Properties

Label 700.2.k.b.43.3
Level $700$
Weight $2$
Character 700.43
Analytic conductor $5.590$
Analytic rank $0$
Dimension $36$
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(43,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 700.k (of order \(4\), degree \(2\), 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: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 43.3
Character \(\chi\) \(=\) 700.43
Dual form 700.2.k.b.407.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.29055 + 0.578354i) q^{2} +(1.27396 - 1.27396i) q^{3} +(1.33101 - 1.49278i) q^{4} +(-0.907305 + 2.38090i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.854378 + 2.69630i) q^{8} -0.245954i q^{9} +O(q^{10})\) \(q+(-1.29055 + 0.578354i) q^{2} +(1.27396 - 1.27396i) q^{3} +(1.33101 - 1.49278i) q^{4} +(-0.907305 + 2.38090i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(-0.854378 + 2.69630i) q^{8} -0.245954i q^{9} -3.36566i q^{11} +(-0.206087 - 3.59741i) q^{12} +(2.69086 + 2.69086i) q^{13} +(1.32151 + 0.503596i) q^{14} +(-0.456801 - 3.97383i) q^{16} +(1.60569 - 1.60569i) q^{17} +(0.142248 + 0.317415i) q^{18} +1.20346 q^{19} -1.80165 q^{21} +(1.94654 + 4.34353i) q^{22} +(5.40015 - 5.40015i) q^{23} +(2.34654 + 4.52343i) q^{24} +(-5.02894 - 1.91641i) q^{26} +(3.50855 + 3.50855i) q^{27} +(-1.99673 + 0.114388i) q^{28} -6.53311i q^{29} -4.21966i q^{31} +(2.88780 + 4.86422i) q^{32} +(-4.28772 - 4.28772i) q^{33} +(-1.14356 + 3.00087i) q^{34} +(-0.367156 - 0.327368i) q^{36} +(-1.99424 + 1.99424i) q^{37} +(-1.55312 + 0.696024i) q^{38} +6.85610 q^{39} -2.68876 q^{41} +(2.32512 - 1.04199i) q^{42} +(-1.90124 + 1.90124i) q^{43} +(-5.02420 - 4.47974i) q^{44} +(-3.84594 + 10.0923i) q^{46} +(-7.59113 - 7.59113i) q^{47} +(-5.64445 - 4.48056i) q^{48} +1.00000i q^{49} -4.09116i q^{51} +(7.59844 - 0.435296i) q^{52} +(-9.24717 - 9.24717i) q^{53} +(-6.55712 - 2.49876i) q^{54} +(2.51071 - 1.30244i) q^{56} +(1.53316 - 1.53316i) q^{57} +(3.77844 + 8.43127i) q^{58} +7.21162 q^{59} -5.22203 q^{61} +(2.44046 + 5.44567i) q^{62} +(-0.173916 + 0.173916i) q^{63} +(-6.54008 - 4.60732i) q^{64} +(8.01331 + 3.05368i) q^{66} +(0.247826 + 0.247826i) q^{67} +(-0.259749 - 4.53413i) q^{68} -13.7592i q^{69} +11.5976i q^{71} +(0.663166 + 0.210138i) q^{72} +(10.2421 + 10.2421i) q^{73} +(1.42028 - 3.72702i) q^{74} +(1.60182 - 1.79650i) q^{76} +(-2.37988 + 2.37988i) q^{77} +(-8.84810 + 3.96525i) q^{78} +8.10604 q^{79} +9.67737 q^{81} +(3.46997 - 1.55506i) q^{82} +(11.4358 - 11.4358i) q^{83} +(-2.39803 + 2.68948i) q^{84} +(1.35405 - 3.55323i) q^{86} +(-8.32292 - 8.32292i) q^{87} +(9.07483 + 2.87554i) q^{88} +7.55643i q^{89} -3.80545i q^{91} +(-0.873574 - 15.2489i) q^{92} +(-5.37569 - 5.37569i) q^{93} +(14.1871 + 5.40634i) q^{94} +(9.87577 + 2.51787i) q^{96} +(-0.0167624 + 0.0167624i) q^{97} +(-0.578354 - 1.29055i) q^{98} -0.827797 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36 q - 8 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 36 q - 8 q^{6} + 16 q^{12} + 4 q^{13} - 8 q^{16} + 20 q^{17} - 28 q^{18} - 4 q^{22} - 32 q^{26} - 20 q^{37} + 20 q^{42} + 16 q^{46} + 24 q^{48} - 16 q^{52} + 44 q^{53} - 24 q^{56} + 16 q^{57} + 4 q^{58} - 64 q^{61} - 40 q^{62} + 32 q^{66} - 80 q^{68} - 80 q^{72} - 52 q^{73} + 8 q^{76} + 76 q^{78} - 36 q^{81} - 56 q^{82} + 56 q^{86} + 40 q^{88} + 56 q^{92} - 32 q^{93} + 120 q^{96} - 20 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.29055 + 0.578354i −0.912553 + 0.408958i
\(3\) 1.27396 1.27396i 0.735522 0.735522i −0.236186 0.971708i \(-0.575897\pi\)
0.971708 + 0.236186i \(0.0758975\pi\)
\(4\) 1.33101 1.49278i 0.665507 0.746391i
\(5\) 0 0
\(6\) −0.907305 + 2.38090i −0.370406 + 0.972000i
\(7\) −0.707107 0.707107i −0.267261 0.267261i
\(8\) −0.854378 + 2.69630i −0.302068 + 0.953286i
\(9\) 0.245954i 0.0819847i
\(10\) 0 0
\(11\) 3.36566i 1.01478i −0.861715 0.507392i \(-0.830610\pi\)
0.861715 0.507392i \(-0.169390\pi\)
\(12\) −0.206087 3.59741i −0.0594921 1.03848i
\(13\) 2.69086 + 2.69086i 0.746310 + 0.746310i 0.973784 0.227474i \(-0.0730468\pi\)
−0.227474 + 0.973784i \(0.573047\pi\)
\(14\) 1.32151 + 0.503596i 0.353189 + 0.134592i
\(15\) 0 0
\(16\) −0.456801 3.97383i −0.114200 0.993458i
\(17\) 1.60569 1.60569i 0.389436 0.389436i −0.485050 0.874486i \(-0.661199\pi\)
0.874486 + 0.485050i \(0.161199\pi\)
\(18\) 0.142248 + 0.317415i 0.0335283 + 0.0748154i
\(19\) 1.20346 0.276092 0.138046 0.990426i \(-0.455918\pi\)
0.138046 + 0.990426i \(0.455918\pi\)
\(20\) 0 0
\(21\) −1.80165 −0.393153
\(22\) 1.94654 + 4.34353i 0.415004 + 0.926045i
\(23\) 5.40015 5.40015i 1.12601 1.12601i 0.135189 0.990820i \(-0.456836\pi\)
0.990820 0.135189i \(-0.0431643\pi\)
\(24\) 2.34654 + 4.52343i 0.478985 + 0.923341i
\(25\) 0 0
\(26\) −5.02894 1.91641i −0.986257 0.375838i
\(27\) 3.50855 + 3.50855i 0.675220 + 0.675220i
\(28\) −1.99673 + 0.114388i −0.377346 + 0.0216172i
\(29\) 6.53311i 1.21317i −0.795020 0.606584i \(-0.792540\pi\)
0.795020 0.606584i \(-0.207460\pi\)
\(30\) 0 0
\(31\) 4.21966i 0.757874i −0.925423 0.378937i \(-0.876290\pi\)
0.925423 0.378937i \(-0.123710\pi\)
\(32\) 2.88780 + 4.86422i 0.510496 + 0.859880i
\(33\) −4.28772 4.28772i −0.746396 0.746396i
\(34\) −1.14356 + 3.00087i −0.196118 + 0.514644i
\(35\) 0 0
\(36\) −0.367156 0.327368i −0.0611927 0.0545614i
\(37\) −1.99424 + 1.99424i −0.327850 + 0.327850i −0.851769 0.523918i \(-0.824470\pi\)
0.523918 + 0.851769i \(0.324470\pi\)
\(38\) −1.55312 + 0.696024i −0.251949 + 0.112910i
\(39\) 6.85610 1.09785
\(40\) 0 0
\(41\) −2.68876 −0.419914 −0.209957 0.977711i \(-0.567332\pi\)
−0.209957 + 0.977711i \(0.567332\pi\)
\(42\) 2.32512 1.04199i 0.358773 0.160783i
\(43\) −1.90124 + 1.90124i −0.289937 + 0.289937i −0.837055 0.547118i \(-0.815725\pi\)
0.547118 + 0.837055i \(0.315725\pi\)
\(44\) −5.02420 4.47974i −0.757426 0.675346i
\(45\) 0 0
\(46\) −3.84594 + 10.0923i −0.567053 + 1.48803i
\(47\) −7.59113 7.59113i −1.10728 1.10728i −0.993507 0.113774i \(-0.963706\pi\)
−0.113774 0.993507i \(-0.536294\pi\)
\(48\) −5.64445 4.48056i −0.814707 0.646713i
\(49\) 1.00000i 0.142857i
\(50\) 0 0
\(51\) 4.09116i 0.572877i
\(52\) 7.59844 0.435296i 1.05371 0.0603647i
\(53\) −9.24717 9.24717i −1.27020 1.27020i −0.945984 0.324213i \(-0.894901\pi\)
−0.324213 0.945984i \(-0.605099\pi\)
\(54\) −6.55712 2.49876i −0.892311 0.340038i
\(55\) 0 0
\(56\) 2.51071 1.30244i 0.335508 0.174045i
\(57\) 1.53316 1.53316i 0.203072 0.203072i
\(58\) 3.77844 + 8.43127i 0.496134 + 1.10708i
\(59\) 7.21162 0.938873 0.469437 0.882966i \(-0.344457\pi\)
0.469437 + 0.882966i \(0.344457\pi\)
\(60\) 0 0
\(61\) −5.22203 −0.668612 −0.334306 0.942465i \(-0.608502\pi\)
−0.334306 + 0.942465i \(0.608502\pi\)
\(62\) 2.44046 + 5.44567i 0.309938 + 0.691600i
\(63\) −0.173916 + 0.173916i −0.0219113 + 0.0219113i
\(64\) −6.54008 4.60732i −0.817510 0.575915i
\(65\) 0 0
\(66\) 8.01331 + 3.05368i 0.986370 + 0.375882i
\(67\) 0.247826 + 0.247826i 0.0302767 + 0.0302767i 0.722083 0.691806i \(-0.243185\pi\)
−0.691806 + 0.722083i \(0.743185\pi\)
\(68\) −0.259749 4.53413i −0.0314992 0.549844i
\(69\) 13.7592i 1.65641i
\(70\) 0 0
\(71\) 11.5976i 1.37638i 0.725529 + 0.688192i \(0.241595\pi\)
−0.725529 + 0.688192i \(0.758405\pi\)
\(72\) 0.663166 + 0.210138i 0.0781549 + 0.0247650i
\(73\) 10.2421 + 10.2421i 1.19875 + 1.19875i 0.974542 + 0.224203i \(0.0719779\pi\)
0.224203 + 0.974542i \(0.428022\pi\)
\(74\) 1.42028 3.72702i 0.165104 0.433258i
\(75\) 0 0
\(76\) 1.60182 1.79650i 0.183741 0.206073i
\(77\) −2.37988 + 2.37988i −0.271212 + 0.271212i
\(78\) −8.84810 + 3.96525i −1.00185 + 0.448976i
\(79\) 8.10604 0.912001 0.456000 0.889980i \(-0.349282\pi\)
0.456000 + 0.889980i \(0.349282\pi\)
\(80\) 0 0
\(81\) 9.67737 1.07526
\(82\) 3.46997 1.55506i 0.383194 0.171727i
\(83\) 11.4358 11.4358i 1.25524 1.25524i 0.301900 0.953339i \(-0.402379\pi\)
0.953339 0.301900i \(-0.0976210\pi\)
\(84\) −2.39803 + 2.68948i −0.261646 + 0.293446i
\(85\) 0 0
\(86\) 1.35405 3.55323i 0.146011 0.383155i
\(87\) −8.32292 8.32292i −0.892311 0.892311i
\(88\) 9.07483 + 2.87554i 0.967380 + 0.306534i
\(89\) 7.55643i 0.800980i 0.916301 + 0.400490i \(0.131160\pi\)
−0.916301 + 0.400490i \(0.868840\pi\)
\(90\) 0 0
\(91\) 3.80545i 0.398919i
\(92\) −0.873574 15.2489i −0.0910764 1.58981i
\(93\) −5.37569 5.37569i −0.557433 0.557433i
\(94\) 14.1871 + 5.40634i 1.46328 + 0.557622i
\(95\) 0 0
\(96\) 9.87577 + 2.51787i 1.00794 + 0.256980i
\(97\) −0.0167624 + 0.0167624i −0.00170197 + 0.00170197i −0.707957 0.706255i \(-0.750383\pi\)
0.706255 + 0.707957i \(0.250383\pi\)
\(98\) −0.578354 1.29055i −0.0584225 0.130365i
\(99\) −0.827797 −0.0831967
\(100\) 0 0
\(101\) 2.33818 0.232658 0.116329 0.993211i \(-0.462887\pi\)
0.116329 + 0.993211i \(0.462887\pi\)
\(102\) 2.36614 + 5.27983i 0.234283 + 0.522781i
\(103\) −5.19389 + 5.19389i −0.511769 + 0.511769i −0.915068 0.403299i \(-0.867863\pi\)
0.403299 + 0.915068i \(0.367863\pi\)
\(104\) −9.55437 + 4.95635i −0.936883 + 0.486010i
\(105\) 0 0
\(106\) 17.2820 + 6.58576i 1.67858 + 0.639666i
\(107\) 8.66705 + 8.66705i 0.837875 + 0.837875i 0.988579 0.150704i \(-0.0481540\pi\)
−0.150704 + 0.988579i \(0.548154\pi\)
\(108\) 9.90743 0.567572i 0.953343 0.0546147i
\(109\) 11.3693i 1.08898i 0.838766 + 0.544492i \(0.183278\pi\)
−0.838766 + 0.544492i \(0.816722\pi\)
\(110\) 0 0
\(111\) 5.08116i 0.482282i
\(112\) −2.48692 + 3.13293i −0.234991 + 0.296034i
\(113\) −2.22660 2.22660i −0.209461 0.209461i 0.594577 0.804038i \(-0.297319\pi\)
−0.804038 + 0.594577i \(0.797319\pi\)
\(114\) −1.09190 + 2.86532i −0.102266 + 0.268361i
\(115\) 0 0
\(116\) −9.75251 8.69566i −0.905498 0.807372i
\(117\) 0.661827 0.661827i 0.0611860 0.0611860i
\(118\) −9.30692 + 4.17087i −0.856772 + 0.383959i
\(119\) −2.27078 −0.208162
\(120\) 0 0
\(121\) −0.327654 −0.0297867
\(122\) 6.73926 3.02018i 0.610144 0.273434i
\(123\) −3.42538 + 3.42538i −0.308856 + 0.308856i
\(124\) −6.29904 5.61643i −0.565670 0.504370i
\(125\) 0 0
\(126\) 0.123861 0.325031i 0.0110344 0.0289561i
\(127\) 2.39506 + 2.39506i 0.212527 + 0.212527i 0.805340 0.592813i \(-0.201983\pi\)
−0.592813 + 0.805340i \(0.701983\pi\)
\(128\) 11.1049 + 2.16348i 0.981546 + 0.191226i
\(129\) 4.84422i 0.426510i
\(130\) 0 0
\(131\) 8.15491i 0.712497i −0.934391 0.356249i \(-0.884056\pi\)
0.934391 0.356249i \(-0.115944\pi\)
\(132\) −12.1076 + 0.693618i −1.05384 + 0.0603717i
\(133\) −0.850973 0.850973i −0.0737887 0.0737887i
\(134\) −0.463161 0.176499i −0.0400110 0.0152472i
\(135\) 0 0
\(136\) 2.95755 + 5.70128i 0.253608 + 0.488880i
\(137\) −5.54560 + 5.54560i −0.473793 + 0.473793i −0.903140 0.429347i \(-0.858744\pi\)
0.429347 + 0.903140i \(0.358744\pi\)
\(138\) 7.95766 + 17.7568i 0.677401 + 1.51156i
\(139\) −10.7453 −0.911405 −0.455702 0.890132i \(-0.650612\pi\)
−0.455702 + 0.890132i \(0.650612\pi\)
\(140\) 0 0
\(141\) −19.3416 −1.62886
\(142\) −6.70752 14.9673i −0.562883 1.25602i
\(143\) 9.05651 9.05651i 0.757343 0.757343i
\(144\) −0.977380 + 0.112352i −0.0814483 + 0.00936268i
\(145\) 0 0
\(146\) −19.1414 7.29433i −1.58416 0.603683i
\(147\) 1.27396 + 1.27396i 0.105075 + 0.105075i
\(148\) 0.322604 + 5.63132i 0.0265179 + 0.462891i
\(149\) 17.7579i 1.45479i 0.686221 + 0.727394i \(0.259268\pi\)
−0.686221 + 0.727394i \(0.740732\pi\)
\(150\) 0 0
\(151\) 3.57930i 0.291279i −0.989338 0.145640i \(-0.953476\pi\)
0.989338 0.145640i \(-0.0465240\pi\)
\(152\) −1.02821 + 3.24488i −0.0833986 + 0.263195i
\(153\) −0.394925 0.394925i −0.0319278 0.0319278i
\(154\) 1.69493 4.44775i 0.136581 0.358410i
\(155\) 0 0
\(156\) 9.12556 10.2347i 0.730630 0.819429i
\(157\) −2.41513 + 2.41513i −0.192748 + 0.192748i −0.796883 0.604134i \(-0.793519\pi\)
0.604134 + 0.796883i \(0.293519\pi\)
\(158\) −10.4612 + 4.68816i −0.832249 + 0.372970i
\(159\) −23.5611 −1.86852
\(160\) 0 0
\(161\) −7.63697 −0.601877
\(162\) −12.4891 + 5.59694i −0.981235 + 0.439737i
\(163\) −0.475698 + 0.475698i −0.0372595 + 0.0372595i −0.725491 0.688232i \(-0.758387\pi\)
0.688232 + 0.725491i \(0.258387\pi\)
\(164\) −3.57878 + 4.01374i −0.279456 + 0.313420i
\(165\) 0 0
\(166\) −8.14447 + 21.3723i −0.632133 + 1.65881i
\(167\) −7.18363 7.18363i −0.555886 0.555886i 0.372248 0.928133i \(-0.378587\pi\)
−0.928133 + 0.372248i \(0.878587\pi\)
\(168\) 1.53929 4.85780i 0.118759 0.374787i
\(169\) 1.48144i 0.113957i
\(170\) 0 0
\(171\) 0.295995i 0.0226353i
\(172\) 0.307561 + 5.36872i 0.0234513 + 0.409361i
\(173\) −1.21290 1.21290i −0.0922149 0.0922149i 0.659495 0.751709i \(-0.270770\pi\)
−0.751709 + 0.659495i \(0.770770\pi\)
\(174\) 15.5547 + 5.92752i 1.17920 + 0.449364i
\(175\) 0 0
\(176\) −13.3746 + 1.53744i −1.00815 + 0.115889i
\(177\) 9.18732 9.18732i 0.690562 0.690562i
\(178\) −4.37029 9.75191i −0.327567 0.730937i
\(179\) −11.5214 −0.861152 −0.430576 0.902554i \(-0.641690\pi\)
−0.430576 + 0.902554i \(0.641690\pi\)
\(180\) 0 0
\(181\) 21.4955 1.59775 0.798873 0.601500i \(-0.205430\pi\)
0.798873 + 0.601500i \(0.205430\pi\)
\(182\) 2.20089 + 4.91110i 0.163141 + 0.364035i
\(183\) −6.65266 + 6.65266i −0.491779 + 0.491779i
\(184\) 9.94666 + 19.1742i 0.733278 + 1.41354i
\(185\) 0 0
\(186\) 10.0466 + 3.82852i 0.736653 + 0.280721i
\(187\) −5.40419 5.40419i −0.395194 0.395194i
\(188\) −21.4358 + 1.22801i −1.56337 + 0.0895616i
\(189\) 4.96184i 0.360920i
\(190\) 0 0
\(191\) 22.2319i 1.60864i 0.594195 + 0.804321i \(0.297471\pi\)
−0.594195 + 0.804321i \(0.702529\pi\)
\(192\) −14.2014 + 2.46226i −1.02489 + 0.177698i
\(193\) 13.8546 + 13.8546i 0.997276 + 0.997276i 0.999996 0.00272045i \(-0.000865947\pi\)
−0.00272045 + 0.999996i \(0.500866\pi\)
\(194\) 0.0119381 0.0313273i 0.000857103 0.00224917i
\(195\) 0 0
\(196\) 1.49278 + 1.33101i 0.106627 + 0.0950725i
\(197\) −16.2434 + 16.2434i −1.15729 + 1.15729i −0.172235 + 0.985056i \(0.555099\pi\)
−0.985056 + 0.172235i \(0.944901\pi\)
\(198\) 1.06831 0.478759i 0.0759215 0.0340240i
\(199\) −3.80096 −0.269443 −0.134722 0.990884i \(-0.543014\pi\)
−0.134722 + 0.990884i \(0.543014\pi\)
\(200\) 0 0
\(201\) 0.631441 0.0445384
\(202\) −3.01753 + 1.35230i −0.212313 + 0.0951473i
\(203\) −4.61960 + 4.61960i −0.324233 + 0.324233i
\(204\) −6.10722 5.44540i −0.427591 0.381254i
\(205\) 0 0
\(206\) 3.69905 9.70685i 0.257725 0.676309i
\(207\) −1.32819 1.32819i −0.0923155 0.0923155i
\(208\) 9.46383 11.9222i 0.656198 0.826656i
\(209\) 4.05042i 0.280174i
\(210\) 0 0
\(211\) 4.29202i 0.295475i −0.989027 0.147737i \(-0.952801\pi\)
0.989027 0.147737i \(-0.0471990\pi\)
\(212\) −26.1121 + 1.49590i −1.79339 + 0.102739i
\(213\) 14.7749 + 14.7749i 1.01236 + 1.01236i
\(214\) −16.1978 6.17260i −1.10726 0.421950i
\(215\) 0 0
\(216\) −12.4577 + 6.46247i −0.847641 + 0.439716i
\(217\) −2.98375 + 2.98375i −0.202550 + 0.202550i
\(218\) −6.57549 14.6726i −0.445349 0.993756i
\(219\) 26.0960 1.76341
\(220\) 0 0
\(221\) 8.64135 0.581280
\(222\) −2.93870 6.55746i −0.197233 0.440108i
\(223\) −17.3042 + 17.3042i −1.15877 + 1.15877i −0.174035 + 0.984739i \(0.555681\pi\)
−0.984739 + 0.174035i \(0.944319\pi\)
\(224\) 1.39754 5.48150i 0.0933768 0.366248i
\(225\) 0 0
\(226\) 4.16129 + 1.58577i 0.276805 + 0.105484i
\(227\) 2.06226 + 2.06226i 0.136877 + 0.136877i 0.772226 0.635349i \(-0.219144\pi\)
−0.635349 + 0.772226i \(0.719144\pi\)
\(228\) −0.248017 4.32933i −0.0164253 0.286717i
\(229\) 3.85248i 0.254579i −0.991866 0.127290i \(-0.959372\pi\)
0.991866 0.127290i \(-0.0406278\pi\)
\(230\) 0 0
\(231\) 6.06375i 0.398965i
\(232\) 17.6152 + 5.58174i 1.15650 + 0.366459i
\(233\) 2.10259 + 2.10259i 0.137745 + 0.137745i 0.772617 0.634872i \(-0.218947\pi\)
−0.634872 + 0.772617i \(0.718947\pi\)
\(234\) −0.471348 + 1.23689i −0.0308130 + 0.0808579i
\(235\) 0 0
\(236\) 9.59877 10.7654i 0.624827 0.700767i
\(237\) 10.3268 10.3268i 0.670796 0.670796i
\(238\) 2.93055 1.31332i 0.189959 0.0851296i
\(239\) −12.4700 −0.806615 −0.403308 0.915064i \(-0.632140\pi\)
−0.403308 + 0.915064i \(0.632140\pi\)
\(240\) 0 0
\(241\) 12.0460 0.775948 0.387974 0.921670i \(-0.373175\pi\)
0.387974 + 0.921670i \(0.373175\pi\)
\(242\) 0.422852 0.189500i 0.0271819 0.0121815i
\(243\) 1.80295 1.80295i 0.115659 0.115659i
\(244\) −6.95059 + 7.79535i −0.444966 + 0.499046i
\(245\) 0 0
\(246\) 2.43953 6.40169i 0.155539 0.408157i
\(247\) 3.23833 + 3.23833i 0.206050 + 0.206050i
\(248\) 11.3775 + 3.60519i 0.722471 + 0.228930i
\(249\) 29.1375i 1.84651i
\(250\) 0 0
\(251\) 9.65552i 0.609451i −0.952440 0.304725i \(-0.901435\pi\)
0.952440 0.304725i \(-0.0985647\pi\)
\(252\) 0.0281341 + 0.491103i 0.00177228 + 0.0309366i
\(253\) −18.1751 18.1751i −1.14266 1.14266i
\(254\) −4.47612 1.70574i −0.280857 0.107028i
\(255\) 0 0
\(256\) −15.5827 + 3.63050i −0.973917 + 0.226906i
\(257\) −3.85614 + 3.85614i −0.240539 + 0.240539i −0.817073 0.576534i \(-0.804405\pi\)
0.576534 + 0.817073i \(0.304405\pi\)
\(258\) −2.80167 6.25168i −0.174424 0.389213i
\(259\) 2.82027 0.175243
\(260\) 0 0
\(261\) −1.60684 −0.0994611
\(262\) 4.71642 + 10.5243i 0.291381 + 0.650192i
\(263\) −12.3977 + 12.3977i −0.764476 + 0.764476i −0.977128 0.212652i \(-0.931790\pi\)
0.212652 + 0.977128i \(0.431790\pi\)
\(264\) 15.2243 7.89764i 0.936991 0.486066i
\(265\) 0 0
\(266\) 1.59038 + 0.606056i 0.0975126 + 0.0371597i
\(267\) 9.62659 + 9.62659i 0.589138 + 0.589138i
\(268\) 0.699810 0.0400904i 0.0427477 0.00244891i
\(269\) 5.80512i 0.353944i −0.984216 0.176972i \(-0.943370\pi\)
0.984216 0.176972i \(-0.0566302\pi\)
\(270\) 0 0
\(271\) 13.9056i 0.844703i 0.906432 + 0.422351i \(0.138795\pi\)
−0.906432 + 0.422351i \(0.861205\pi\)
\(272\) −7.11421 5.64725i −0.431362 0.342415i
\(273\) −4.84799 4.84799i −0.293414 0.293414i
\(274\) 3.94953 10.3642i 0.238600 0.626122i
\(275\) 0 0
\(276\) −20.5394 18.3136i −1.23633 1.10235i
\(277\) 10.1031 10.1031i 0.607038 0.607038i −0.335133 0.942171i \(-0.608781\pi\)
0.942171 + 0.335133i \(0.108781\pi\)
\(278\) 13.8673 6.21459i 0.831706 0.372726i
\(279\) −1.03784 −0.0621340
\(280\) 0 0
\(281\) −0.575310 −0.0343201 −0.0171601 0.999853i \(-0.505462\pi\)
−0.0171601 + 0.999853i \(0.505462\pi\)
\(282\) 24.9612 11.1863i 1.48642 0.666134i
\(283\) −2.62044 + 2.62044i −0.155769 + 0.155769i −0.780689 0.624920i \(-0.785132\pi\)
0.624920 + 0.780689i \(0.285132\pi\)
\(284\) 17.3127 + 15.4366i 1.02732 + 0.915993i
\(285\) 0 0
\(286\) −6.44997 + 16.9257i −0.381395 + 1.00084i
\(287\) 1.90124 + 1.90124i 0.112227 + 0.112227i
\(288\) 1.19637 0.710267i 0.0704970 0.0418529i
\(289\) 11.8435i 0.696679i
\(290\) 0 0
\(291\) 0.0427094i 0.00250367i
\(292\) 28.9216 1.65685i 1.69251 0.0969596i
\(293\) 14.2036 + 14.2036i 0.829783 + 0.829783i 0.987487 0.157703i \(-0.0504090\pi\)
−0.157703 + 0.987487i \(0.550409\pi\)
\(294\) −2.38090 0.907305i −0.138857 0.0529151i
\(295\) 0 0
\(296\) −3.67323 7.08089i −0.213502 0.411568i
\(297\) 11.8086 11.8086i 0.685203 0.685203i
\(298\) −10.2704 22.9174i −0.594946 1.32757i
\(299\) 29.0621 1.68070
\(300\) 0 0
\(301\) 2.68876 0.154978
\(302\) 2.07010 + 4.61925i 0.119121 + 0.265808i
\(303\) 2.97875 2.97875i 0.171125 0.171125i
\(304\) −0.549741 4.78233i −0.0315298 0.274286i
\(305\) 0 0
\(306\) 0.738075 + 0.281262i 0.0421929 + 0.0160787i
\(307\) 1.65503 + 1.65503i 0.0944578 + 0.0944578i 0.752757 0.658299i \(-0.228724\pi\)
−0.658299 + 0.752757i \(0.728724\pi\)
\(308\) 0.384990 + 6.72030i 0.0219368 + 0.382924i
\(309\) 13.2336i 0.752835i
\(310\) 0 0
\(311\) 32.5815i 1.84753i −0.382962 0.923764i \(-0.625096\pi\)
0.382962 0.923764i \(-0.374904\pi\)
\(312\) −5.85770 + 18.4861i −0.331627 + 1.04657i
\(313\) 13.6347 + 13.6347i 0.770676 + 0.770676i 0.978225 0.207548i \(-0.0665485\pi\)
−0.207548 + 0.978225i \(0.566548\pi\)
\(314\) 1.72003 4.51363i 0.0970672 0.254719i
\(315\) 0 0
\(316\) 10.7893 12.1006i 0.606943 0.680709i
\(317\) 1.67160 1.67160i 0.0938866 0.0938866i −0.658604 0.752490i \(-0.728853\pi\)
0.752490 + 0.658604i \(0.228853\pi\)
\(318\) 30.4066 13.6266i 1.70512 0.764144i
\(319\) −21.9882 −1.23110
\(320\) 0 0
\(321\) 22.0830 1.23255
\(322\) 9.85585 4.41687i 0.549245 0.246142i
\(323\) 1.93237 1.93237i 0.107520 0.107520i
\(324\) 12.8807 14.4462i 0.715595 0.802567i
\(325\) 0 0
\(326\) 0.338788 0.889031i 0.0187637 0.0492389i
\(327\) 14.4841 + 14.4841i 0.800972 + 0.800972i
\(328\) 2.29722 7.24971i 0.126843 0.400299i
\(329\) 10.7355i 0.591866i
\(330\) 0 0
\(331\) 3.90436i 0.214603i 0.994227 + 0.107302i \(0.0342210\pi\)
−0.994227 + 0.107302i \(0.965779\pi\)
\(332\) −1.84995 32.2923i −0.101529 1.77227i
\(333\) 0.490490 + 0.490490i 0.0268787 + 0.0268787i
\(334\) 13.4255 + 5.11612i 0.734609 + 0.279942i
\(335\) 0 0
\(336\) 0.822998 + 7.15947i 0.0448982 + 0.390581i
\(337\) 10.4913 10.4913i 0.571500 0.571500i −0.361047 0.932547i \(-0.617581\pi\)
0.932547 + 0.361047i \(0.117581\pi\)
\(338\) −0.856793 1.91186i −0.0466034 0.103991i
\(339\) −5.67321 −0.308126
\(340\) 0 0
\(341\) −14.2019 −0.769078
\(342\) 0.171190 + 0.381995i 0.00925688 + 0.0206559i
\(343\) 0.707107 0.707107i 0.0381802 0.0381802i
\(344\) −3.50194 6.75070i −0.188812 0.363974i
\(345\) 0 0
\(346\) 2.26678 + 0.863815i 0.121863 + 0.0464390i
\(347\) 12.3223 + 12.3223i 0.661495 + 0.661495i 0.955732 0.294238i \(-0.0950657\pi\)
−0.294238 + 0.955732i \(0.595066\pi\)
\(348\) −23.5022 + 1.34639i −1.25985 + 0.0721739i
\(349\) 16.2876i 0.871854i −0.899982 0.435927i \(-0.856421\pi\)
0.899982 0.435927i \(-0.143579\pi\)
\(350\) 0 0
\(351\) 18.8820i 1.00785i
\(352\) 16.3713 9.71935i 0.872593 0.518043i
\(353\) −9.05677 9.05677i −0.482043 0.482043i 0.423740 0.905784i \(-0.360717\pi\)
−0.905784 + 0.423740i \(0.860717\pi\)
\(354\) −6.54314 + 17.1702i −0.347764 + 0.912585i
\(355\) 0 0
\(356\) 11.2801 + 10.0577i 0.597844 + 0.533058i
\(357\) −2.89289 + 2.89289i −0.153108 + 0.153108i
\(358\) 14.8689 6.66346i 0.785848 0.352175i
\(359\) −15.5546 −0.820940 −0.410470 0.911874i \(-0.634635\pi\)
−0.410470 + 0.911874i \(0.634635\pi\)
\(360\) 0 0
\(361\) −17.5517 −0.923773
\(362\) −27.7409 + 12.4320i −1.45803 + 0.653410i
\(363\) −0.417418 + 0.417418i −0.0219088 + 0.0219088i
\(364\) −5.68071 5.06511i −0.297750 0.265484i
\(365\) 0 0
\(366\) 4.73797 12.4331i 0.247658 0.649891i
\(367\) −13.5723 13.5723i −0.708469 0.708469i 0.257744 0.966213i \(-0.417021\pi\)
−0.966213 + 0.257744i \(0.917021\pi\)
\(368\) −23.9261 18.9925i −1.24723 0.990052i
\(369\) 0.661312i 0.0344265i
\(370\) 0 0
\(371\) 13.0775i 0.678949i
\(372\) −15.1798 + 0.869617i −0.787038 + 0.0450875i
\(373\) −3.46506 3.46506i −0.179414 0.179414i 0.611686 0.791100i \(-0.290491\pi\)
−0.791100 + 0.611686i \(0.790491\pi\)
\(374\) 10.0999 + 3.84882i 0.522253 + 0.199018i
\(375\) 0 0
\(376\) 26.9537 13.9823i 1.39003 0.721081i
\(377\) 17.5797 17.5797i 0.905399 0.905399i
\(378\) 2.86970 + 6.40347i 0.147601 + 0.329359i
\(379\) 14.0417 0.721273 0.360636 0.932706i \(-0.382560\pi\)
0.360636 + 0.932706i \(0.382560\pi\)
\(380\) 0 0
\(381\) 6.10243 0.312637
\(382\) −12.8579 28.6912i −0.657866 1.46797i
\(383\) 2.98618 2.98618i 0.152586 0.152586i −0.626686 0.779272i \(-0.715589\pi\)
0.779272 + 0.626686i \(0.215589\pi\)
\(384\) 16.9034 11.3911i 0.862600 0.581297i
\(385\) 0 0
\(386\) −25.8928 9.86713i −1.31791 0.502224i
\(387\) 0.467618 + 0.467618i 0.0237704 + 0.0237704i
\(388\) 0.00271163 + 0.0473337i 0.000137662 + 0.00240300i
\(389\) 14.8325i 0.752040i −0.926612 0.376020i \(-0.877292\pi\)
0.926612 0.376020i \(-0.122708\pi\)
\(390\) 0 0
\(391\) 17.3419i 0.877017i
\(392\) −2.69630 0.854378i −0.136184 0.0431526i
\(393\) −10.3890 10.3890i −0.524057 0.524057i
\(394\) 11.5684 30.3572i 0.582807 1.52937i
\(395\) 0 0
\(396\) −1.10181 + 1.23572i −0.0553680 + 0.0620973i
\(397\) 1.69597 1.69597i 0.0851182 0.0851182i −0.663266 0.748384i \(-0.730830\pi\)
0.748384 + 0.663266i \(0.230830\pi\)
\(398\) 4.90531 2.19830i 0.245881 0.110191i
\(399\) −2.16821 −0.108546
\(400\) 0 0
\(401\) −27.6833 −1.38244 −0.691218 0.722646i \(-0.742926\pi\)
−0.691218 + 0.722646i \(0.742926\pi\)
\(402\) −0.814903 + 0.365196i −0.0406437 + 0.0182143i
\(403\) 11.3545 11.3545i 0.565609 0.565609i
\(404\) 3.11216 3.49040i 0.154836 0.173654i
\(405\) 0 0
\(406\) 3.29004 8.63357i 0.163282 0.428477i
\(407\) 6.71191 + 6.71191i 0.332697 + 0.332697i
\(408\) 11.0310 + 3.49540i 0.546116 + 0.173048i
\(409\) 33.8549i 1.67402i 0.547190 + 0.837009i \(0.315698\pi\)
−0.547190 + 0.837009i \(0.684302\pi\)
\(410\) 0 0
\(411\) 14.1298i 0.696970i
\(412\) 0.840208 + 14.6665i 0.0413941 + 0.722566i
\(413\) −5.09939 5.09939i −0.250924 0.250924i
\(414\) 2.48225 + 0.945925i 0.121996 + 0.0464897i
\(415\) 0 0
\(416\) −5.31825 + 20.8596i −0.260749 + 1.02273i
\(417\) −13.6891 + 13.6891i −0.670358 + 0.670358i
\(418\) 2.34258 + 5.22726i 0.114579 + 0.255673i
\(419\) 3.80167 0.185724 0.0928619 0.995679i \(-0.470398\pi\)
0.0928619 + 0.995679i \(0.470398\pi\)
\(420\) 0 0
\(421\) −15.5662 −0.758648 −0.379324 0.925264i \(-0.623843\pi\)
−0.379324 + 0.925264i \(0.623843\pi\)
\(422\) 2.48230 + 5.53904i 0.120837 + 0.269636i
\(423\) −1.86707 + 1.86707i −0.0907801 + 0.0907801i
\(424\) 32.8337 17.0326i 1.59455 0.827175i
\(425\) 0 0
\(426\) −27.6128 10.5226i −1.33785 0.509820i
\(427\) 3.69253 + 3.69253i 0.178694 + 0.178694i
\(428\) 24.4740 1.40206i 1.18299 0.0677709i
\(429\) 23.0753i 1.11408i
\(430\) 0 0
\(431\) 1.56818i 0.0755367i −0.999287 0.0377684i \(-0.987975\pi\)
0.999287 0.0377684i \(-0.0120249\pi\)
\(432\) 12.3397 15.5451i 0.593692 0.747913i
\(433\) −5.56380 5.56380i −0.267379 0.267379i 0.560664 0.828043i \(-0.310546\pi\)
−0.828043 + 0.560664i \(0.810546\pi\)
\(434\) 2.12500 5.57633i 0.102003 0.267672i
\(435\) 0 0
\(436\) 16.9719 + 15.1327i 0.812809 + 0.724727i
\(437\) 6.49885 6.49885i 0.310882 0.310882i
\(438\) −33.6781 + 15.0927i −1.60920 + 0.721159i
\(439\) 3.73785 0.178398 0.0891990 0.996014i \(-0.471569\pi\)
0.0891990 + 0.996014i \(0.471569\pi\)
\(440\) 0 0
\(441\) 0.245954 0.0117121
\(442\) −11.1521 + 4.99775i −0.530449 + 0.237719i
\(443\) 0.224928 0.224928i 0.0106866 0.0106866i −0.701743 0.712430i \(-0.747595\pi\)
0.712430 + 0.701743i \(0.247595\pi\)
\(444\) 7.58506 + 6.76309i 0.359971 + 0.320962i
\(445\) 0 0
\(446\) 12.3239 32.3398i 0.583554 1.53133i
\(447\) 22.6229 + 22.6229i 1.07003 + 1.07003i
\(448\) 1.36666 + 7.88240i 0.0645688 + 0.372408i
\(449\) 18.9314i 0.893428i 0.894677 + 0.446714i \(0.147406\pi\)
−0.894677 + 0.446714i \(0.852594\pi\)
\(450\) 0 0
\(451\) 9.04946i 0.426122i
\(452\) −6.28747 + 0.360194i −0.295738 + 0.0169421i
\(453\) −4.55989 4.55989i −0.214242 0.214242i
\(454\) −3.85416 1.46872i −0.180884 0.0689307i
\(455\) 0 0
\(456\) 2.82396 + 5.44375i 0.132244 + 0.254927i
\(457\) −24.5750 + 24.5750i −1.14957 + 1.14957i −0.162934 + 0.986637i \(0.552096\pi\)
−0.986637 + 0.162934i \(0.947904\pi\)
\(458\) 2.22810 + 4.97180i 0.104112 + 0.232317i
\(459\) 11.2673 0.525910
\(460\) 0 0
\(461\) 29.3095 1.36508 0.682541 0.730848i \(-0.260875\pi\)
0.682541 + 0.730848i \(0.260875\pi\)
\(462\) −3.50699 7.82554i −0.163160 0.364077i
\(463\) −10.7432 + 10.7432i −0.499280 + 0.499280i −0.911214 0.411934i \(-0.864853\pi\)
0.411934 + 0.911214i \(0.364853\pi\)
\(464\) −25.9615 + 2.98433i −1.20523 + 0.138544i
\(465\) 0 0
\(466\) −3.92953 1.49745i −0.182032 0.0693680i
\(467\) 15.6434 + 15.6434i 0.723890 + 0.723890i 0.969395 0.245505i \(-0.0789538\pi\)
−0.245505 + 0.969395i \(0.578954\pi\)
\(468\) −0.107063 1.86887i −0.00494898 0.0863884i
\(469\) 0.350479i 0.0161836i
\(470\) 0 0
\(471\) 6.15356i 0.283541i
\(472\) −6.16145 + 19.4447i −0.283604 + 0.895015i
\(473\) 6.39893 + 6.39893i 0.294223 + 0.294223i
\(474\) −7.35465 + 19.2997i −0.337810 + 0.886465i
\(475\) 0 0
\(476\) −3.02245 + 3.38979i −0.138534 + 0.155371i
\(477\) −2.27438 + 2.27438i −0.104137 + 0.104137i
\(478\) 16.0931 7.21205i 0.736080 0.329872i
\(479\) 0.447947 0.0204672 0.0102336 0.999948i \(-0.496742\pi\)
0.0102336 + 0.999948i \(0.496742\pi\)
\(480\) 0 0
\(481\) −10.7324 −0.489356
\(482\) −15.5459 + 6.96682i −0.708094 + 0.317330i
\(483\) −9.72920 + 9.72920i −0.442694 + 0.442694i
\(484\) −0.436112 + 0.489116i −0.0198233 + 0.0222325i
\(485\) 0 0
\(486\) −1.28405 + 3.36953i −0.0582455 + 0.152845i
\(487\) −23.7240 23.7240i −1.07504 1.07504i −0.996946 0.0780899i \(-0.975118\pi\)
−0.0780899 0.996946i \(-0.524882\pi\)
\(488\) 4.46158 14.0802i 0.201966 0.637378i
\(489\) 1.21204i 0.0548104i
\(490\) 0 0
\(491\) 18.3824i 0.829587i −0.909916 0.414793i \(-0.863854\pi\)
0.909916 0.414793i \(-0.136146\pi\)
\(492\) 0.554119 + 9.67258i 0.0249816 + 0.436074i
\(493\) −10.4901 10.4901i −0.472451 0.472451i
\(494\) −6.05211 2.30631i −0.272298 0.103766i
\(495\) 0 0
\(496\) −16.7682 + 1.92755i −0.752915 + 0.0865494i
\(497\) 8.20075 8.20075i 0.367854 0.367854i
\(498\) 16.8518 + 37.6032i 0.755146 + 1.68504i
\(499\) −37.0968 −1.66068 −0.830340 0.557257i \(-0.811854\pi\)
−0.830340 + 0.557257i \(0.811854\pi\)
\(500\) 0 0
\(501\) −18.3033 −0.817732
\(502\) 5.58430 + 12.4609i 0.249240 + 0.556156i
\(503\) −3.17576 + 3.17576i −0.141600 + 0.141600i −0.774353 0.632753i \(-0.781925\pi\)
0.632753 + 0.774353i \(0.281925\pi\)
\(504\) −0.320339 0.617519i −0.0142691 0.0275065i
\(505\) 0 0
\(506\) 33.9673 + 12.9441i 1.51003 + 0.575437i
\(507\) 1.88729 + 1.88729i 0.0838175 + 0.0838175i
\(508\) 6.76316 0.387445i 0.300067 0.0171901i
\(509\) 24.5955i 1.09018i 0.838379 + 0.545088i \(0.183504\pi\)
−0.838379 + 0.545088i \(0.816496\pi\)
\(510\) 0 0
\(511\) 14.4845i 0.640756i
\(512\) 18.0104 13.6976i 0.795956 0.605355i
\(513\) 4.22239 + 4.22239i 0.186423 + 0.186423i
\(514\) 2.74631 7.20673i 0.121135 0.317875i
\(515\) 0 0
\(516\) 7.23137 + 6.44773i 0.318343 + 0.283845i
\(517\) −25.5492 + 25.5492i −1.12365 + 1.12365i
\(518\) −3.63969 + 1.63112i −0.159919 + 0.0716671i
\(519\) −3.09037 −0.135652
\(520\) 0 0
\(521\) 11.9594 0.523951 0.261976 0.965075i \(-0.415626\pi\)
0.261976 + 0.965075i \(0.415626\pi\)
\(522\) 2.07370 0.929324i 0.0907636 0.0406754i
\(523\) −8.87100 + 8.87100i −0.387902 + 0.387902i −0.873938 0.486037i \(-0.838442\pi\)
0.486037 + 0.873938i \(0.338442\pi\)
\(524\) −12.1735 10.8543i −0.531802 0.474172i
\(525\) 0 0
\(526\) 8.82956 23.1701i 0.384987 1.01026i
\(527\) −6.77545 6.77545i −0.295143 0.295143i
\(528\) −15.0800 + 18.9973i −0.656274 + 0.826751i
\(529\) 35.3233i 1.53579i
\(530\) 0 0
\(531\) 1.77373i 0.0769732i
\(532\) −2.40297 + 0.137661i −0.104182 + 0.00596834i
\(533\) −7.23508 7.23508i −0.313386 0.313386i
\(534\) −17.9911 6.85598i −0.778552 0.296687i
\(535\) 0 0
\(536\) −0.879950 + 0.456476i −0.0380080 + 0.0197168i
\(537\) −14.6779 + 14.6779i −0.633396 + 0.633396i
\(538\) 3.35741 + 7.49177i 0.144748 + 0.322993i
\(539\) 3.36566 0.144969
\(540\) 0 0
\(541\) −23.7774 −1.02227 −0.511136 0.859500i \(-0.670775\pi\)
−0.511136 + 0.859500i \(0.670775\pi\)
\(542\) −8.04233 17.9458i −0.345448 0.770836i
\(543\) 27.3844 27.3844i 1.17518 1.17518i
\(544\) 12.4473 + 3.17350i 0.533674 + 0.136063i
\(545\) 0 0
\(546\) 9.06041 + 3.45270i 0.387750 + 0.147762i
\(547\) −19.2873 19.2873i −0.824667 0.824667i 0.162106 0.986773i \(-0.448171\pi\)
−0.986773 + 0.162106i \(0.948171\pi\)
\(548\) 0.897104 + 15.6597i 0.0383224 + 0.668947i
\(549\) 1.28438i 0.0548159i
\(550\) 0 0
\(551\) 7.86231i 0.334946i
\(552\) 37.0988 + 11.7555i 1.57903 + 0.500349i
\(553\) −5.73184 5.73184i −0.243742 0.243742i
\(554\) −7.19536 + 18.8817i −0.305702 + 0.802207i
\(555\) 0 0
\(556\) −14.3022 + 16.0404i −0.606547 + 0.680265i
\(557\) 24.6576 24.6576i 1.04478 1.04478i 0.0458256 0.998949i \(-0.485408\pi\)
0.998949 0.0458256i \(-0.0145918\pi\)
\(558\) 1.33938 0.600240i 0.0567006 0.0254102i
\(559\) −10.2319 −0.432765
\(560\) 0 0
\(561\) −13.7695 −0.581347
\(562\) 0.742464 0.332733i 0.0313190 0.0140355i
\(563\) 8.25606 8.25606i 0.347952 0.347952i −0.511394 0.859346i \(-0.670871\pi\)
0.859346 + 0.511394i \(0.170871\pi\)
\(564\) −25.7440 + 28.8728i −1.08402 + 1.21577i
\(565\) 0 0
\(566\) 1.86626 4.89735i 0.0784447 0.205851i
\(567\) −6.84293 6.84293i −0.287376 0.287376i
\(568\) −31.2707 9.90875i −1.31209 0.415762i
\(569\) 0.397613i 0.0166688i −0.999965 0.00833440i \(-0.997347\pi\)
0.999965 0.00833440i \(-0.00265295\pi\)
\(570\) 0 0
\(571\) 17.7372i 0.742278i 0.928577 + 0.371139i \(0.121033\pi\)
−0.928577 + 0.371139i \(0.878967\pi\)
\(572\) −1.46506 25.5737i −0.0612571 1.06929i
\(573\) 28.3225 + 28.3225i 1.18319 + 1.18319i
\(574\) −3.55323 1.35405i −0.148309 0.0565169i
\(575\) 0 0
\(576\) −1.13319 + 1.60856i −0.0472162 + 0.0670233i
\(577\) 10.2591 10.2591i 0.427092 0.427092i −0.460545 0.887637i \(-0.652346\pi\)
0.887637 + 0.460545i \(0.152346\pi\)
\(578\) −6.84976 15.2846i −0.284912 0.635757i
\(579\) 35.3004 1.46704
\(580\) 0 0
\(581\) −16.1726 −0.670954
\(582\) −0.0247011 0.0551184i −0.00102389 0.00228473i
\(583\) −31.1228 + 31.1228i −1.28898 + 1.28898i
\(584\) −36.3664 + 18.8651i −1.50485 + 0.780645i
\(585\) 0 0
\(586\) −26.5451 10.1157i −1.09657 0.417875i
\(587\) −24.8170 24.8170i −1.02431 1.02431i −0.999697 0.0246102i \(-0.992166\pi\)
−0.0246102 0.999697i \(-0.507834\pi\)
\(588\) 3.59741 0.206087i 0.148355 0.00849888i
\(589\) 5.07818i 0.209243i
\(590\) 0 0
\(591\) 41.3868i 1.70243i
\(592\) 8.83572 + 7.01378i 0.363146 + 0.288265i
\(593\) 3.67231 + 3.67231i 0.150804 + 0.150804i 0.778477 0.627673i \(-0.215993\pi\)
−0.627673 + 0.778477i \(0.715993\pi\)
\(594\) −8.40997 + 22.0690i −0.345065 + 0.905503i
\(595\) 0 0
\(596\) 26.5087 + 23.6361i 1.08584 + 0.968171i
\(597\) −4.84228 + 4.84228i −0.198181 + 0.198181i
\(598\) −37.5059 + 16.8082i −1.53373 + 0.687337i
\(599\) −30.7130 −1.25490 −0.627449 0.778658i \(-0.715901\pi\)
−0.627449 + 0.778658i \(0.715901\pi\)
\(600\) 0 0
\(601\) 19.5093 0.795800 0.397900 0.917429i \(-0.369739\pi\)
0.397900 + 0.917429i \(0.369739\pi\)
\(602\) −3.46997 + 1.55506i −0.141425 + 0.0633793i
\(603\) 0.0609538 0.0609538i 0.00248223 0.00248223i
\(604\) −5.34312 4.76410i −0.217408 0.193848i
\(605\) 0 0
\(606\) −2.12144 + 5.56699i −0.0861778 + 0.226144i
\(607\) −3.15281 3.15281i −0.127969 0.127969i 0.640222 0.768190i \(-0.278843\pi\)
−0.768190 + 0.640222i \(0.778843\pi\)
\(608\) 3.47535 + 5.85387i 0.140944 + 0.237406i
\(609\) 11.7704i 0.476960i
\(610\) 0 0
\(611\) 40.8533i 1.65275i
\(612\) −1.11519 + 0.0638864i −0.0450788 + 0.00258246i
\(613\) 24.5054 + 24.5054i 0.989762 + 0.989762i 0.999948 0.0101859i \(-0.00324232\pi\)
−0.0101859 + 0.999948i \(0.503242\pi\)
\(614\) −3.09309 1.17870i −0.124827 0.0475685i
\(615\) 0 0
\(616\) −4.38355 8.45019i −0.176618 0.340468i
\(617\) −29.0478 + 29.0478i −1.16942 + 1.16942i −0.187076 + 0.982345i \(0.559901\pi\)
−0.982345 + 0.187076i \(0.940099\pi\)
\(618\) −7.65371 17.0786i −0.307878 0.687002i
\(619\) 44.8275 1.80177 0.900885 0.434059i \(-0.142919\pi\)
0.900885 + 0.434059i \(0.142919\pi\)
\(620\) 0 0
\(621\) 37.8934 1.52061
\(622\) 18.8436 + 42.0479i 0.755561 + 1.68597i
\(623\) 5.34320 5.34320i 0.214071 0.214071i
\(624\) −3.13188 27.2450i −0.125375 1.09067i
\(625\) 0 0
\(626\) −25.4818 9.71049i −1.01846 0.388109i
\(627\) −5.16008 5.16008i −0.206074 0.206074i
\(628\) 0.390692 + 6.81983i 0.0155903 + 0.272141i
\(629\) 6.40423i 0.255353i
\(630\) 0 0
\(631\) 29.6696i 1.18113i −0.806991 0.590564i \(-0.798905\pi\)
0.806991 0.590564i \(-0.201095\pi\)
\(632\) −6.92562 + 21.8563i −0.275486 + 0.869398i
\(633\) −5.46786 5.46786i −0.217328 0.217328i
\(634\) −1.19050 + 3.12406i −0.0472809 + 0.124072i
\(635\) 0 0
\(636\) −31.3601 + 35.1716i −1.24351 + 1.39464i
\(637\) −2.69086 + 2.69086i −0.106616 + 0.106616i
\(638\) 28.3768 12.7170i 1.12345 0.503469i
\(639\) 2.85248 0.112842
\(640\) 0 0
\(641\) 34.4006 1.35874 0.679372 0.733794i \(-0.262252\pi\)
0.679372 + 0.733794i \(0.262252\pi\)
\(642\) −28.4991 + 12.7718i −1.12477 + 0.504061i
\(643\) 33.2995 33.2995i 1.31321 1.31321i 0.394167 0.919039i \(-0.371033\pi\)
0.919039 0.394167i \(-0.128967\pi\)
\(644\) −10.1649 + 11.4003i −0.400554 + 0.449236i
\(645\) 0 0
\(646\) −1.37622 + 3.61141i −0.0541467 + 0.142089i
\(647\) 14.9070 + 14.9070i 0.586055 + 0.586055i 0.936561 0.350505i \(-0.113990\pi\)
−0.350505 + 0.936561i \(0.613990\pi\)
\(648\) −8.26813 + 26.0931i −0.324803 + 1.02503i
\(649\) 24.2718i 0.952753i
\(650\) 0 0
\(651\) 7.60237i 0.297960i
\(652\) 0.0769530 + 1.34327i 0.00301371 + 0.0526067i
\(653\) −2.33344 2.33344i −0.0913146 0.0913146i 0.659974 0.751289i \(-0.270567\pi\)
−0.751289 + 0.659974i \(0.770567\pi\)
\(654\) −27.0693 10.3154i −1.05849 0.403366i
\(655\) 0 0
\(656\) 1.22823 + 10.6847i 0.0479544 + 0.417167i
\(657\) 2.51908 2.51908i 0.0982788 0.0982788i
\(658\) −6.20891 13.8546i −0.242048 0.540110i
\(659\) 26.8019 1.04405 0.522027 0.852929i \(-0.325176\pi\)
0.522027 + 0.852929i \(0.325176\pi\)
\(660\) 0 0
\(661\) −4.38663 −0.170620 −0.0853101 0.996354i \(-0.527188\pi\)
−0.0853101 + 0.996354i \(0.527188\pi\)
\(662\) −2.25810 5.03876i −0.0877636 0.195837i
\(663\) 11.0087 11.0087i 0.427544 0.427544i
\(664\) 21.0638 + 40.6048i 0.817435 + 1.57577i
\(665\) 0 0
\(666\) −0.916677 0.349323i −0.0355205 0.0135360i
\(667\) −35.2798 35.2798i −1.36604 1.36604i
\(668\) −20.2851 + 1.16208i −0.784854 + 0.0449624i
\(669\) 44.0897i 1.70461i
\(670\) 0 0
\(671\) 17.5756i 0.678497i
\(672\) −5.20282 8.76363i −0.200703 0.338064i
\(673\) 14.1769 + 14.1769i 0.546479 + 0.546479i 0.925421 0.378942i \(-0.123712\pi\)
−0.378942 + 0.925421i \(0.623712\pi\)
\(674\) −7.47185 + 19.6073i −0.287805 + 0.755244i
\(675\) 0 0
\(676\) 2.21146 + 1.97181i 0.0850562 + 0.0758389i
\(677\) 17.4009 17.4009i 0.668772 0.668772i −0.288660 0.957432i \(-0.593210\pi\)
0.957432 + 0.288660i \(0.0932097\pi\)
\(678\) 7.32153 3.28112i 0.281182 0.126011i
\(679\) 0.0237057 0.000909740
\(680\) 0 0
\(681\) 5.25448 0.201352
\(682\) 18.3282 8.21374i 0.701825 0.314520i
\(683\) −15.5454 + 15.5454i −0.594828 + 0.594828i −0.938932 0.344103i \(-0.888183\pi\)
0.344103 + 0.938932i \(0.388183\pi\)
\(684\) −0.441856 0.393974i −0.0168948 0.0150640i
\(685\) 0 0
\(686\) −0.503596 + 1.32151i −0.0192274 + 0.0504555i
\(687\) −4.90791 4.90791i −0.187249 0.187249i
\(688\) 8.42371 + 6.68673i 0.321151 + 0.254929i
\(689\) 49.7657i 1.89592i
\(690\) 0 0
\(691\) 12.6703i 0.481999i −0.970525 0.241000i \(-0.922525\pi\)
0.970525 0.241000i \(-0.0774753\pi\)
\(692\) −3.42498 + 0.196209i −0.130198 + 0.00745873i
\(693\) 0.585341 + 0.585341i 0.0222353 + 0.0222353i
\(694\) −23.0291 8.77583i −0.874173 0.333126i
\(695\) 0 0
\(696\) 29.5520 15.3302i 1.12017 0.581089i
\(697\) −4.31731 + 4.31731i −0.163530 + 0.163530i
\(698\) 9.41997 + 21.0198i 0.356551 + 0.795613i
\(699\) 5.35725 0.202630
\(700\) 0 0
\(701\) 23.4415 0.885373 0.442686 0.896677i \(-0.354026\pi\)
0.442686 + 0.896677i \(0.354026\pi\)
\(702\) −10.9205 24.3681i −0.412167 0.919714i
\(703\) −2.39998 + 2.39998i −0.0905168 + 0.0905168i
\(704\) −15.5067 + 22.0117i −0.584429 + 0.829596i
\(705\) 0 0
\(706\) 16.9262 + 6.45016i 0.637025 + 0.242755i
\(707\) −1.65335 1.65335i −0.0621804 0.0621804i
\(708\) −1.48622 25.9431i −0.0558556 0.975003i
\(709\) 19.6258i 0.737063i 0.929615 + 0.368531i \(0.120139\pi\)
−0.929615 + 0.368531i \(0.879861\pi\)
\(710\) 0 0
\(711\) 1.99371i 0.0747701i
\(712\) −20.3744 6.45605i −0.763563 0.241951i
\(713\) −22.7868 22.7868i −0.853373 0.853373i
\(714\) 2.06029 5.40652i 0.0771045 0.202334i
\(715\) 0 0
\(716\) −15.3352 + 17.1990i −0.573103 + 0.642757i
\(717\) −15.8863 + 15.8863i −0.593283 + 0.593283i
\(718\) 20.0739 8.99605i 0.749151 0.335730i
\(719\) 11.1079 0.414254 0.207127 0.978314i \(-0.433589\pi\)
0.207127 + 0.978314i \(0.433589\pi\)
\(720\) 0 0
\(721\) 7.34527 0.273552
\(722\) 22.6513 10.1511i 0.842992 0.377784i
\(723\) 15.3461 15.3461i 0.570727 0.570727i
\(724\) 28.6108 32.0881i 1.06331 1.19254i
\(725\) 0 0
\(726\) 0.297282 0.780112i 0.0110332 0.0289527i
\(727\) −30.5258 30.5258i −1.13214 1.13214i −0.989821 0.142320i \(-0.954544\pi\)
−0.142320 0.989821i \(-0.545456\pi\)
\(728\) 10.2606 + 3.25129i 0.380284 + 0.120501i
\(729\) 24.4383i 0.905123i
\(730\) 0 0
\(731\) 6.10560i 0.225824i
\(732\) 1.07619 + 18.7858i 0.0397771 + 0.694342i
\(733\) −29.8413 29.8413i −1.10221 1.10221i −0.994143 0.108069i \(-0.965533\pi\)
−0.108069 0.994143i \(-0.534467\pi\)
\(734\) 25.3653 + 9.66610i 0.936250 + 0.356782i
\(735\) 0 0
\(736\) 41.8621 + 10.6729i 1.54306 + 0.393410i
\(737\) 0.834097 0.834097i 0.0307244 0.0307244i
\(738\) −0.382472 0.853453i −0.0140790 0.0314161i
\(739\) 23.6530 0.870091 0.435046 0.900408i \(-0.356732\pi\)
0.435046 + 0.900408i \(0.356732\pi\)
\(740\) 0 0
\(741\) 8.25102 0.303109
\(742\) −7.56341 16.8771i −0.277661 0.619577i
\(743\) 12.8370 12.8370i 0.470945 0.470945i −0.431275 0.902220i \(-0.641936\pi\)
0.902220 + 0.431275i \(0.141936\pi\)
\(744\) 19.0873 9.90160i 0.699776 0.363010i
\(745\) 0 0
\(746\) 6.47585 + 2.46779i 0.237098 + 0.0903521i
\(747\) −2.81268 2.81268i −0.102910 0.102910i
\(748\) −15.2603 + 0.874228i −0.557973 + 0.0319649i
\(749\) 12.2571i 0.447863i
\(750\) 0 0
\(751\) 15.5499i 0.567426i 0.958909 + 0.283713i \(0.0915662\pi\)
−0.958909 + 0.283713i \(0.908434\pi\)
\(752\) −26.6982 + 33.6335i −0.973585 + 1.22649i
\(753\) −12.3008 12.3008i −0.448264 0.448264i
\(754\) −12.5201 + 32.8546i −0.455955 + 1.19649i
\(755\) 0 0
\(756\) −7.40694 6.60427i −0.269388 0.240195i
\(757\) 1.06506 1.06506i 0.0387104 0.0387104i −0.687487 0.726197i \(-0.741286\pi\)
0.726197 + 0.687487i \(0.241286\pi\)
\(758\) −18.1214 + 8.12106i −0.658200 + 0.294970i
\(759\) −46.3086 −1.68090
\(760\) 0 0
\(761\) −33.7471 −1.22333 −0.611665 0.791117i \(-0.709500\pi\)
−0.611665 + 0.791117i \(0.709500\pi\)
\(762\) −7.87546 + 3.52936i −0.285298 + 0.127855i
\(763\) 8.03933 8.03933i 0.291043 0.291043i
\(764\) 33.1874 + 29.5909i 1.20068 + 1.07056i
\(765\) 0 0
\(766\) −2.12673 + 5.58086i −0.0768419 + 0.201645i
\(767\) 19.4054 + 19.4054i 0.700690 + 0.700690i
\(768\) −15.2266 + 24.4768i −0.549442 + 0.883232i
\(769\) 25.8245i 0.931254i −0.884981 0.465627i \(-0.845829\pi\)
0.884981 0.465627i \(-0.154171\pi\)
\(770\) 0 0
\(771\) 9.82514i 0.353844i
\(772\) 39.1226 2.24124i 1.40805 0.0806639i
\(773\) 17.2373 + 17.2373i 0.619981 + 0.619981i 0.945526 0.325545i \(-0.105548\pi\)
−0.325545 + 0.945526i \(0.605548\pi\)
\(774\) −0.873931 0.333034i −0.0314128 0.0119707i
\(775\) 0 0
\(776\) −0.0308751 0.0595180i −0.00110835 0.00213657i
\(777\) 3.59292 3.59292i 0.128895 0.128895i
\(778\) 8.57846 + 19.1421i 0.307553 + 0.686277i
\(779\) −3.23581 −0.115935
\(780\) 0 0
\(781\) 39.0336 1.39673
\(782\) 10.0297 + 22.3805i 0.358663 + 0.800325i
\(783\) 22.9217 22.9217i 0.819155 0.819155i
\(784\) 3.97383 0.456801i 0.141923 0.0163143i
\(785\) 0 0
\(786\) 19.4161 + 7.39898i 0.692548 + 0.263913i
\(787\) 21.5133 + 21.5133i 0.766866 + 0.766866i 0.977553 0.210688i \(-0.0675703\pi\)
−0.210688 + 0.977553i \(0.567570\pi\)
\(788\) 2.62766 + 45.8679i 0.0936066 + 1.63398i
\(789\) 31.5884i 1.12458i
\(790\) 0 0
\(791\) 3.14889i 0.111962i
\(792\) 0.707252 2.23199i 0.0251311 0.0793103i
\(793\) −14.0517 14.0517i −0.498992 0.498992i
\(794\) −1.20785 + 3.16959i −0.0428651 + 0.112485i
\(795\) 0 0
\(796\) −5.05913 + 5.67401i −0.179316 + 0.201110i
\(797\) 35.0680 35.0680i 1.24217 1.24217i 0.283074 0.959098i \(-0.408646\pi\)
0.959098 0.283074i \(-0.0913540\pi\)
\(798\) 2.79818 1.25399i 0.0990543 0.0443909i
\(799\) −24.3780 −0.862430
\(800\) 0 0
\(801\) 1.85853 0.0656681
\(802\) 35.7265 16.0107i 1.26155 0.565358i
\(803\) 34.4714 34.4714i 1.21647 1.21647i
\(804\) 0.840457 0.942604i 0.0296406 0.0332431i
\(805\) 0 0
\(806\) −8.08659 + 21.2204i −0.284838 + 0.747458i
\(807\) −7.39549 7.39549i −0.260334 0.260334i
\(808\) −1.99769 + 6.30445i −0.0702786 + 0.221790i
\(809\) 24.0099i 0.844143i −0.906563 0.422072i \(-0.861303\pi\)
0.906563 0.422072i \(-0.138697\pi\)
\(810\) 0 0
\(811\) 52.4070i 1.84026i −0.391615 0.920129i \(-0.628084\pi\)
0.391615 0.920129i \(-0.371916\pi\)
\(812\) 0.747306 + 13.0448i 0.0262253 + 0.457784i
\(813\) 17.7151 + 17.7151i 0.621297 + 0.621297i
\(814\) −12.5439 4.78017i −0.439663 0.167545i
\(815\) 0 0
\(816\) −16.2576 + 1.86885i −0.569130 + 0.0654228i
\(817\) −2.28806 + 2.28806i −0.0800492 + 0.0800492i
\(818\) −19.5801 43.6913i −0.684602 1.52763i
\(819\) −0.935965 −0.0327053
\(820\) 0 0
\(821\) −19.1519 −0.668406 −0.334203 0.942501i \(-0.608467\pi\)
−0.334203 + 0.942501i \(0.608467\pi\)
\(822\) −8.17200 18.2351i −0.285031 0.636022i
\(823\) 8.97203 8.97203i 0.312745 0.312745i −0.533227 0.845972i \(-0.679021\pi\)
0.845972 + 0.533227i \(0.179021\pi\)
\(824\) −9.56674 18.4418i −0.333273 0.642452i
\(825\) 0 0
\(826\) 9.53024 + 3.63174i 0.331599 + 0.126364i
\(827\) 26.1556 + 26.1556i 0.909520 + 0.909520i 0.996233 0.0867129i \(-0.0276363\pi\)
−0.0867129 + 0.996233i \(0.527636\pi\)
\(828\) −3.75054 + 0.214859i −0.130340 + 0.00746687i
\(829\) 31.1844i 1.08308i −0.840675 0.541540i \(-0.817842\pi\)
0.840675 0.541540i \(-0.182158\pi\)
\(830\) 0 0
\(831\) 25.7420i 0.892979i
\(832\) −5.20077 29.9961i −0.180304 1.03993i
\(833\) 1.60569 + 1.60569i 0.0556337 + 0.0556337i
\(834\) 9.74927 25.5835i 0.337589 0.885886i
\(835\) 0 0
\(836\) −6.04640 5.39117i −0.209119 0.186458i
\(837\) 14.8049 14.8049i 0.511732 0.511732i
\(838\) −4.90623 + 2.19871i −0.169483 + 0.0759532i
\(839\) −8.19874 −0.283052 −0.141526 0.989935i \(-0.545201\pi\)
−0.141526 + 0.989935i \(0.545201\pi\)
\(840\) 0 0
\(841\) −13.6815 −0.471775
\(842\) 20.0888 9.00274i 0.692307 0.310255i
\(843\) −0.732923 + 0.732923i −0.0252432 + 0.0252432i
\(844\) −6.40705 5.71274i −0.220540 0.196641i
\(845\) 0 0
\(846\) 1.32971 3.48937i 0.0457164 0.119967i
\(847\) 0.231686 + 0.231686i 0.00796083 + 0.00796083i
\(848\) −32.5226 + 40.9708i −1.11683 + 1.40694i
\(849\) 6.67669i 0.229143i
\(850\) 0 0
\(851\) 21.5383i 0.738325i
\(852\) 41.7214 2.39012i 1.42935 0.0818840i
\(853\) 28.0841 + 28.0841i 0.961580 + 0.961580i 0.999289 0.0377085i \(-0.0120058\pi\)
−0.0377085 + 0.999289i \(0.512006\pi\)
\(854\) −6.90096 2.62979i −0.236146 0.0899895i
\(855\) 0 0
\(856\) −30.7739 + 15.9640i −1.05183 + 0.545639i
\(857\) −17.0185 + 17.0185i −0.581342 + 0.581342i −0.935272 0.353930i \(-0.884845\pi\)
0.353930 + 0.935272i \(0.384845\pi\)
\(858\) 13.3457 + 29.7797i 0.455614 + 1.01666i
\(859\) −53.0951 −1.81158 −0.905790 0.423726i \(-0.860722\pi\)
−0.905790 + 0.423726i \(0.860722\pi\)
\(860\) 0 0
\(861\) 4.84422 0.165091
\(862\) 0.906964 + 2.02381i 0.0308913 + 0.0689313i
\(863\) −36.5447 + 36.5447i −1.24399 + 1.24399i −0.285665 + 0.958329i \(0.592215\pi\)
−0.958329 + 0.285665i \(0.907785\pi\)
\(864\) −6.93434 + 27.1983i −0.235911 + 0.925306i
\(865\) 0 0
\(866\) 10.3982 + 3.96249i 0.353345 + 0.134651i
\(867\) 15.0882 + 15.0882i 0.512423 + 0.512423i
\(868\) 0.482677 + 8.42551i 0.0163831 + 0.285980i
\(869\) 27.2822i 0.925484i
\(870\) 0 0
\(871\) 1.33373i 0.0451917i
\(872\) −30.6551 9.71371i −1.03811 0.328948i
\(873\) 0.00412279 + 0.00412279i 0.000139535 + 0.000139535i
\(874\) −4.62843 + 12.1457i −0.156559 + 0.410834i
\(875\) 0 0
\(876\) 34.7342 38.9557i 1.17356 1.31619i
\(877\) 3.12021 3.12021i 0.105362 0.105362i −0.652461 0.757823i \(-0.726263\pi\)
0.757823 + 0.652461i \(0.226263\pi\)
\(878\) −4.82387 + 2.16180i −0.162798 + 0.0729573i
\(879\) 36.1897 1.22065
\(880\) 0 0
\(881\) −36.4751 −1.22888 −0.614439 0.788964i \(-0.710618\pi\)
−0.614439 + 0.788964i \(0.710618\pi\)
\(882\) −0.317415 + 0.142248i −0.0106879 + 0.00478975i
\(883\) 10.3357 10.3357i 0.347823 0.347823i −0.511475 0.859298i \(-0.670901\pi\)
0.859298 + 0.511475i \(0.170901\pi\)
\(884\) 11.5018 12.8997i 0.386846 0.433862i
\(885\) 0 0
\(886\) −0.160192 + 0.420367i −0.00538175 + 0.0141225i
\(887\) −4.14097 4.14097i −0.139040 0.139040i 0.634161 0.773201i \(-0.281346\pi\)
−0.773201 + 0.634161i \(0.781346\pi\)
\(888\) −13.7003 4.34123i −0.459753 0.145682i
\(889\) 3.38713i 0.113601i
\(890\) 0 0
\(891\) 32.5707i 1.09116i
\(892\) 2.79927 + 48.8635i 0.0937266 + 1.63607i
\(893\) −9.13560 9.13560i −0.305711 0.305711i
\(894\) −42.2800 16.1119i −1.41405 0.538861i
\(895\) 0 0
\(896\) −6.32256 9.38218i −0.211222 0.313437i
\(897\) 37.0240 37.0240i 1.23619 1.23619i
\(898\) −10.9490 24.4318i −0.365374 0.815300i
\(899\) −27.5675 −0.919428
\(900\) 0 0
\(901\) −29.6961 −0.989321
\(902\) −5.23379 11.6787i −0.174266 0.388859i
\(903\) 3.42538 3.42538i 0.113990 0.113990i
\(904\) 7.90595 4.10123i 0.262948 0.136405i
\(905\) 0 0
\(906\) 8.52197 + 3.24751i 0.283123 + 0.107891i
\(907\) 22.9113 + 22.9113i 0.760758 + 0.760758i 0.976459 0.215702i \(-0.0692039\pi\)
−0.215702 + 0.976459i \(0.569204\pi\)
\(908\) 5.82340 0.333609i 0.193256 0.0110712i
\(909\) 0.575086i 0.0190744i
\(910\) 0 0
\(911\) 35.7663i 1.18499i 0.805574 + 0.592496i \(0.201857\pi\)
−0.805574 + 0.592496i \(0.798143\pi\)
\(912\) −6.79286 5.39216i −0.224934 0.178552i
\(913\) −38.4889 38.4889i −1.27380 1.27380i
\(914\) 17.5021 45.9282i 0.578919 1.51917i
\(915\) 0 0
\(916\) −5.75092 5.12771i −0.190016 0.169424i
\(917\) −5.76639 + 5.76639i −0.190423 + 0.190423i
\(918\) −14.5409 + 6.51646i −0.479921 + 0.215075i
\(919\) 32.6970 1.07857 0.539287 0.842122i \(-0.318694\pi\)
0.539287 + 0.842122i \(0.318694\pi\)
\(920\) 0 0
\(921\) 4.21690 0.138952
\(922\) −37.8253 + 16.9513i −1.24571 + 0.558261i
\(923\) −31.2075 + 31.2075i −1.02721 + 1.02721i
\(924\) 9.05186 + 8.07094i 0.297784 + 0.265514i
\(925\) 0 0
\(926\) 7.65124 20.0780i 0.251435 0.659804i
\(927\) 1.27746 + 1.27746i 0.0419572 + 0.0419572i
\(928\) 31.7784 18.8663i 1.04318 0.619317i
\(929\) 1.91098i 0.0626971i 0.999509 + 0.0313485i \(0.00998019\pi\)
−0.999509 + 0.0313485i \(0.990020\pi\)
\(930\) 0 0
\(931\) 1.20346i 0.0394417i
\(932\) 5.93730 0.340133i 0.194483 0.0111414i
\(933\) −41.5076 41.5076i −1.35890 1.35890i
\(934\) −29.2359 11.1411i −0.956629 0.364548i
\(935\) 0 0
\(936\) 1.21903 + 2.34994i 0.0398454 + 0.0768101i
\(937\) −16.4547 + 16.4547i −0.537553 + 0.537553i −0.922810 0.385256i \(-0.874113\pi\)
0.385256 + 0.922810i \(0.374113\pi\)
\(938\) 0.202701 + 0.452309i 0.00661841 + 0.0147684i
\(939\) 34.7400 1.13370
\(940\) 0 0
\(941\) 6.06433 0.197691 0.0988457 0.995103i \(-0.468485\pi\)
0.0988457 + 0.995103i \(0.468485\pi\)
\(942\) −3.55893 7.94145i −0.115956 0.258746i
\(943\) −14.5197 + 14.5197i −0.472827 + 0.472827i
\(944\) −3.29428 28.6578i −0.107220 0.932731i
\(945\) 0 0
\(946\) −11.9590 4.55727i −0.388819 0.148170i
\(947\) −7.66311 7.66311i −0.249018 0.249018i 0.571550 0.820567i \(-0.306342\pi\)
−0.820567 + 0.571550i \(0.806342\pi\)
\(948\) −1.67055 29.1607i −0.0542569 0.947096i
\(949\) 55.1200i 1.78927i
\(950\) 0 0
\(951\) 4.25912i 0.138111i
\(952\) 1.94011 6.12271i 0.0628792 0.198438i
\(953\) 4.85409 + 4.85409i 0.157239 + 0.157239i 0.781342 0.624103i \(-0.214535\pi\)
−0.624103 + 0.781342i \(0.714535\pi\)
\(954\) 1.61979 4.25059i 0.0524428 0.137618i
\(955\) 0 0
\(956\) −16.5977 + 18.6150i −0.536808 + 0.602051i
\(957\) −28.0121 + 28.0121i −0.905503 + 0.905503i
\(958\) −0.578096 + 0.259072i −0.0186774 + 0.00837023i
\(959\) 7.84267 0.253253
\(960\) 0 0
\(961\) 13.1945 0.425627
\(962\) 13.8507 6.20713i 0.446563 0.200126i
\(963\) 2.13170 2.13170i 0.0686929 0.0686929i
\(964\) 16.0333 17.9820i 0.516399 0.579161i
\(965\) 0 0
\(966\) 6.92906 18.1829i 0.222939 0.585025i
\(967\) −37.2034 37.2034i −1.19638 1.19638i −0.975242 0.221139i \(-0.929022\pi\)
−0.221139 0.975242i \(-0.570978\pi\)
\(968\) 0.279940 0.883453i 0.00899761 0.0283952i
\(969\) 4.92354i 0.158167i
\(970\) 0 0
\(971\) 43.1866i 1.38592i 0.720974 + 0.692962i \(0.243695\pi\)
−0.720974 + 0.692962i \(0.756305\pi\)
\(972\) −0.291660 5.09116i −0.00935501 0.163299i
\(973\) 7.59808 + 7.59808i 0.243583 + 0.243583i
\(974\) 44.3377 + 16.8960i 1.42067 + 0.541384i
\(975\) 0 0
\(976\) 2.38543 + 20.7514i 0.0763557 + 0.664238i
\(977\) −13.0089 + 13.0089i −0.416191 + 0.416191i −0.883888 0.467698i \(-0.845084\pi\)
0.467698 + 0.883888i \(0.345084\pi\)
\(978\) −0.700989 1.56419i −0.0224151 0.0500174i
\(979\) 25.4323 0.812821
\(980\) 0 0
\(981\) 2.79633 0.0892800
\(982\) 10.6315 + 23.7233i 0.339266 + 0.757042i
\(983\) 9.22607 9.22607i 0.294266 0.294266i −0.544497 0.838763i \(-0.683279\pi\)
0.838763 + 0.544497i \(0.183279\pi\)
\(984\) −6.30929 12.1624i −0.201133 0.387724i
\(985\) 0 0
\(986\) 19.6050 + 7.47098i 0.624349 + 0.237924i
\(987\) 13.6766 + 13.6766i 0.435331 + 0.435331i
\(988\) 9.14439 0.523860i 0.290922 0.0166662i
\(989\) 20.5340i 0.652943i
\(990\) 0 0
\(991\) 38.4314i 1.22081i −0.792088 0.610407i \(-0.791006\pi\)
0.792088 0.610407i \(-0.208994\pi\)
\(992\) 20.5253 12.1855i 0.651680 0.386892i
\(993\) 4.97401 + 4.97401i 0.157845 + 0.157845i
\(994\) −5.84051 + 15.3264i −0.185250 + 0.486123i
\(995\) 0 0
\(996\) −43.4959 38.7824i −1.37822 1.22887i
\(997\) −15.2830 + 15.2830i −0.484017 + 0.484017i −0.906412 0.422395i \(-0.861189\pi\)
0.422395 + 0.906412i \(0.361189\pi\)
\(998\) 47.8751 21.4551i 1.51546 0.679148i
\(999\) −13.9937 −0.442742
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.k.b.43.3 36
4.3 odd 2 inner 700.2.k.b.43.7 36
5.2 odd 4 inner 700.2.k.b.407.7 36
5.3 odd 4 140.2.k.a.127.12 yes 36
5.4 even 2 140.2.k.a.43.16 yes 36
20.3 even 4 140.2.k.a.127.16 yes 36
20.7 even 4 inner 700.2.k.b.407.3 36
20.19 odd 2 140.2.k.a.43.12 36
35.3 even 12 980.2.x.l.667.1 72
35.4 even 6 980.2.x.k.863.9 72
35.9 even 6 980.2.x.k.263.3 72
35.13 even 4 980.2.k.l.687.12 36
35.18 odd 12 980.2.x.k.667.1 72
35.19 odd 6 980.2.x.l.263.3 72
35.23 odd 12 980.2.x.k.67.12 72
35.24 odd 6 980.2.x.l.863.9 72
35.33 even 12 980.2.x.l.67.12 72
35.34 odd 2 980.2.k.l.883.16 36
140.3 odd 12 980.2.x.l.667.3 72
140.19 even 6 980.2.x.l.263.1 72
140.23 even 12 980.2.x.k.67.9 72
140.39 odd 6 980.2.x.k.863.12 72
140.59 even 6 980.2.x.l.863.12 72
140.79 odd 6 980.2.x.k.263.1 72
140.83 odd 4 980.2.k.l.687.16 36
140.103 odd 12 980.2.x.l.67.9 72
140.123 even 12 980.2.x.k.667.3 72
140.139 even 2 980.2.k.l.883.12 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.k.a.43.12 36 20.19 odd 2
140.2.k.a.43.16 yes 36 5.4 even 2
140.2.k.a.127.12 yes 36 5.3 odd 4
140.2.k.a.127.16 yes 36 20.3 even 4
700.2.k.b.43.3 36 1.1 even 1 trivial
700.2.k.b.43.7 36 4.3 odd 2 inner
700.2.k.b.407.3 36 20.7 even 4 inner
700.2.k.b.407.7 36 5.2 odd 4 inner
980.2.k.l.687.12 36 35.13 even 4
980.2.k.l.687.16 36 140.83 odd 4
980.2.k.l.883.12 36 140.139 even 2
980.2.k.l.883.16 36 35.34 odd 2
980.2.x.k.67.9 72 140.23 even 12
980.2.x.k.67.12 72 35.23 odd 12
980.2.x.k.263.1 72 140.79 odd 6
980.2.x.k.263.3 72 35.9 even 6
980.2.x.k.667.1 72 35.18 odd 12
980.2.x.k.667.3 72 140.123 even 12
980.2.x.k.863.9 72 35.4 even 6
980.2.x.k.863.12 72 140.39 odd 6
980.2.x.l.67.9 72 140.103 odd 12
980.2.x.l.67.12 72 35.33 even 12
980.2.x.l.263.1 72 140.19 even 6
980.2.x.l.263.3 72 35.19 odd 6
980.2.x.l.667.1 72 35.3 even 12
980.2.x.l.667.3 72 140.3 odd 12
980.2.x.l.863.9 72 35.24 odd 6
980.2.x.l.863.12 72 140.59 even 6