.9733i 0.334633 + 0.579602i
\(502\) −1.19140 0.873470i −0.0531746 0.0389849i
\(503\) 7.19624i 0.320864i −0.987047 0.160432i \(-0.948711\pi\)
0.987047 0.160432i \(-0.0512888\pi\)
\(504\) 40.6885 21.7153i 1.81241 0.967277i
\(505\) 0 0
\(506\) −5.81155 + 7.92684i −0.258355 + 0.352391i
\(507\) 27.2528 15.7344i 1.21034 0.698790i
\(508\) 1.28766 + 4.08243i 0.0571308 + 0.181128i
\(509\) −4.45357 2.57127i −0.197401 0.113970i 0.398042 0.917367i \(-0.369690\pi\)
−0.595443 + 0.803398i \(0.703023\pi\)
\(510\) 0 0
\(511\) −0.271248 + 0.0820469i −0.0119993 + 0.00362954i
\(512\) 18.8080 12.5802i 0.831203 0.555970i
\(513\) −11.7937 6.80907i −0.520703 0.300628i
\(514\) −6.34765 + 2.79344i −0.279983 + 0.123213i
\(515\) 0 0
\(516\) 6.16934 + 5.65195i 0.271590 + 0.248813i
\(517\) 1.28177 0.0563721
\(518\) −18.7921 + 3.51092i −0.825678 + 0.154261i
\(519\) 20.9797i 0.920905i
\(520\) 0 0
\(521\) 7.85043 4.53245i 0.343934 0.198570i −0.318077 0.948065i \(-0.603037\pi\)
0.662010 + 0.749495i \(0.269704\pi\)
\(522\) −6.17656 + 2.71815i −0.270341 + 0.118970i
\(523\) −15.2485 8.80370i −0.666768 0.384959i 0.128083 0.991764i \(-0.459118\pi\)
−0.794851 + 0.606805i \(0.792451\pi\)
\(524\) 18.8737 + 4.18209i 0.824502 + 0.182695i
\(525\) 0 0
\(526\) 1.19975 10.9603i 0.0523117 0.477890i
\(527\) −8.44869 + 14.6336i −0.368031 + 0.637448i
\(528\) 1.26624 + 14.4376i 0.0551058 + 0.628318i
\(529\) −5.35780 9.27999i −0.232948 0.403478i
\(530\) 0 0
\(531\) 60.9171 2.64358
\(532\) 3.25946 6.78344i 0.141315 0.294099i
\(533\) 36.1166i 1.56438i
\(534\) 13.6071 + 9.97602i 0.588837 + 0.431705i
\(535\) 0 0
\(536\) 29.2809 5.82921i 1.26474 0.251784i
\(537\) 31.9542 55.3462i 1.37892 2.38837i
\(538\) 29.6801 + 3.24890i 1.27960 + 0.140070i
\(539\) −8.36161 + 0.534711i −0.360160 + 0.0230316i
\(540\) 0 0
\(541\) 13.9811 24.2160i 0.601094 1.04113i −0.391561 0.920152i \(-0.628065\pi\)
0.992656 0.120974i \(-0.0386018\pi\)
\(542\) −27.8568 + 12.2591i −1.19655 + 0.526573i
\(543\) 9.23918 + 16.0027i 0.396491 + 0.686743i
\(544\) −6.92884 12.6216i −0.297072 0.541148i
\(545\) 0 0
\(546\) −18.2129 + 51.6681i −0.779440 + 2.21119i
\(547\) −29.6385 −1.26725 −0.633626 0.773640i \(-0.718434\pi\)
−0.633626 + 0.773640i \(0.718434\pi\)
\(548\) 6.30534 + 5.77654i 0.269351 + 0.246762i
\(549\) 51.2227 29.5735i 2.18613 1.26216i
\(550\) 0 0
\(551\) −0.550581 + 0.953634i −0.0234555 + 0.0406262i
\(552\) −47.0786 15.9726i −2.00380 0.679841i
\(553\) −19.4932 + 20.7796i −0.828935 + 0.883638i
\(554\) −7.26446 0.795196i −0.308637 0.0337846i
\(555\) 0 0
\(556\) −4.53463 14.3766i −0.192311 0.609706i
\(557\) 30.9460 17.8667i 1.31123 0.757037i 0.328927 0.944355i \(-0.393313\pi\)
0.982299 + 0.187319i \(0.0599798\pi\)
\(558\) 46.6646 + 34.2121i 1.97547 + 1.44831i
\(559\) −6.68471 −0.282733
\(560\) 0 0
\(561\) 9.22231 0.389366
\(562\) 17.8290 + 13.0713i 0.752071 + 0.551379i
\(563\) 19.9226 11.5023i 0.839639 0.484766i −0.0175025 0.999847i \(-0.505571\pi\)
0.857142 + 0.515081i \(0.172238\pi\)
\(564\) 1.95017 + 6.18284i 0.0821169 + 0.260345i
\(565\) 0 0
\(566\) −40.1642 4.39653i −1.68823 0.184800i
\(567\) −26.5773 + 8.03910i −1.11614 + 0.337611i
\(568\) 43.7333 + 14.8377i 1.83501 + 0.622574i
\(569\) −9.43937 + 16.3495i −0.395719 + 0.685405i −0.993193 0.116483i \(-0.962838\pi\)
0.597474 + 0.801888i \(0.296171\pi\)
\(570\) 0 0
\(571\) −20.7520 + 11.9812i −0.868446 + 0.501397i −0.866831 0.498601i \(-0.833847\pi\)
−0.00161422 + 0.999999i \(0.500514\pi\)
\(572\) −8.53789 7.82186i −0.356987 0.327048i
\(573\) 11.2401 0.469561
\(574\) 18.1751 + 21.2184i 0.758616 + 0.885638i
\(575\) 0 0
\(576\) −45.5459 + 18.8828i −1.89774 + 0.786784i
\(577\) 5.31557 + 9.20684i 0.221290 + 0.383286i 0.955200 0.295961i \(-0.0956399\pi\)
−0.733910 + 0.679247i \(0.762307\pi\)
\(578\) 13.6191 5.99341i 0.566480 0.249293i
\(579\) −23.2038 + 40.1902i −0.964318 + 1.67025i
\(580\) 0 0
\(581\) −40.7103 9.52641i −1.68895 0.395222i
\(582\) 37.0819 + 4.05912i 1.53709 + 0.168256i
\(583\) −2.01207 + 3.48501i −0.0833316 + 0.144335i
\(584\) 0.297120 0.0591504i 0.0122949 0.00244766i
\(585\) 0 0
\(586\) −0.749527 0.549514i −0.0309627 0.0227002i
\(587\) 0.240690i 0.00993436i 0.999988 + 0.00496718i \(0.00158111\pi\)
−0.999988 + 0.00496718i \(0.998419\pi\)
\(588\) −15.3012 39.5202i −0.631011 1.62979i
\(589\) 9.44189 0.389046
\(590\) 0 0
\(591\) −37.0214 64.1229i −1.52286 2.63766i
\(592\) 20.3591 1.78557i 0.836753 0.0733864i
\(593\) −15.4627 + 26.7822i −0.634977 + 1.09981i 0.351543 + 0.936172i \(0.385657\pi\)
−0.986520 + 0.163640i \(0.947676\pi\)
\(594\) 1.76366 16.1119i 0.0723640 0.661077i
\(595\) 0 0
\(596\) −5.57995 1.23642i −0.228564 0.0506458i
\(597\) −33.7290 19.4734i −1.38044 0.796995i
\(598\) 36.3545 15.9987i 1.48665 0.654235i
\(599\) −25.9364 + 14.9744i −1.05973 + 0.611838i −0.925359 0.379092i \(-0.876236\pi\)
−0.134376 + 0.990930i \(0.542903\pi\)
\(600\) 0 0
\(601\) 23.0748i 0.941241i −0.882336 0.470621i \(-0.844030\pi\)
0.882336 0.470621i \(-0.155970\pi\)
\(602\) 3.92724 3.36398i 0.160062 0.137106i
\(603\) −65.0550 −2.64925
\(604\) −9.74633 8.92895i −0.396572 0.363314i
\(605\) 0 0
\(606\) −11.7762 + 5.18238i −0.478374 + 0.210520i
\(607\) −15.4846 8.94004i −0.628501 0.362865i 0.151670 0.988431i \(-0.451535\pi\)
−0.780171 + 0.625566i \(0.784868\pi\)
\(608\) −4.17197 + 6.87932i −0.169196 + 0.278993i
\(609\) 1.79526 + 5.93516i 0.0727477 + 0.240505i
\(610\) 0 0
\(611\) −4.48571 2.58982i −0.181472 0.104773i
\(612\) 9.43756 + 29.9210i 0.381491 + 1.20948i
\(613\) 7.24872 4.18505i 0.292773 0.169033i −0.346419 0.938080i \(-0.612602\pi\)
0.639192 + 0.769047i \(0.279269\pi\)
\(614\) −4.08090 + 5.56626i −0.164692 + 0.224636i
\(615\) 0 0
\(616\) 8.95221 + 0.298748i 0.360695 + 0.0120369i
\(617\) 33.7886i 1.36028i 0.733084 + 0.680139i \(0.238080\pi\)
−0.733084 + 0.680139i \(0.761920\pi\)
\(618\) 1.32142 + 0.968800i 0.0531555 + 0.0389708i
\(619\) 16.6442 + 28.8285i 0.668986 + 1.15872i 0.978188 + 0.207721i \(0.0666046\pi\)
−0.309203 + 0.950996i \(0.600062\pi\)
\(620\) 0 0
\(621\) 48.1487 + 27.7987i 1.93214 + 1.11552i
\(622\) −1.83075 + 16.7247i −0.0734065 + 0.670600i
\(623\) 7.13430 7.60510i 0.285830 0.304692i
\(624\) 24.7400 53.0848i 0.990394 2.12509i
\(625\) 0 0
\(626\) 34.4410 15.1566i 1.37654 0.605780i
\(627\) −2.57661 4.46283i −0.102900 0.178228i
\(628\) 21.0531 22.9804i 0.840112 0.917017i
\(629\) 13.0047i 0.518533i
\(630\) 0 0
\(631\) 43.1690i 1.71853i 0.511528 + 0.859266i \(0.329079\pi\)
−0.511528 + 0.859266i \(0.670921\pi\)
\(632\) 22.8970 20.0866i 0.910793 0.799002i
\(633\) −25.6368 44.4043i −1.01897 1.76491i
\(634\) 15.0702 + 34.2446i 0.598514 + 1.36003i
\(635\) 0 0
\(636\) −19.8719 4.40327i −0.787972 0.174601i
\(637\) 30.3429 + 15.0234i 1.20223 + 0.595250i
\(638\) −1.30280 0.142610i −0.0515784 0.00564597i
\(639\) −87.1481 50.3150i −3.44753 1.99043i
\(640\) 0 0
\(641\) −16.0131 27.7355i −0.632479 1.09548i −0.987043 0.160454i \(-0.948704\pi\)
0.354565 0.935031i \(-0.384629\pi\)
\(642\) 2.13243 2.90859i 0.0841602 0.114793i
\(643\) 37.9515i 1.49666i 0.663326 + 0.748331i \(0.269144\pi\)
−0.663326 + 0.748331i \(0.730856\pi\)
\(644\) −13.3070 + 27.6940i −0.524371 + 1.09130i
\(645\) 0 0
\(646\) 4.12882 + 3.02703i 0.162446 + 0.119097i
\(647\) 7.78359 4.49386i 0.306004 0.176672i −0.339133 0.940739i \(-0.610134\pi\)
0.645137 + 0.764067i \(0.276800\pi\)
\(648\) 29.1124 5.79567i 1.14364 0.227675i
\(649\) 10.2458 + 5.91543i 0.402184 + 0.232201i
\(650\) 0 0
\(651\) 36.3761 38.7766i 1.42569 1.51977i
\(652\) −18.8240 4.17108i −0.737205 0.163352i
\(653\) 15.8302 + 9.13956i 0.619483 + 0.357658i 0.776668 0.629911i \(-0.216909\pi\)
−0.157185 + 0.987569i \(0.550242\pi\)
\(654\) 6.81230 + 15.4799i 0.266382 + 0.605312i
\(655\) 0 0
\(656\) −17.1365 24.4623i −0.669067 0.955092i
\(657\) −0.660129 −0.0257541
\(658\) 3.93863 0.735853i 0.153544 0.0286865i
\(659\) 36.9643i 1.43992i −0.694014 0.719962i \(-0.744159\pi\)
0.694014 0.719962i \(-0.255841\pi\)
\(660\) 0 0
\(661\) −19.9261 + 11.5043i −0.775035 + 0.447466i −0.834668 0.550754i \(-0.814340\pi\)
0.0596330 + 0.998220i \(0.481007\pi\)
\(662\) 13.8324 + 31.4319i 0.537610 + 1.22164i
\(663\) −32.2746 18.6338i −1.25344 0.723676i
\(664\) 42.3271 + 14.3606i 1.64261 + 0.557298i
\(665\) 0 0
\(666\) −44.2682 4.84576i −1.71536 0.187769i
\(667\) 2.24780 3.89330i 0.0870351 0.150749i
\(668\) −9.43911 + 2.97725i −0.365210 + 0.115193i
\(669\) −28.7098 49.7268i −1.10998 1.92255i
\(670\) 0 0
\(671\) 11.4871 0.443453
\(672\) 12.1794 + 43.6372i 0.469832 + 1.68334i
\(673\) 42.0925i 1.62255i 0.584668 + 0.811273i \(0.301225\pi\)
−0.584668 + 0.811273i \(0.698775\pi\)
\(674\) −16.4791 + 22.4772i −0.634753 + 0.865791i
\(675\) 0 0
\(676\) 6.25428 + 19.8287i 0.240549 + 0.762641i
\(677\) −12.1626 + 21.0662i −0.467447 + 0.809642i −0.999308 0.0371897i \(-0.988159\pi\)
0.531861 + 0.846831i \(0.321493\pi\)
\(678\) 1.24934 11.4133i 0.0479807 0.438325i
\(679\) 5.25302 22.4483i 0.201592 0.861487i
\(680\) 0 0
\(681\) −1.41433 + 2.44969i −0.0541972 + 0.0938723i
\(682\) 4.52645 + 10.2856i 0.173327 + 0.393858i
\(683\) −9.59853 16.6251i −0.367278 0.636144i 0.621861 0.783127i \(-0.286377\pi\)
−0.989139 + 0.146984i \(0.953043\pi\)
\(684\) 11.8425 12.9266i 0.452809 0.494260i
\(685\) 0 0
\(686\) −25.3867 + 6.44340i −0.969267 + 0.246010i
\(687\) 39.5963 1.51069
\(688\) −4.52765 + 3.17174i −0.172615 + 0.120921i
\(689\) 14.0830 8.13083i 0.536520 0.309760i
\(690\) 0 0
\(691\) 7.00274 12.1291i 0.266397 0.461413i −0.701532 0.712638i \(-0.747500\pi\)
0.967929 + 0.251225i \(0.0808335\pi\)
\(692\) −13.5331 2.99871i −0.514453 0.113994i
\(693\) −19.0043 4.44710i −0.721914 0.168931i
\(694\) 1.29834 11.8609i 0.0492842 0.450233i
\(695\) 0 0
\(696\) −1.29427 6.50128i −0.0490591 0.246430i
\(697\) −16.4592 + 9.50271i −0.623436 + 0.359941i
\(698\) −19.7157 + 26.8919i −0.746252 + 1.01787i
\(699\) −47.2271 −1.78629
\(700\) 0 0
\(701\) 11.9124 0.449923 0.224962 0.974368i \(-0.427774\pi\)
0.224962 + 0.974368i \(0.427774\pi\)
\(702\) −38.7263 + 52.8220i −1.46163 + 1.99364i
\(703\) −6.29320 + 3.63338i −0.237353 + 0.137036i
\(704\) −9.49413 1.24683i −0.357823 0.0469918i
\(705\) 0 0
\(706\) −3.18120 + 29.0616i −0.119726 + 1.09375i
\(707\) 2.30220 + 7.61108i 0.0865830 + 0.286244i
\(708\) −12.9455 + 58.4227i −0.486520 + 2.19566i
\(709\) 23.6490 40.9613i 0.888158 1.53833i 0.0461071 0.998937i \(-0.485318\pi\)
0.842051 0.539398i \(-0.181348\pi\)
\(710\) 0 0
\(711\) −57.4779 + 33.1849i −2.15559 + 1.24453i
\(712\) −8.38004 + 7.35148i −0.314055 + 0.275508i
\(713\) −38.5474 −1.44361
\(714\) 28.3384 5.29446i 1.06054 0.198140i
\(715\) 0 0
\(716\) 31.1343 + 28.5232i 1.16354 + 1.06596i
\(717\) 21.3903 + 37.0491i 0.798835 + 1.38362i
\(718\) 15.6377 + 35.5342i 0.583593 + 1.32613i
\(719\) −0.888951 + 1.53971i −0.0331523 + 0.0574214i −0.882125 0.471014i \(-0.843888\pi\)
0.848973 + 0.528436i \(0.177221\pi\)
\(720\) 0 0
\(721\) 0.692832 0.738552i 0.0258024 0.0275051i
\(722\) −2.61255 + 23.8668i −0.0972290 + 0.888230i
\(723\) 32.6668 56.5806i 1.21489 2.10425i
\(724\) −11.6433 + 3.67249i −0.432720 + 0.136487i
\(725\) 0 0
\(726\) −24.2164 + 33.0307i −0.898755 + 1.22588i
\(727\) 27.1619i 1.00738i 0.863885 + 0.503689i \(0.168024\pi\)
−0.863885 + 0.503689i \(0.831976\pi\)
\(728\) −30.7258 19.1335i −1.13877 0.709136i
\(729\) 22.2718 0.824883
\(730\) 0 0
\(731\) 1.75883 + 3.04638i 0.0650526 + 0.112674i
\(732\) 17.4772 + 55.4099i 0.645975 + 2.04801i
\(733\) 11.3880 19.7246i 0.420625 0.728543i −0.575376 0.817889i \(-0.695144\pi\)
0.996001 + 0.0893459i \(0.0284777\pi\)
\(734\) −28.1763 3.08428i −1.04001 0.113843i
\(735\) 0 0
\(736\) 17.0324 28.0855i 0.627824 1.03525i
\(737\) −10.9418 6.31725i −0.403046 0.232699i
\(738\) 26.2143 + 59.5680i 0.964963 + 2.19273i
\(739\) −28.1611 + 16.2588i −1.03592 + 0.598091i −0.918676 0.395012i \(-0.870740\pi\)
−0.117247 + 0.993103i \(0.537407\pi\)
\(740\) 0 0
\(741\) 20.8243i 0.764999i
\(742\) −4.18200 + 11.8639i −0.153526 + 0.435537i
\(743\) 9.19402 0.337296 0.168648 0.985676i \(-0.446060\pi\)
0.168648 + 0.985676i \(0.446060\pi\)
\(744\) −42.7279 + 37.4834i −1.56648 + 1.37421i
\(745\) 0 0
\(746\) 11.7295 + 26.6535i 0.429449 + 0.975855i
\(747\) −84.3459 48.6971i −3.08605 1.78173i
\(748\) −1.31818 + 5.94894i −0.0481975 + 0.217515i
\(749\) −1.62563 1.52499i −0.0593993 0.0557221i
\(750\) 0 0
\(751\) −17.5852 10.1528i −0.641692 0.370481i 0.143574 0.989640i \(-0.454140\pi\)
−0.785266 + 0.619159i \(0.787474\pi\)
\(752\) −4.26705 + 0.374236i −0.155603 + 0.0136470i
\(753\) −2.73843 + 1.58104i −0.0997941 + 0.0576161i
\(754\) 4.27118 + 3.13141i 0.155547 + 0.114039i
\(755\) 0 0
\(756\) −3.83028 50.5212i −0.139306 1.83744i
\(757\) 10.9555i 0.398184i 0.979981 + 0.199092i \(0.0637992\pi\)
−0.979981 + 0.199092i \(0.936201\pi\)
\(758\) −2.72877 + 3.72199i −0.0991134 + 0.135189i
\(759\) 10.5193 + 18.2199i 0.381825 + 0.661341i
\(760\) 0 0
\(761\) −27.2104 15.7099i −0.986375 0.569484i −0.0821860 0.996617i \(-0.526190\pi\)
−0.904189 + 0.427133i \(0.859523\pi\)
\(762\) 9.10823 + 0.997022i 0.329957 + 0.0361183i
\(763\) 10.0048 3.02626i 0.362200 0.109558i
\(764\) −1.60659 + 7.25052i −0.0581243 + 0.262314i
\(765\) 0 0
\(766\) 19.2259 + 43.6879i 0.694661 + 1.57851i
\(767\) −23.9044 41.4036i −0.863137 1.49500i
\(768\) −8.43068 47.6937i −0.304216 1.72100i
\(769\) 23.9511i 0.863700i −0.901945 0.431850i \(-0.857861\pi\)
0.901945 0.431850i \(-0.142139\pi\)
\(770\) 0 0
\(771\) 14.8444i 0.534606i
\(772\) −22.6085 20.7124i −0.813696 0.745455i
\(773\) 7.59249 + 13.1506i 0.273083 + 0.472993i 0.969650 0.244499i \(-0.0786234\pi\)
−0.696567 + 0.717492i \(0.745290\pi\)
\(774\) 11.0252 4.85193i 0.396294 0.174399i
\(775\) 0 0
\(776\) −7.91864 + 23.3398i −0.284263 + 0.837851i
\(777\) −9.32355 + 39.8434i −0.334480 + 1.42937i
\(778\) 0.555850 5.07793i 0.0199282 0.182053i
\(779\) 9.19703 + 5.30991i 0.329518 + 0.190247i
\(780\) 0 0
\(781\) −9.77179 16.9252i −0.349662 0.605633i
\(782\) −16.8563 12.3582i −0.602779 0.441927i
\(783\) 7.41329i 0.264929i
\(784\) 27.6800 4.22140i 0.988570 0.150764i
\(785\) 0 0
\(786\) 24.4656 33.3706i 0.872659 1.19029i
\(787\) −15.8480 + 9.14982i −0.564919 + 0.326156i −0.755117 0.655590i \(-0.772420\pi\)
0.190199 + 0.981746i \(0.439087\pi\)
\(788\) 46.6547 14.7157i 1.66201 0.524223i
\(789\) −20.4383 11.8001i −0.727624 0.420094i
\(790\) 0 0
\(791\) −6.90929 1.61681i −0.245666 0.0574870i
\(792\) 19.7590 + 6.70376i 0.702107 + 0.238208i
\(793\) −40.2004 23.2097i −1.42756 0.824201i
\(794\) 9.67866 4.25933i 0.343483 0.151158i
\(795\) 0 0
\(796\) 17.3825 18.9738i 0.616108 0.672508i
\(797\) 15.0960 0.534728 0.267364 0.963596i \(-0.413847\pi\)
0.267364 + 0.963596i \(0.413847\pi\)
\(798\) −10.4795 12.2342i −0.370971 0.433086i
\(799\) 2.72566i 0.0964268i
\(800\) 0 0
\(801\) 21.0363 12.1453i 0.743280 0.429133i
\(802\) 12.3574 5.43820i 0.436357 0.192029i
\(803\) −0.111029 0.0641026i −0.00391813 0.00226213i
\(804\) 13.8248 62.3912i 0.487563 2.20037i
\(805\) 0 0
\(806\) 4.94138 45.1417i 0.174053 1.59005i
\(807\) 31.9543 55.3464i 1.12484 1.94829i
\(808\) −1.65973 8.33706i −0.0583892 0.293297i
\(809\) 22.2240 + 38.4931i 0.781355 + 1.35335i 0.931153 + 0.364630i \(0.118804\pi\)
−0.149797 + 0.988717i \(0.547862\pi\)
\(810\) 0 0
\(811\) −34.6449 −1.21655 −0.608274 0.793727i \(-0.708138\pi\)
−0.608274 + 0.793727i \(0.708138\pi\)
\(812\) −4.08513 + 0.309716i −0.143360 + 0.0108689i
\(813\) 65.1449i 2.28473i
\(814\) −6.97504 5.11374i −0.244475 0.179236i
\(815\) 0 0
\(816\) −30.7014 + 2.69263i −1.07476 + 0.0942608i
\(817\) 0.982794 1.70225i 0.0343836 0.0595542i
\(818\) −30.4663 3.33496i −1.06523 0.116604i
\(819\) 57.5225 + 53.9616i 2.01000 + 1.88557i
\(820\) 0 0
\(821\) −11.8550 + 20.5335i −0.413742 + 0.716622i −0.995296 0.0968858i \(-0.969112\pi\)
0.581553 + 0.813508i \(0.302445\pi\)
\(822\) 16.7533 7.37270i 0.584339 0.257152i
\(823\) 3.24588 + 5.62203i 0.113144 + 0.195972i 0.917036 0.398803i \(-0.130574\pi\)
−0.803892 + 0.594775i \(0.797241\pi\)
\(824\) −0.813810 + 0.713923i −0.0283504 + 0.0248707i
\(825\) 0 0
\(826\) 34.8795 + 12.2949i 1.21361 + 0.427796i
\(827\) −39.4872 −1.37310 −0.686552 0.727081i \(-0.740877\pi\)
−0.686552 + 0.727081i \(0.740877\pi\)
\(828\) −48.3481 + 52.7740i −1.68021 + 1.83402i
\(829\) 2.82562 1.63137i 0.0981377 0.0566598i −0.450128 0.892964i \(-0.648622\pi\)
0.548266 + 0.836304i \(0.315288\pi\)
\(830\) 0 0
\(831\) −7.82108 + 13.5465i −0.271310 + 0.469923i
\(832\) 30.7067 + 23.5464i 1.06456 + 0.816325i
\(833\) −1.13705 17.7808i −0.0393966 0.616069i
\(834\) −32.0755 3.51110i −1.11068 0.121580i
\(835\) 0 0
\(836\) 3.24707 1.02418i 0.112302 0.0354220i
\(837\) 55.0490 31.7826i 1.90277 1.09857i
\(838\) −14.8642 10.8977i −0.513475 0.376454i
\(839\) −5.39522 −0.186264 −0.0931318 0.995654i \(-0.529688\pi\)
−0.0931318 + 0.995654i \(0.529688\pi\)
\(840\) 0 0
\(841\) −28.4006 −0.979330
\(842\) −39.0973 28.6642i −1.34738 0.987832i
\(843\) 40.9801 23.6599i 1.41143 0.814889i
\(844\) 32.3078 10.1904i 1.11208 0.350768i
\(845\) 0 0
\(846\) 9.27814 + 1.01562i 0.318989 + 0.0349178i
\(847\) 18.4611 + 17.3182i 0.634330 + 0.595061i
\(848\) 5.68074 12.1892i 0.195077 0.418578i
\(849\) −43.2417 + 74.8968i −1.48405 + 2.57045i
\(850\) 0 0
\(851\) 25.6926 14.8336i 0.880731 0.508490i
\(852\) 66.7745 72.8872i 2.28766 2.49707i
\(853\) 10.7675 0.368672 0.184336 0.982863i \(-0.440987\pi\)
0.184336 + 0.982863i \(0.440987\pi\)
\(854\) 35.2975 6.59463i 1.20786 0.225664i
\(855\) 0 0
\(856\) 1.57142 + 1.79128i 0.0537100 + 0.0612247i
\(857\) −17.5949 30.4752i −0.601029 1.04101i −0.992666 0.120892i \(-0.961424\pi\)
0.391637 0.920120i \(-0.371909\pi\)
\(858\) −22.6852 + 9.98318i −0.774460 + 0.340820i
\(859\) 20.6193 35.7136i 0.703520 1.21853i −0.263703 0.964604i \(-0.584944\pi\)
0.967223 0.253929i \(-0.0817228\pi\)
\(860\) 0 0
\(861\) 57.2398 17.3139i 1.95073 0.590055i
\(862\) 4.01010 + 0.438960i 0.136584 + 0.0149510i
\(863\) −11.5147 + 19.9441i −0.391966 + 0.678906i −0.992709 0.120537i \(-0.961538\pi\)
0.600742 + 0.799443i \(0.294872\pi\)
\(864\) −1.16714 + 54.1518i −0.0397069 + 1.84228i
\(865\) 0 0
\(866\) 39.4827 + 28.9467i 1.34168 + 0.983649i
\(867\) 31.8491i 1.08165i
\(868\) 19.8138 + 29.0072i 0.672525 + 0.984570i
\(869\) −12.8898 −0.437258
\(870\) 0 0
\(871\) 25.5281 + 44.2160i 0.864987 + 1.49820i
\(872\) −10.9592 + 2.18174i −0.371124 + 0.0738829i
\(873\) 26.8524 46.5097i 0.908815 1.57411i
\(874\) −1.27085 + 11.6098i −0.0429871 + 0.392706i
\(875\) 0 0
\(876\) 0.140284 0.633098i 0.00473974 0.0213904i
\(877\) −3.51842 2.03136i −0.118809 0.0685941i 0.439418 0.898283i \(-0.355185\pi\)
−0.558227 + 0.829689i \(0.688518\pi\)
\(878\) 14.1584 6.23077i 0.477824 0.210278i
\(879\) −1.72279 + 0.994655i −0.0581084 + 0.0335489i
\(880\) 0 0
\(881\) 42.0606i 1.41706i 0.705682 + 0.708529i \(0.250641\pi\)
−0.705682 + 0.708529i \(0.749359\pi\)
\(882\) −60.9496 2.75487i −2.05228 0.0927612i
\(883\) −54.8918 −1.84725 −0.923627 0.383291i \(-0.874790\pi\)
−0.923627 + 0.383291i \(0.874790\pi\)
\(884\) 16.6330 18.1557i 0.559430 0.610641i
\(885\) 0 0
\(886\) 45.8147 20.1619i 1.53918 0.677352i
\(887\) 33.0168 + 19.0622i 1.10859 + 0.640047i 0.938465 0.345375i \(-0.112248\pi\)
0.170129 + 0.985422i \(0.445581\pi\)
\(888\) 14.0547 41.4257i 0.471646 1.39016i
\(889\) 1.29027 5.51387i 0.0432743 0.184929i
\(890\) 0 0
\(891\) −10.8788 6.28089i −0.364454 0.210418i
\(892\) 36.1803 11.4119i 1.21141 0.382097i
\(893\) 1.31899 0.761518i 0.0441383 0.0254832i
\(894\) −7.23317 + 9.86591i −0.241913 + 0.329965i
\(895\) 0 0
\(896\) −29.8894 + 1.61922i −0.998536 + 0.0540945i
\(897\) 85.0171i 2.83864i
\(898\) −31.9381 23.4154i −1.06579 0.781380i
\(899\) −2.56993 4.45125i −0.0857121 0.148458i
\(900\) 0 0
\(901\) −7.41082 4.27864i −0.246890 0.142542i
\(902\) −1.37536 + 12.5645i −0.0457943 + 0.418351i
\(903\) −3.20457 10.5943i −0.106641 0.352557i
\(904\) 7.18369 + 2.43725i 0.238926 + 0.0810617i
\(905\) 0 0
\(906\) −25.8960 + 11.3962i −0.860338 + 0.378613i
\(907\) 0.177354 + 0.307186i 0.00588894 + 0.0101999i 0.868955 0.494891i \(-0.164792\pi\)
−0.863066 + 0.505091i \(0.831459\pi\)
\(908\) −1.37804 1.26247i −0.0457319 0.0418966i
\(909\) 18.5229i 0.614366i
\(910\) 0 0
\(911\) 12.2958i 0.407379i −0.979036 0.203690i \(-0.934707\pi\)
0.979036 0.203690i \(-0.0652934\pi\)
\(912\) 9.88063 + 14.1046i 0.327180 + 0.467050i
\(913\) −9.45758 16.3810i −0.313000 0.542132i
\(914\) −11.5009 26.1340i −0.380416 0.864436i
\(915\) 0 0
\(916\) −5.65967 + 25.5420i −0.187001 + 0.843932i
\(917\) −18.6510 17.4964i −0.615912 0.577783i
\(918\) 34.2616 + 3.75040i 1.13080 + 0.123782i
\(919\) −0.243118 0.140364i −0.00801973 0.00463019i 0.495985 0.868331i \(-0.334807\pi\)
−0.504005 + 0.863701i \(0.668141\pi\)
\(920\) 0 0
\(921\) 7.38668 + 12.7941i 0.243399 + 0.421580i
\(922\) −0.106901 + 0.145811i −0.00352060 + 0.00480203i
\(923\) 78.9760i 2.59953i
\(924\) 8.30360 17.2811i 0.273168 0.568506i
\(925\) 0 0
\(926\) −20.3762 14.9388i −0.669603 0.490918i
\(927\) 2.04289 1.17946i 0.0670974 0.0387387i
\(928\) 4.37871 + 0.0943747i 0.143738 + 0.00309800i
\(929\) −28.1316 16.2418i −0.922967 0.532875i −0.0383868 0.999263i \(-0.512222\pi\)
−0.884580 + 0.466388i \(0.845555\pi\)
\(930\) 0 0
\(931\) −8.28674 + 5.51800i −0.271587 + 0.180845i
\(932\) 6.75036 30.4643i 0.221115 0.997891i
\(933\) 31.1877 + 18.0062i 1.02104 + 0.589497i
\(934\) 8.35634 + 18.9885i 0.273428 + 0.621322i
\(935\) 0 0
\(936\) −55.6042 63.3840i −1.81748 2.07177i
\(937\) −59.7020 −1.95038 −0.975190 0.221368i \(-0.928948\pi\)
−0.975190 + 0.221368i \(0.928948\pi\)
\(938\) −37.2487 13.1301i −1.21621 0.428713i
\(939\) 80.5424i 2.62840i
\(940\) 0 0
\(941\) 12.3373 7.12292i 0.402183 0.232201i −0.285242 0.958455i \(-0.592074\pi\)
0.687426 + 0.726255i \(0.258741\pi\)
\(942\) −26.8705 61.0590i −0.875488 1.98941i
\(943\) −37.5477 21.6782i −1.22272 0.705939i
\(944\) −35.8358 16.7012i −1.16636 0.543578i
\(945\) 0 0
\(946\) 2.32552 + 0.254560i 0.0756092 + 0.00827647i
\(947\) 15.0513 26.0696i 0.489101 0.847148i −0.510820 0.859688i \(-0.670658\pi\)
0.999921 + 0.0125394i \(0.00399152\pi\)
\(948\) −19.6115 62.1764i −0.636950 2.01940i
\(949\) 0.259040 + 0.448670i 0.00840879 + 0.0145645i
\(950\) 0 0
\(951\) 80.0831 2.59687
\(952\) −0.635283 + 19.0367i −0.0205896 + 0.616984i
\(953\) 3.58515i 0.116134i −0.998313 0.0580672i \(-0.981506\pi\)
0.998313 0.0580672i \(-0.0184938\pi\)
\(954\) −17.3259 + 23.6322i −0.560946 + 0.765120i
\(955\) 0 0
\(956\) −26.9563 + 8.50244i −0.871827 + 0.274988i
\(957\) −1.40263 + 2.42942i −0.0453405 + 0.0785320i
\(958\) 4.02433 36.7640i 0.130020 1.18779i
\(959\) −3.27521 10.8279i −0.105762 0.349650i
\(960\) 0 0
\(961\) −6.53585 + 11.3204i −0.210834 + 0.365175i
\(962\) 14.0777 + 31.9893i 0.453882 + 1.03138i
\(963\) −2.59612 4.49662i −0.0836589 0.144902i
\(964\) 31.8286 + 29.1593i 1.02513 + 0.939159i
\(965\) 0 0
\(966\) 42.7836 + 49.9473i 1.37654 + 1.60703i
\(967\) −46.1614 −1.48445 −0.742226 0.670150i \(-0.766230\pi\)
−0.742226 + 0.670150i \(0.766230\pi\)
\(968\) −17.8454 20.3422i −0.573574 0.653824i
\(969\) 9.49011 5.47912i 0.304866 0.176015i
\(970\) 0 0
\(971\) 5.83113 10.0998i 0.187130 0.324118i −0.757162 0.653227i \(-0.773415\pi\)
0.944292 + 0.329108i \(0.106748\pi\)
\(972\) 1.31678 5.94261i 0.0422357 0.190609i
\(973\) −4.54381 + 19.4176i −0.145668 + 0.622499i
\(974\) 2.55828 23.3710i 0.0819727 0.748856i
\(975\) 0 0
\(976\) −38.2408 + 3.35386i −1.22406 + 0.107355i
\(977\) −36.7913 + 21.2415i −1.17706 + 0.679575i −0.955332 0.295534i \(-0.904503\pi\)
−0.221726 + 0.975109i \(0.571169\pi\)
\(978\) −24.4012 + 33.2827i −0.780263 + 1.06426i
\(979\) 4.71754 0.150773
\(980\) 0 0
\(981\) 24.3486 0.777390
\(982\) 18.3202 24.9883i 0.584620 0.797410i
\(983\) 27.4903 15.8715i 0.876804 0.506223i 0.00720094 0.999974i \(-0.497708\pi\)
0.869603 + 0.493751i \(0.164375\pi\)
\(984\) −62.6996 + 12.4822i −1.99879 + 0.397917i
\(985\) 0 0
\(986\) 0.303257 2.77039i 0.00965767 0.0882270i
\(987\) 1.95412 8.35075i 0.0622002 0.265807i
\(988\) −13.4329 2.97650i −0.427358 0.0946951i
\(989\) −4.01235 + 6.94960i −0.127585 + 0.220984i
\(990\) 0 0
\(991\) 25.4182 14.6752i 0.807436 0.466173i −0.0386286 0.999254i \(-0.512299\pi\)
0.846065 + 0.533080i \(0.178966\pi\)
\(992\) −18.0718 32.9197i −0.573780 1.04520i
\(993\) 73.5053 2.33262
\(994\) −39.7435 46.3981i −1.26059 1.47166i
\(995\) 0 0
\(996\) 64.6274 70.5435i 2.04780 2.23526i
\(997\) 5.40341 + 9.35899i 0.171128 + 0.296402i 0.938814 0.344423i \(-0.111926\pi\)
−0.767687 + 0.640825i \(0.778592\pi\)
\(998\) 23.1780 + 52.6685i 0.733688 + 1.66719i
\(999\) −24.4608 + 42.3673i −0.773905 + 1.34044i
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 700.2.t.c.299.13 32
4.3 odd 2 inner 700.2.t.c.299.14 32
5.2 odd 4 700.2.p.c.551.6 32
5.3 odd 4 140.2.o.a.131.11 yes 32
5.4 even 2 700.2.t.d.299.4 32
7.3 odd 6 700.2.t.d.199.3 32
20.3 even 4 140.2.o.a.131.10 yes 32
20.7 even 4 700.2.p.c.551.7 32
20.19 odd 2 700.2.t.d.299.3 32
28.3 even 6 700.2.t.d.199.4 32
35.3 even 12 140.2.o.a.31.10 32
35.13 even 4 980.2.o.f.411.11 32
35.17 even 12 700.2.p.c.451.7 32
35.18 odd 12 980.2.o.f.31.10 32
35.23 odd 12 980.2.g.a.391.1 32
35.24 odd 6 inner 700.2.t.c.199.14 32
35.33 even 12 980.2.g.a.391.2 32
140.3 odd 12 140.2.o.a.31.11 yes 32
140.23 even 12 980.2.g.a.391.4 32
140.59 even 6 inner 700.2.t.c.199.13 32
140.83 odd 4 980.2.o.f.411.10 32
140.87 odd 12 700.2.p.c.451.6 32
140.103 odd 12 980.2.g.a.391.3 32
140.123 even 12 980.2.o.f.31.11 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.10 32 35.3 even 12
140.2.o.a.31.11 yes 32 140.3 odd 12
140.2.o.a.131.10 yes 32 20.3 even 4
140.2.o.a.131.11 yes 32 5.3 odd 4
700.2.p.c.451.6 32 140.87 odd 12
700.2.p.c.451.7 32 35.17 even 12
700.2.p.c.551.6 32 5.2 odd 4
700.2.p.c.551.7 32 20.7 even 4
700.2.t.c.199.13 32 140.59 even 6 inner
700.2.t.c.199.14 32 35.24 odd 6 inner
700.2.t.c.299.13 32 1.1 even 1 trivial
700.2.t.c.299.14 32 4.3 odd 2 inner
700.2.t.d.199.3 32 7.3 odd 6
700.2.t.d.199.4 32 28.3 even 6
700.2.t.d.299.3 32 20.19 odd 2
700.2.t.d.299.4 32 5.4 even 2
980.2.g.a.391.1 32 35.23 odd 12
980.2.g.a.391.2 32 35.33 even 12
980.2.g.a.391.3 32 140.103 odd 12
980.2.g.a.391.4 32 140.23 even 12
980.2.o.f.31.10 32 35.18 odd 12
980.2.o.f.31.11 32 140.123 even 12
980.2.o.f.411.10 32 140.83 odd 4
980.2.o.f.411.11 32 35.13 even 4