Properties

Label 240.3.bn.a.91.19
Level $240$
Weight $3$
Character 240.91
Analytic conductor $6.540$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [240,3,Mod(91,240)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(240, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 0, 0]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("240.91");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 240.bn (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: \(6.53952634465\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 91.19
Character \(\chi\) \(=\) 240.91
Dual form 240.3.bn.a.211.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.405730 - 1.95841i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.67077 - 1.58918i) q^{4} +(1.58114 + 1.58114i) q^{5} +(2.89547 - 1.90164i) q^{6} +0.712173 q^{7} +(-4.60160 + 6.54410i) q^{8} +3.00000i q^{9} +O(q^{10})\) \(q+(0.405730 - 1.95841i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-3.67077 - 1.58918i) q^{4} +(1.58114 + 1.58114i) q^{5} +(2.89547 - 1.90164i) q^{6} +0.712173 q^{7} +(-4.60160 + 6.54410i) q^{8} +3.00000i q^{9} +(3.73804 - 2.45501i) q^{10} +(14.0558 - 14.0558i) q^{11} +(-2.54942 - 6.44209i) q^{12} +(17.1589 - 17.1589i) q^{13} +(0.288950 - 1.39473i) q^{14} +3.87298i q^{15} +(10.9490 + 11.6670i) q^{16} -7.75861 q^{17} +(5.87524 + 1.21719i) q^{18} +(4.72770 + 4.72770i) q^{19} +(-3.29128 - 8.31670i) q^{20} +(0.872230 + 0.872230i) q^{21} +(-21.8242 - 33.2300i) q^{22} +12.5543 q^{23} +(-13.6506 + 2.37906i) q^{24} +5.00000i q^{25} +(-26.6423 - 40.5661i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(-2.61422 - 1.13177i) q^{28} +(-5.44794 + 5.44794i) q^{29} +(7.58490 + 1.57139i) q^{30} +21.7832i q^{31} +(27.2911 - 16.7091i) q^{32} +34.4296 q^{33} +(-3.14791 + 15.1946i) q^{34} +(1.12604 + 1.12604i) q^{35} +(4.76753 - 11.0123i) q^{36} +(4.04870 + 4.04870i) q^{37} +(11.1770 - 7.34062i) q^{38} +42.0305 q^{39} +(-17.6229 + 3.07136i) q^{40} -59.9360i q^{41} +(2.06208 - 1.35430i) q^{42} +(-57.7031 + 57.7031i) q^{43} +(-73.9327 + 29.2584i) q^{44} +(-4.74342 + 4.74342i) q^{45} +(5.09368 - 24.5866i) q^{46} -0.267084i q^{47} +(-0.879295 + 27.6989i) q^{48} -48.4928 q^{49} +(9.79207 + 2.02865i) q^{50} +(-9.50232 - 9.50232i) q^{51} +(-90.2548 + 35.7178i) q^{52} +(-20.9268 - 20.9268i) q^{53} +(5.70492 + 8.68642i) q^{54} +44.4484 q^{55} +(-3.27714 + 4.66053i) q^{56} +11.5805i q^{57} +(8.45892 + 12.8797i) q^{58} +(-12.9641 + 12.9641i) q^{59} +(6.15485 - 14.2168i) q^{60} +(-32.4174 + 32.4174i) q^{61} +(42.6605 + 8.83809i) q^{62} +2.13652i q^{63} +(-21.6505 - 60.2267i) q^{64} +54.2612 q^{65} +(13.9691 - 67.4273i) q^{66} +(55.3331 + 55.3331i) q^{67} +(28.4801 + 12.3298i) q^{68} +(15.3759 + 15.3759i) q^{69} +(2.66213 - 1.74839i) q^{70} +106.273 q^{71} +(-19.6323 - 13.8048i) q^{72} +84.4739i q^{73} +(9.57170 - 6.28634i) q^{74} +(-6.12372 + 6.12372i) q^{75} +(-9.84113 - 24.8674i) q^{76} +(10.0102 - 10.0102i) q^{77} +(17.0531 - 82.3132i) q^{78} +17.9978i q^{79} +(-1.13516 + 35.7591i) q^{80} -9.00000 q^{81} +(-117.379 - 24.3178i) q^{82} +(-0.0906551 - 0.0906551i) q^{83} +(-1.81563 - 4.58788i) q^{84} +(-12.2674 - 12.2674i) q^{85} +(89.5946 + 136.418i) q^{86} -13.3447 q^{87} +(27.3034 + 156.662i) q^{88} -84.9533i q^{89} +(7.36502 + 11.2141i) q^{90} +(12.2201 - 12.2201i) q^{91} +(-46.0840 - 19.9510i) q^{92} +(-26.6788 + 26.6788i) q^{93} +(-0.523060 - 0.108364i) q^{94} +14.9503i q^{95} +(53.8891 + 12.9603i) q^{96} -174.548 q^{97} +(-19.6750 + 94.9690i) q^{98} +(42.1674 + 42.1674i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 24 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 24 q^{4} + 20 q^{10} - 64 q^{11} + 72 q^{14} - 36 q^{16} - 24 q^{18} + 32 q^{19} - 80 q^{20} + 48 q^{22} + 256 q^{23} - 36 q^{24} + 240 q^{28} - 64 q^{29} - 40 q^{32} - 76 q^{34} - 12 q^{36} + 192 q^{37} - 280 q^{38} - 192 q^{43} - 280 q^{44} - 300 q^{46} + 448 q^{49} - 40 q^{50} + 96 q^{51} + 104 q^{52} + 320 q^{53} + 36 q^{54} + 112 q^{56} + 64 q^{58} + 128 q^{59} + 32 q^{61} + 48 q^{62} + 48 q^{64} - 72 q^{66} - 64 q^{67} + 280 q^{68} - 96 q^{69} + 240 q^{70} - 512 q^{71} - 120 q^{72} - 608 q^{74} - 308 q^{76} - 448 q^{77} - 360 q^{78} - 576 q^{81} - 200 q^{82} - 144 q^{84} - 160 q^{85} - 560 q^{86} - 184 q^{88} + 576 q^{91} - 56 q^{92} + 460 q^{94} + 360 q^{96} + 368 q^{98} - 192 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(97\) \(161\) \(181\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.405730 1.95841i 0.202865 0.979207i
\(3\) 1.22474 + 1.22474i 0.408248 + 0.408248i
\(4\) −3.67077 1.58918i −0.917691 0.397294i
\(5\) 1.58114 + 1.58114i 0.316228 + 0.316228i
\(6\) 2.89547 1.90164i 0.482579 0.316940i
\(7\) 0.712173 0.101739 0.0508695 0.998705i \(-0.483801\pi\)
0.0508695 + 0.998705i \(0.483801\pi\)
\(8\) −4.60160 + 6.54410i −0.575200 + 0.818012i
\(9\) 3.00000i 0.333333i
\(10\) 3.73804 2.45501i 0.373804 0.245501i
\(11\) 14.0558 14.0558i 1.27780 1.27780i 0.335905 0.941896i \(-0.390958\pi\)
0.941896 0.335905i \(-0.109042\pi\)
\(12\) −2.54942 6.44209i −0.212451 0.536841i
\(13\) 17.1589 17.1589i 1.31992 1.31992i 0.406076 0.913839i \(-0.366897\pi\)
0.913839 0.406076i \(-0.133103\pi\)
\(14\) 0.288950 1.39473i 0.0206393 0.0996235i
\(15\) 3.87298i 0.258199i
\(16\) 10.9490 + 11.6670i 0.684315 + 0.729186i
\(17\) −7.75861 −0.456389 −0.228195 0.973616i \(-0.573282\pi\)
−0.228195 + 0.973616i \(0.573282\pi\)
\(18\) 5.87524 + 1.21719i 0.326402 + 0.0676217i
\(19\) 4.72770 + 4.72770i 0.248826 + 0.248826i 0.820489 0.571663i \(-0.193701\pi\)
−0.571663 + 0.820489i \(0.693701\pi\)
\(20\) −3.29128 8.31670i −0.164564 0.415835i
\(21\) 0.872230 + 0.872230i 0.0415348 + 0.0415348i
\(22\) −21.8242 33.2300i −0.992010 1.51045i
\(23\) 12.5543 0.545841 0.272920 0.962037i \(-0.412010\pi\)
0.272920 + 0.962037i \(0.412010\pi\)
\(24\) −13.6506 + 2.37906i −0.568777 + 0.0991276i
\(25\) 5.00000i 0.200000i
\(26\) −26.6423 40.5661i −1.02470 1.56023i
\(27\) −3.67423 + 3.67423i −0.136083 + 0.136083i
\(28\) −2.61422 1.13177i −0.0933650 0.0404203i
\(29\) −5.44794 + 5.44794i −0.187860 + 0.187860i −0.794770 0.606910i \(-0.792409\pi\)
0.606910 + 0.794770i \(0.292409\pi\)
\(30\) 7.58490 + 1.57139i 0.252830 + 0.0523796i
\(31\) 21.7832i 0.702683i 0.936247 + 0.351341i \(0.114274\pi\)
−0.936247 + 0.351341i \(0.885726\pi\)
\(32\) 27.2911 16.7091i 0.852848 0.522159i
\(33\) 34.4296 1.04332
\(34\) −3.14791 + 15.1946i −0.0925854 + 0.446899i
\(35\) 1.12604 + 1.12604i 0.0321727 + 0.0321727i
\(36\) 4.76753 11.0123i 0.132431 0.305897i
\(37\) 4.04870 + 4.04870i 0.109424 + 0.109424i 0.759699 0.650275i \(-0.225346\pi\)
−0.650275 + 0.759699i \(0.725346\pi\)
\(38\) 11.1770 7.34062i 0.294131 0.193174i
\(39\) 42.0305 1.07771
\(40\) −17.6229 + 3.07136i −0.440573 + 0.0767839i
\(41\) 59.9360i 1.46185i −0.682456 0.730927i \(-0.739088\pi\)
0.682456 0.730927i \(-0.260912\pi\)
\(42\) 2.06208 1.35430i 0.0490971 0.0322452i
\(43\) −57.7031 + 57.7031i −1.34193 + 1.34193i −0.447798 + 0.894135i \(0.647792\pi\)
−0.894135 + 0.447798i \(0.852208\pi\)
\(44\) −73.9327 + 29.2584i −1.68029 + 0.664965i
\(45\) −4.74342 + 4.74342i −0.105409 + 0.105409i
\(46\) 5.09368 24.5866i 0.110732 0.534491i
\(47\) 0.267084i 0.00568263i −0.999996 0.00284132i \(-0.999096\pi\)
0.999996 0.00284132i \(-0.000904420\pi\)
\(48\) −0.879295 + 27.6989i −0.0183186 + 0.577060i
\(49\) −48.4928 −0.989649
\(50\) 9.79207 + 2.02865i 0.195841 + 0.0405730i
\(51\) −9.50232 9.50232i −0.186320 0.186320i
\(52\) −90.2548 + 35.7178i −1.73567 + 0.686881i
\(53\) −20.9268 20.9268i −0.394846 0.394846i 0.481565 0.876411i \(-0.340069\pi\)
−0.876411 + 0.481565i \(0.840069\pi\)
\(54\) 5.70492 + 8.68642i 0.105647 + 0.160860i
\(55\) 44.4484 0.808152
\(56\) −3.27714 + 4.66053i −0.0585203 + 0.0832238i
\(57\) 11.5805i 0.203166i
\(58\) 8.45892 + 12.8797i 0.145843 + 0.222064i
\(59\) −12.9641 + 12.9641i −0.219731 + 0.219731i −0.808385 0.588654i \(-0.799658\pi\)
0.588654 + 0.808385i \(0.299658\pi\)
\(60\) 6.15485 14.2168i 0.102581 0.236947i
\(61\) −32.4174 + 32.4174i −0.531433 + 0.531433i −0.920999 0.389565i \(-0.872625\pi\)
0.389565 + 0.920999i \(0.372625\pi\)
\(62\) 42.6605 + 8.83809i 0.688072 + 0.142550i
\(63\) 2.13652i 0.0339130i
\(64\) −21.6505 60.2267i −0.338289 0.941042i
\(65\) 54.2612 0.834788
\(66\) 13.9691 67.4273i 0.211653 1.02163i
\(67\) 55.3331 + 55.3331i 0.825867 + 0.825867i 0.986942 0.161075i \(-0.0514960\pi\)
−0.161075 + 0.986942i \(0.551496\pi\)
\(68\) 28.4801 + 12.3298i 0.418824 + 0.181321i
\(69\) 15.3759 + 15.3759i 0.222839 + 0.222839i
\(70\) 2.66213 1.74839i 0.0380304 0.0249770i
\(71\) 106.273 1.49681 0.748403 0.663245i \(-0.230821\pi\)
0.748403 + 0.663245i \(0.230821\pi\)
\(72\) −19.6323 13.8048i −0.272671 0.191733i
\(73\) 84.4739i 1.15718i 0.815620 + 0.578588i \(0.196396\pi\)
−0.815620 + 0.578588i \(0.803604\pi\)
\(74\) 9.57170 6.28634i 0.129347 0.0849506i
\(75\) −6.12372 + 6.12372i −0.0816497 + 0.0816497i
\(76\) −9.84113 24.8674i −0.129489 0.327203i
\(77\) 10.0102 10.0102i 0.130002 0.130002i
\(78\) 17.0531 82.3132i 0.218629 1.05530i
\(79\) 17.9978i 0.227820i 0.993491 + 0.113910i \(0.0363376\pi\)
−0.993491 + 0.113910i \(0.963662\pi\)
\(80\) −1.13516 + 35.7591i −0.0141896 + 0.446988i
\(81\) −9.00000 −0.111111
\(82\) −117.379 24.3178i −1.43146 0.296559i
\(83\) −0.0906551 0.0906551i −0.00109223 0.00109223i 0.706560 0.707653i \(-0.250246\pi\)
−0.707653 + 0.706560i \(0.750246\pi\)
\(84\) −1.81563 4.58788i −0.0216146 0.0546176i
\(85\) −12.2674 12.2674i −0.144323 0.144323i
\(86\) 89.5946 + 136.418i 1.04180 + 1.58626i
\(87\) −13.3447 −0.153387
\(88\) 27.3034 + 156.662i 0.310265 + 1.78025i
\(89\) 84.9533i 0.954532i −0.878759 0.477266i \(-0.841628\pi\)
0.878759 0.477266i \(-0.158372\pi\)
\(90\) 7.36502 + 11.2141i 0.0818336 + 0.124601i
\(91\) 12.2201 12.2201i 0.134287 0.134287i
\(92\) −46.0840 19.9510i −0.500913 0.216859i
\(93\) −26.6788 + 26.6788i −0.286869 + 0.286869i
\(94\) −0.523060 0.108364i −0.00556447 0.00115281i
\(95\) 14.9503i 0.157372i
\(96\) 53.8891 + 12.9603i 0.561344 + 0.135003i
\(97\) −174.548 −1.79947 −0.899733 0.436440i \(-0.856239\pi\)
−0.899733 + 0.436440i \(0.856239\pi\)
\(98\) −19.6750 + 94.9690i −0.200765 + 0.969071i
\(99\) 42.1674 + 42.1674i 0.425934 + 0.425934i
\(100\) 7.94588 18.3538i 0.0794588 0.183538i
\(101\) 15.2996 + 15.2996i 0.151481 + 0.151481i 0.778779 0.627298i \(-0.215839\pi\)
−0.627298 + 0.778779i \(0.715839\pi\)
\(102\) −22.4649 + 14.7541i −0.220244 + 0.144648i
\(103\) 84.2191 0.817661 0.408831 0.912610i \(-0.365937\pi\)
0.408831 + 0.912610i \(0.365937\pi\)
\(104\) 33.3311 + 191.248i 0.320491 + 1.83892i
\(105\) 2.75823i 0.0262689i
\(106\) −49.4741 + 32.4928i −0.466736 + 0.306535i
\(107\) −81.3788 + 81.3788i −0.760549 + 0.760549i −0.976422 0.215872i \(-0.930741\pi\)
0.215872 + 0.976422i \(0.430741\pi\)
\(108\) 19.3263 7.64825i 0.178947 0.0708171i
\(109\) 115.221 115.221i 1.05707 1.05707i 0.0587998 0.998270i \(-0.481273\pi\)
0.998270 0.0587998i \(-0.0187274\pi\)
\(110\) 18.0341 87.0483i 0.163946 0.791348i
\(111\) 9.91724i 0.0893445i
\(112\) 7.79761 + 8.30891i 0.0696215 + 0.0741867i
\(113\) −184.682 −1.63435 −0.817177 0.576387i \(-0.804462\pi\)
−0.817177 + 0.576387i \(0.804462\pi\)
\(114\) 22.6793 + 4.69854i 0.198941 + 0.0412153i
\(115\) 19.8501 + 19.8501i 0.172610 + 0.172610i
\(116\) 28.6558 11.3404i 0.247033 0.0977618i
\(117\) 51.4767 + 51.4767i 0.439972 + 0.439972i
\(118\) 20.1292 + 30.6491i 0.170586 + 0.259738i
\(119\) −5.52548 −0.0464326
\(120\) −25.3452 17.8219i −0.211210 0.148516i
\(121\) 274.132i 2.26555i
\(122\) 50.3340 + 76.6395i 0.412574 + 0.628192i
\(123\) 73.4063 73.4063i 0.596799 0.596799i
\(124\) 34.6173 79.9609i 0.279172 0.644846i
\(125\) −7.90569 + 7.90569i −0.0632456 + 0.0632456i
\(126\) 4.18419 + 0.866851i 0.0332078 + 0.00687977i
\(127\) 216.049i 1.70117i 0.525834 + 0.850587i \(0.323753\pi\)
−0.525834 + 0.850587i \(0.676247\pi\)
\(128\) −126.733 + 17.9648i −0.990102 + 0.140350i
\(129\) −141.343 −1.09568
\(130\) 22.0154 106.266i 0.169349 0.817430i
\(131\) 37.8658 + 37.8658i 0.289052 + 0.289052i 0.836705 0.547653i \(-0.184479\pi\)
−0.547653 + 0.836705i \(0.684479\pi\)
\(132\) −126.383 54.7146i −0.957446 0.414505i
\(133\) 3.36694 + 3.36694i 0.0253153 + 0.0253153i
\(134\) 130.815 85.9148i 0.976235 0.641155i
\(135\) −11.6190 −0.0860663
\(136\) 35.7021 50.7731i 0.262515 0.373332i
\(137\) 13.6374i 0.0995429i 0.998761 + 0.0497715i \(0.0158493\pi\)
−0.998761 + 0.0497715i \(0.984151\pi\)
\(138\) 36.3507 23.8738i 0.263411 0.172999i
\(139\) −96.9009 + 96.9009i −0.697129 + 0.697129i −0.963790 0.266661i \(-0.914079\pi\)
0.266661 + 0.963790i \(0.414079\pi\)
\(140\) −2.34396 5.92293i −0.0167426 0.0423066i
\(141\) 0.327109 0.327109i 0.00231993 0.00231993i
\(142\) 43.1183 208.127i 0.303650 1.46568i
\(143\) 482.364i 3.37318i
\(144\) −35.0009 + 32.8471i −0.243062 + 0.228105i
\(145\) −17.2279 −0.118813
\(146\) 165.435 + 34.2736i 1.13312 + 0.234751i
\(147\) −59.3913 59.3913i −0.404023 0.404023i
\(148\) −8.42773 21.2959i −0.0569441 0.143891i
\(149\) −118.690 118.690i −0.796575 0.796575i 0.185979 0.982554i \(-0.440454\pi\)
−0.982554 + 0.185979i \(0.940454\pi\)
\(150\) 9.50820 + 14.4774i 0.0633880 + 0.0965158i
\(151\) 24.8100 0.164304 0.0821522 0.996620i \(-0.473821\pi\)
0.0821522 + 0.996620i \(0.473821\pi\)
\(152\) −52.6935 + 9.18354i −0.346668 + 0.0604180i
\(153\) 23.2758i 0.152130i
\(154\) −15.5426 23.6655i −0.100926 0.153672i
\(155\) −34.4422 + 34.4422i −0.222208 + 0.222208i
\(156\) −154.284 66.7939i −0.989002 0.428166i
\(157\) −154.956 + 154.956i −0.986983 + 0.986983i −0.999916 0.0129334i \(-0.995883\pi\)
0.0129334 + 0.999916i \(0.495883\pi\)
\(158\) 35.2472 + 7.30226i 0.223083 + 0.0462168i
\(159\) 51.2601i 0.322390i
\(160\) 69.5705 + 16.7317i 0.434815 + 0.104573i
\(161\) 8.94086 0.0555333
\(162\) −3.65157 + 17.6257i −0.0225406 + 0.108801i
\(163\) −153.579 153.579i −0.942203 0.942203i 0.0562155 0.998419i \(-0.482097\pi\)
−0.998419 + 0.0562155i \(0.982097\pi\)
\(164\) −95.2488 + 220.011i −0.580785 + 1.34153i
\(165\) 54.4379 + 54.4379i 0.329927 + 0.329927i
\(166\) −0.214322 + 0.140759i −0.00129109 + 0.000847944i
\(167\) 199.626 1.19537 0.597683 0.801733i \(-0.296088\pi\)
0.597683 + 0.801733i \(0.296088\pi\)
\(168\) −9.72162 + 1.69430i −0.0578668 + 0.0100851i
\(169\) 419.855i 2.48435i
\(170\) −29.0020 + 19.0475i −0.170600 + 0.112044i
\(171\) −14.1831 + 14.1831i −0.0829421 + 0.0829421i
\(172\) 303.515 120.114i 1.76462 0.698339i
\(173\) −62.5227 + 62.5227i −0.361403 + 0.361403i −0.864329 0.502926i \(-0.832257\pi\)
0.502926 + 0.864329i \(0.332257\pi\)
\(174\) −5.41434 + 26.1344i −0.0311169 + 0.150197i
\(175\) 3.56087i 0.0203478i
\(176\) 317.887 + 10.0912i 1.80617 + 0.0573366i
\(177\) −31.7555 −0.179410
\(178\) −166.374 34.4681i −0.934684 0.193641i
\(179\) −127.410 127.410i −0.711789 0.711789i 0.255120 0.966909i \(-0.417885\pi\)
−0.966909 + 0.255120i \(0.917885\pi\)
\(180\) 24.9501 9.87385i 0.138612 0.0548547i
\(181\) 117.968 + 117.968i 0.651757 + 0.651757i 0.953416 0.301659i \(-0.0975403\pi\)
−0.301659 + 0.953416i \(0.597540\pi\)
\(182\) −18.9739 28.8901i −0.104252 0.158737i
\(183\) −79.4062 −0.433913
\(184\) −57.7701 + 82.1568i −0.313968 + 0.446505i
\(185\) 12.8031i 0.0692060i
\(186\) 41.4238 + 63.0726i 0.222708 + 0.339100i
\(187\) −109.054 + 109.054i −0.583174 + 0.583174i
\(188\) −0.424443 + 0.980402i −0.00225768 + 0.00521490i
\(189\) −2.61669 + 2.61669i −0.0138449 + 0.0138449i
\(190\) 29.2789 + 6.06579i 0.154099 + 0.0319252i
\(191\) 348.778i 1.82606i −0.407889 0.913032i \(-0.633735\pi\)
0.407889 0.913032i \(-0.366265\pi\)
\(192\) 47.2460 100.279i 0.246073 0.522285i
\(193\) 107.882 0.558976 0.279488 0.960149i \(-0.409835\pi\)
0.279488 + 0.960149i \(0.409835\pi\)
\(194\) −70.8195 + 341.838i −0.365049 + 1.76205i
\(195\) 66.4561 + 66.4561i 0.340801 + 0.340801i
\(196\) 178.006 + 77.0636i 0.908193 + 0.393182i
\(197\) 107.663 + 107.663i 0.546514 + 0.546514i 0.925431 0.378917i \(-0.123703\pi\)
−0.378917 + 0.925431i \(0.623703\pi\)
\(198\) 99.6899 65.4727i 0.503484 0.330670i
\(199\) −0.0802168 −0.000403099 −0.000201550 1.00000i \(-0.500064\pi\)
−0.000201550 1.00000i \(0.500064\pi\)
\(200\) −32.7205 23.0080i −0.163602 0.115040i
\(201\) 135.538i 0.674318i
\(202\) 36.1704 23.7554i 0.179062 0.117601i
\(203\) −3.87987 + 3.87987i −0.0191127 + 0.0191127i
\(204\) 19.7799 + 49.9817i 0.0969605 + 0.245008i
\(205\) 94.7671 94.7671i 0.462279 0.462279i
\(206\) 34.1702 164.936i 0.165875 0.800659i
\(207\) 37.6630i 0.181947i
\(208\) 388.066 + 12.3191i 1.86570 + 0.0592263i
\(209\) 132.903 0.635901
\(210\) 5.40176 + 1.11910i 0.0257227 + 0.00532905i
\(211\) 142.068 + 142.068i 0.673306 + 0.673306i 0.958477 0.285171i \(-0.0920502\pi\)
−0.285171 + 0.958477i \(0.592050\pi\)
\(212\) 43.5611 + 110.074i 0.205477 + 0.519217i
\(213\) 130.158 + 130.158i 0.611068 + 0.611068i
\(214\) 126.355 + 192.391i 0.590446 + 0.899024i
\(215\) −182.473 −0.848713
\(216\) −7.13718 40.9519i −0.0330425 0.189592i
\(217\) 15.5134i 0.0714903i
\(218\) −178.901 272.398i −0.820647 1.24953i
\(219\) −103.459 + 103.459i −0.472415 + 0.472415i
\(220\) −163.160 70.6363i −0.741635 0.321074i
\(221\) −133.129 + 133.129i −0.602395 + 0.602395i
\(222\) 19.4221 + 4.02373i 0.0874867 + 0.0181249i
\(223\) 229.927i 1.03106i 0.856871 + 0.515530i \(0.172405\pi\)
−0.856871 + 0.515530i \(0.827595\pi\)
\(224\) 19.4360 11.8998i 0.0867679 0.0531240i
\(225\) −15.0000 −0.0666667
\(226\) −74.9311 + 361.684i −0.331553 + 1.60037i
\(227\) −64.7650 64.7650i −0.285309 0.285309i 0.549913 0.835222i \(-0.314661\pi\)
−0.835222 + 0.549913i \(0.814661\pi\)
\(228\) 18.4034 42.5091i 0.0807165 0.186444i
\(229\) −21.6940 21.6940i −0.0947335 0.0947335i 0.658152 0.752885i \(-0.271339\pi\)
−0.752885 + 0.658152i \(0.771339\pi\)
\(230\) 46.9286 30.8210i 0.204037 0.134004i
\(231\) 24.5198 0.106146
\(232\) −10.5826 60.7211i −0.0456146 0.261729i
\(233\) 167.212i 0.717647i −0.933405 0.358823i \(-0.883178\pi\)
0.933405 0.358823i \(-0.116822\pi\)
\(234\) 121.698 79.9270i 0.520078 0.341568i
\(235\) 0.422297 0.422297i 0.00179701 0.00179701i
\(236\) 68.1906 26.9860i 0.288943 0.114347i
\(237\) −22.0427 + 22.0427i −0.0930073 + 0.0930073i
\(238\) −2.24185 + 10.8212i −0.00941955 + 0.0454671i
\(239\) 89.6407i 0.375066i 0.982258 + 0.187533i \(0.0600491\pi\)
−0.982258 + 0.187533i \(0.939951\pi\)
\(240\) −45.1860 + 42.4055i −0.188275 + 0.176689i
\(241\) 113.390 0.470498 0.235249 0.971935i \(-0.424410\pi\)
0.235249 + 0.971935i \(0.424410\pi\)
\(242\) −536.863 111.224i −2.21844 0.459602i
\(243\) −11.0227 11.0227i −0.0453609 0.0453609i
\(244\) 170.514 67.4798i 0.698827 0.276557i
\(245\) −76.6739 76.6739i −0.312955 0.312955i
\(246\) −113.977 173.543i −0.463320 0.705459i
\(247\) 162.244 0.656859
\(248\) −142.551 100.238i −0.574803 0.404184i
\(249\) 0.222059i 0.000891802i
\(250\) 12.2750 + 18.6902i 0.0491001 + 0.0747608i
\(251\) −263.207 + 263.207i −1.04864 + 1.04864i −0.0498801 + 0.998755i \(0.515884\pi\)
−0.998755 + 0.0498801i \(0.984116\pi\)
\(252\) 3.39530 7.84266i 0.0134734 0.0311217i
\(253\) 176.461 176.461i 0.697476 0.697476i
\(254\) 423.114 + 87.6577i 1.66580 + 0.345109i
\(255\) 30.0490i 0.117839i
\(256\) −16.2370 + 255.485i −0.0634257 + 0.997987i
\(257\) 334.232 1.30052 0.650258 0.759714i \(-0.274661\pi\)
0.650258 + 0.759714i \(0.274661\pi\)
\(258\) −57.3472 + 276.808i −0.222276 + 1.07290i
\(259\) 2.88337 + 2.88337i 0.0111327 + 0.0111327i
\(260\) −199.180 86.2306i −0.766077 0.331656i
\(261\) −16.3438 16.3438i −0.0626199 0.0626199i
\(262\) 89.5203 58.7936i 0.341681 0.224403i
\(263\) −515.255 −1.95914 −0.979572 0.201095i \(-0.935550\pi\)
−0.979572 + 0.201095i \(0.935550\pi\)
\(264\) −158.431 + 225.311i −0.600118 + 0.853449i
\(265\) 66.1765i 0.249723i
\(266\) 7.95993 5.22779i 0.0299246 0.0196533i
\(267\) 104.046 104.046i 0.389686 0.389686i
\(268\) −115.181 291.049i −0.429779 1.08600i
\(269\) −84.4996 + 84.4996i −0.314125 + 0.314125i −0.846505 0.532380i \(-0.821298\pi\)
0.532380 + 0.846505i \(0.321298\pi\)
\(270\) −4.71416 + 22.7547i −0.0174599 + 0.0842767i
\(271\) 269.730i 0.995314i −0.867374 0.497657i \(-0.834194\pi\)
0.867374 0.497657i \(-0.165806\pi\)
\(272\) −84.9494 90.5196i −0.312314 0.332793i
\(273\) 29.9330 0.109645
\(274\) 26.7076 + 5.53310i 0.0974731 + 0.0201938i
\(275\) 70.2791 + 70.2791i 0.255560 + 0.255560i
\(276\) −32.0062 80.8761i −0.115965 0.293029i
\(277\) 252.598 + 252.598i 0.911907 + 0.911907i 0.996422 0.0845154i \(-0.0269342\pi\)
−0.0845154 + 0.996422i \(0.526934\pi\)
\(278\) 150.456 + 229.088i 0.541210 + 0.824057i
\(279\) −65.3495 −0.234228
\(280\) −12.5506 + 2.18734i −0.0448234 + 0.00781192i
\(281\) 314.150i 1.11797i 0.829177 + 0.558986i \(0.188810\pi\)
−0.829177 + 0.558986i \(0.811190\pi\)
\(282\) −0.507897 0.773334i −0.00180105 0.00274232i
\(283\) 203.020 203.020i 0.717385 0.717385i −0.250684 0.968069i \(-0.580656\pi\)
0.968069 + 0.250684i \(0.0806556\pi\)
\(284\) −390.104 168.887i −1.37361 0.594672i
\(285\) −18.3103 + 18.3103i −0.0642467 + 0.0642467i
\(286\) −944.669 195.710i −3.30304 0.684300i
\(287\) 42.6848i 0.148727i
\(288\) 50.1273 + 81.8734i 0.174053 + 0.284283i
\(289\) −228.804 −0.791709
\(290\) −6.98988 + 33.7393i −0.0241030 + 0.116342i
\(291\) −213.777 213.777i −0.734629 0.734629i
\(292\) 134.244 310.084i 0.459739 1.06193i
\(293\) 324.840 + 324.840i 1.10867 + 1.10867i 0.993326 + 0.115342i \(0.0367963\pi\)
0.115342 + 0.993326i \(0.463204\pi\)
\(294\) −140.410 + 92.2159i −0.477584 + 0.313659i
\(295\) −40.9962 −0.138970
\(296\) −45.1256 + 7.86458i −0.152451 + 0.0265695i
\(297\) 103.289i 0.347773i
\(298\) −280.599 + 184.287i −0.941608 + 0.618414i
\(299\) 215.419 215.419i 0.720463 0.720463i
\(300\) 32.2104 12.7471i 0.107368 0.0424903i
\(301\) −41.0946 + 41.0946i −0.136527 + 0.136527i
\(302\) 10.0662 48.5882i 0.0333317 0.160888i
\(303\) 37.4762i 0.123684i
\(304\) −3.39421 + 106.922i −0.0111652 + 0.351716i
\(305\) −102.513 −0.336108
\(306\) −45.5837 9.44372i −0.148966 0.0308618i
\(307\) −25.2674 25.2674i −0.0823042 0.0823042i 0.664756 0.747060i \(-0.268535\pi\)
−0.747060 + 0.664756i \(0.768535\pi\)
\(308\) −52.6529 + 20.8371i −0.170951 + 0.0676528i
\(309\) 103.147 + 103.147i 0.333809 + 0.333809i
\(310\) 53.4778 + 81.4264i 0.172509 + 0.262666i
\(311\) 234.441 0.753829 0.376914 0.926248i \(-0.376985\pi\)
0.376914 + 0.926248i \(0.376985\pi\)
\(312\) −193.408 + 275.052i −0.619897 + 0.881577i
\(313\) 530.682i 1.69547i 0.530421 + 0.847735i \(0.322034\pi\)
−0.530421 + 0.847735i \(0.677966\pi\)
\(314\) 240.598 + 366.339i 0.766236 + 1.16668i
\(315\) −3.37813 + 3.37813i −0.0107242 + 0.0107242i
\(316\) 28.6017 66.0658i 0.0905117 0.209069i
\(317\) −13.0953 + 13.0953i −0.0413102 + 0.0413102i −0.727460 0.686150i \(-0.759299\pi\)
0.686150 + 0.727460i \(0.259299\pi\)
\(318\) −100.388 20.7978i −0.315687 0.0654018i
\(319\) 153.150i 0.480095i
\(320\) 60.9944 129.459i 0.190607 0.404560i
\(321\) −199.337 −0.620986
\(322\) 3.62758 17.5099i 0.0112658 0.0543786i
\(323\) −36.6804 36.6804i −0.113562 0.113562i
\(324\) 33.0369 + 14.3026i 0.101966 + 0.0441438i
\(325\) 85.7945 + 85.7945i 0.263983 + 0.263983i
\(326\) −363.083 + 238.460i −1.11375 + 0.731471i
\(327\) 282.232 0.863094
\(328\) 392.227 + 275.802i 1.19581 + 0.840859i
\(329\) 0.190210i 0.000578146i
\(330\) 128.699 84.5248i 0.389997 0.256136i
\(331\) −52.3836 + 52.3836i −0.158259 + 0.158259i −0.781795 0.623536i \(-0.785695\pi\)
0.623536 + 0.781795i \(0.285695\pi\)
\(332\) 0.188707 + 0.476841i 0.000568394 + 0.00143627i
\(333\) −12.1461 + 12.1461i −0.0364747 + 0.0364747i
\(334\) 80.9944 390.950i 0.242498 1.17051i
\(335\) 174.979i 0.522324i
\(336\) −0.626210 + 19.7264i −0.00186372 + 0.0587095i
\(337\) 148.234 0.439862 0.219931 0.975515i \(-0.429417\pi\)
0.219931 + 0.975515i \(0.429417\pi\)
\(338\) −822.251 170.348i −2.43269 0.503989i
\(339\) −226.188 226.188i −0.667222 0.667222i
\(340\) 25.5358 + 64.5260i 0.0751053 + 0.189782i
\(341\) 306.180 + 306.180i 0.897889 + 0.897889i
\(342\) 22.0219 + 33.5309i 0.0643914 + 0.0980435i
\(343\) −69.4318 −0.202425
\(344\) −112.088 643.142i −0.325837 1.86960i
\(345\) 48.6227i 0.140935i
\(346\) 97.0779 + 147.813i 0.280572 + 0.427204i
\(347\) −238.656 + 238.656i −0.687768 + 0.687768i −0.961738 0.273970i \(-0.911663\pi\)
0.273970 + 0.961738i \(0.411663\pi\)
\(348\) 48.9851 + 21.2070i 0.140762 + 0.0609397i
\(349\) 185.358 185.358i 0.531110 0.531110i −0.389792 0.920903i \(-0.627453\pi\)
0.920903 + 0.389792i \(0.127453\pi\)
\(350\) 6.97365 + 1.44475i 0.0199247 + 0.00412786i
\(351\) 126.092i 0.359235i
\(352\) 148.739 618.459i 0.422554 1.75699i
\(353\) 57.5276 0.162968 0.0814839 0.996675i \(-0.474034\pi\)
0.0814839 + 0.996675i \(0.474034\pi\)
\(354\) −12.8842 + 62.1904i −0.0363960 + 0.175679i
\(355\) 168.033 + 168.033i 0.473331 + 0.473331i
\(356\) −135.006 + 311.844i −0.379230 + 0.875966i
\(357\) −6.76730 6.76730i −0.0189560 0.0189560i
\(358\) −301.216 + 197.828i −0.841386 + 0.552591i
\(359\) 569.374 1.58600 0.793000 0.609222i \(-0.208518\pi\)
0.793000 + 0.609222i \(0.208518\pi\)
\(360\) −9.21407 52.8687i −0.0255946 0.146858i
\(361\) 316.298i 0.876171i
\(362\) 278.893 183.167i 0.770424 0.505986i
\(363\) 335.741 335.741i 0.924907 0.924907i
\(364\) −64.2770 + 25.4372i −0.176585 + 0.0698825i
\(365\) −133.565 + 133.565i −0.365931 + 0.365931i
\(366\) −32.2175 + 155.510i −0.0880259 + 0.424891i
\(367\) 128.973i 0.351425i 0.984441 + 0.175713i \(0.0562230\pi\)
−0.984441 + 0.175713i \(0.943777\pi\)
\(368\) 137.458 + 146.471i 0.373527 + 0.398020i
\(369\) 179.808 0.487284
\(370\) 25.0738 + 5.19461i 0.0677669 + 0.0140395i
\(371\) −14.9035 14.9035i −0.0401712 0.0401712i
\(372\) 140.329 55.5344i 0.377229 0.149286i
\(373\) −61.7297 61.7297i −0.165495 0.165495i 0.619501 0.784996i \(-0.287335\pi\)
−0.784996 + 0.619501i \(0.787335\pi\)
\(374\) 169.326 + 257.818i 0.452742 + 0.689354i
\(375\) −19.3649 −0.0516398
\(376\) 1.74782 + 1.22901i 0.00464846 + 0.00326865i
\(377\) 186.961i 0.495918i
\(378\) 4.06289 + 6.18623i 0.0107484 + 0.0163657i
\(379\) −213.843 + 213.843i −0.564228 + 0.564228i −0.930506 0.366277i \(-0.880632\pi\)
0.366277 + 0.930506i \(0.380632\pi\)
\(380\) 23.7586 54.8790i 0.0625228 0.144419i
\(381\) −264.605 + 264.605i −0.694502 + 0.694502i
\(382\) −683.052 141.510i −1.78809 0.370445i
\(383\) 347.292i 0.906769i −0.891315 0.453384i \(-0.850217\pi\)
0.891315 0.453384i \(-0.149783\pi\)
\(384\) −177.218 133.213i −0.461505 0.346910i
\(385\) 31.6549 0.0822206
\(386\) 43.7712 211.278i 0.113397 0.547354i
\(387\) −173.109 173.109i −0.447311 0.447311i
\(388\) 640.726 + 277.388i 1.65136 + 0.714917i
\(389\) −449.479 449.479i −1.15547 1.15547i −0.985438 0.170035i \(-0.945612\pi\)
−0.170035 0.985438i \(-0.554388\pi\)
\(390\) 157.112 103.185i 0.402851 0.264578i
\(391\) −97.4042 −0.249116
\(392\) 223.145 317.342i 0.569247 0.809545i
\(393\) 92.7520i 0.236010i
\(394\) 254.532 167.167i 0.646019 0.424282i
\(395\) −28.4570 + 28.4570i −0.0720431 + 0.0720431i
\(396\) −87.7753 221.798i −0.221655 0.560097i
\(397\) 258.874 258.874i 0.652075 0.652075i −0.301417 0.953492i \(-0.597460\pi\)
0.953492 + 0.301417i \(0.0974597\pi\)
\(398\) −0.0325464 + 0.157098i −8.17748e−5 + 0.000394717i
\(399\) 8.24729i 0.0206699i
\(400\) −58.3349 + 54.7452i −0.145837 + 0.136863i
\(401\) 525.901 1.31147 0.655737 0.754989i \(-0.272358\pi\)
0.655737 + 0.754989i \(0.272358\pi\)
\(402\) 265.439 + 54.9918i 0.660297 + 0.136796i
\(403\) 373.775 + 373.775i 0.927482 + 0.927482i
\(404\) −31.8475 80.4750i −0.0788304 0.199195i
\(405\) −14.2302 14.2302i −0.0351364 0.0351364i
\(406\) 6.02421 + 9.17258i 0.0148380 + 0.0225926i
\(407\) 113.815 0.279645
\(408\) 105.910 18.4582i 0.259583 0.0452407i
\(409\) 379.578i 0.928063i −0.885819 0.464032i \(-0.846402\pi\)
0.885819 0.464032i \(-0.153598\pi\)
\(410\) −147.143 224.043i −0.358886 0.546446i
\(411\) −16.7023 + 16.7023i −0.0406382 + 0.0406382i
\(412\) −309.149 133.839i −0.750360 0.324852i
\(413\) −9.23270 + 9.23270i −0.0223552 + 0.0223552i
\(414\) 73.7597 + 15.2810i 0.178164 + 0.0369107i
\(415\) 0.286677i 0.000690787i
\(416\) 181.576 754.995i 0.436481 1.81489i
\(417\) −237.358 −0.569203
\(418\) 53.9229 260.280i 0.129002 0.622679i
\(419\) 313.583 + 313.583i 0.748407 + 0.748407i 0.974180 0.225773i \(-0.0724907\pi\)
−0.225773 + 0.974180i \(0.572491\pi\)
\(420\) 4.38332 10.1248i 0.0104365 0.0241067i
\(421\) −419.599 419.599i −0.996672 0.996672i 0.00332199 0.999994i \(-0.498943\pi\)
−0.999994 + 0.00332199i \(0.998943\pi\)
\(422\) 335.868 220.586i 0.795896 0.522716i
\(423\) 0.801251 0.00189421
\(424\) 233.244 40.6503i 0.550105 0.0958733i
\(425\) 38.7931i 0.0912778i
\(426\) 307.711 202.093i 0.722326 0.474398i
\(427\) −23.0868 + 23.0868i −0.0540675 + 0.0540675i
\(428\) 428.048 169.397i 1.00011 0.395788i
\(429\) 590.773 590.773i 1.37709 1.37709i
\(430\) −74.0350 + 357.358i −0.172174 + 0.831065i
\(431\) 50.6765i 0.117579i −0.998270 0.0587895i \(-0.981276\pi\)
0.998270 0.0587895i \(-0.0187241\pi\)
\(432\) −83.0966 2.63788i −0.192353 0.00610621i
\(433\) −417.473 −0.964141 −0.482071 0.876132i \(-0.660115\pi\)
−0.482071 + 0.876132i \(0.660115\pi\)
\(434\) 30.3816 + 6.29425i 0.0700037 + 0.0145029i
\(435\) −21.0998 21.0998i −0.0485052 0.0485052i
\(436\) −606.054 + 239.842i −1.39003 + 0.550096i
\(437\) 59.3531 + 59.3531i 0.135820 + 0.135820i
\(438\) 160.639 + 244.592i 0.366756 + 0.558429i
\(439\) −305.299 −0.695442 −0.347721 0.937598i \(-0.613044\pi\)
−0.347721 + 0.937598i \(0.613044\pi\)
\(440\) −204.534 + 290.875i −0.464850 + 0.661079i
\(441\) 145.478i 0.329883i
\(442\) 206.708 + 314.737i 0.467664 + 0.712074i
\(443\) 211.225 211.225i 0.476806 0.476806i −0.427303 0.904109i \(-0.640536\pi\)
0.904109 + 0.427303i \(0.140536\pi\)
\(444\) 15.7602 36.4039i 0.0354960 0.0819907i
\(445\) 134.323 134.323i 0.301849 0.301849i
\(446\) 450.291 + 93.2882i 1.00962 + 0.209166i
\(447\) 290.729i 0.650400i
\(448\) −15.4189 42.8918i −0.0344172 0.0957407i
\(449\) 577.524 1.28624 0.643122 0.765764i \(-0.277639\pi\)
0.643122 + 0.765764i \(0.277639\pi\)
\(450\) −6.08596 + 29.3762i −0.0135243 + 0.0652804i
\(451\) −842.449 842.449i −1.86796 1.86796i
\(452\) 677.924 + 293.492i 1.49983 + 0.649319i
\(453\) 30.3859 + 30.3859i 0.0670770 + 0.0670770i
\(454\) −153.114 + 100.560i −0.337255 + 0.221497i
\(455\) 38.6434 0.0849305
\(456\) −75.7836 53.2887i −0.166192 0.116861i
\(457\) 226.110i 0.494771i 0.968917 + 0.247386i \(0.0795715\pi\)
−0.968917 + 0.247386i \(0.920429\pi\)
\(458\) −51.2877 + 33.6839i −0.111982 + 0.0735456i
\(459\) 28.5070 28.5070i 0.0621067 0.0621067i
\(460\) −41.3199 104.411i −0.0898258 0.226980i
\(461\) −488.700 + 488.700i −1.06009 + 1.06009i −0.0620116 + 0.998075i \(0.519752\pi\)
−0.998075 + 0.0620116i \(0.980248\pi\)
\(462\) 9.94843 48.0199i 0.0215334 0.103939i
\(463\) 578.737i 1.24997i −0.780636 0.624986i \(-0.785105\pi\)
0.780636 0.624986i \(-0.214895\pi\)
\(464\) −123.211 3.91130i −0.265540 0.00842952i
\(465\) −84.3659 −0.181432
\(466\) −327.470 67.8429i −0.702725 0.145586i
\(467\) 217.803 + 217.803i 0.466387 + 0.466387i 0.900742 0.434355i \(-0.143024\pi\)
−0.434355 + 0.900742i \(0.643024\pi\)
\(468\) −107.153 270.764i −0.228960 0.578556i
\(469\) 39.4068 + 39.4068i 0.0840229 + 0.0840229i
\(470\) −0.655693 0.998370i −0.00139509 0.00212419i
\(471\) −379.564 −0.805868
\(472\) −25.1828 144.494i −0.0533533 0.306132i
\(473\) 1622.13i 3.42945i
\(474\) 34.2254 + 52.1122i 0.0722054 + 0.109941i
\(475\) −23.6385 + 23.6385i −0.0497653 + 0.0497653i
\(476\) 20.2827 + 8.78095i 0.0426108 + 0.0184474i
\(477\) 62.7805 62.7805i 0.131615 0.131615i
\(478\) 175.553 + 36.3699i 0.367267 + 0.0760878i
\(479\) 181.127i 0.378135i −0.981964 0.189068i \(-0.939453\pi\)
0.981964 0.189068i \(-0.0605465\pi\)
\(480\) 64.7141 + 105.698i 0.134821 + 0.220204i
\(481\) 138.942 0.288861
\(482\) 46.0057 222.064i 0.0954476 0.460714i
\(483\) 10.9503 + 10.9503i 0.0226714 + 0.0226714i
\(484\) −435.643 + 1006.27i −0.900090 + 2.07908i
\(485\) −275.985 275.985i −0.569041 0.569041i
\(486\) −26.0593 + 17.1148i −0.0536199 + 0.0352156i
\(487\) −496.984 −1.02050 −0.510250 0.860026i \(-0.670447\pi\)
−0.510250 + 0.860026i \(0.670447\pi\)
\(488\) −62.9707 361.315i −0.129038 0.740400i
\(489\) 376.190i 0.769306i
\(490\) −181.268 + 119.050i −0.369935 + 0.242960i
\(491\) −199.137 + 199.137i −0.405575 + 0.405575i −0.880192 0.474617i \(-0.842586\pi\)
0.474617 + 0.880192i \(0.342586\pi\)
\(492\) −386.113 + 152.802i −0.784782 + 0.310573i
\(493\) 42.2684 42.2684i 0.0857372 0.0857372i
\(494\) 65.8274 317.741i 0.133254 0.643201i
\(495\) 133.345i 0.269384i
\(496\) −254.144 + 238.505i −0.512387 + 0.480857i
\(497\) 75.6849 0.152283
\(498\) −0.434883 0.0900960i −0.000873259 0.000180916i
\(499\) 267.538 + 267.538i 0.536149 + 0.536149i 0.922396 0.386247i \(-0.126229\pi\)
−0.386247 + 0.922396i \(0.626229\pi\)
\(500\) 41.5835 16.4564i 0.0831670 0.0329128i
\(501\) 244.491 + 244.491i 0.488006 + 0.488006i
\(502\) 408.678 + 622.260i 0.814099 + 1.23956i
\(503\) 175.799 0.349501 0.174750 0.984613i \(-0.444088\pi\)
0.174750 + 0.984613i \(0.444088\pi\)
\(504\) −13.9816 9.83142i −0.0277413 0.0195068i
\(505\) 48.3816i 0.0958051i
\(506\) −273.989 417.180i −0.541479 0.824467i
\(507\) 514.216 514.216i 1.01423 1.01423i
\(508\) 343.340 793.066i 0.675866 1.56115i
\(509\) 29.1929 29.1929i 0.0573534 0.0573534i −0.677848 0.735202i \(-0.737087\pi\)
0.735202 + 0.677848i \(0.237087\pi\)
\(510\) −58.8483 12.1918i −0.115389 0.0239055i
\(511\) 60.1600i 0.117730i
\(512\) 493.757 + 135.457i 0.964368 + 0.264564i
\(513\) −34.7414 −0.0677219
\(514\) 135.608 654.565i 0.263829 1.27347i
\(515\) 133.162 + 133.162i 0.258567 + 0.258567i
\(516\) 518.838 + 224.619i 1.00550 + 0.435308i
\(517\) −3.75408 3.75408i −0.00726128 0.00726128i
\(518\) 6.81671 4.47696i 0.0131597 0.00864279i
\(519\) −153.149 −0.295084
\(520\) −249.689 + 355.091i −0.480170 + 0.682867i
\(521\) 53.3664i 0.102431i −0.998688 0.0512154i \(-0.983691\pi\)
0.998688 0.0512154i \(-0.0163095\pi\)
\(522\) −38.6391 + 25.3768i −0.0740213 + 0.0486145i
\(523\) 302.377 302.377i 0.578159 0.578159i −0.356236 0.934396i \(-0.615940\pi\)
0.934396 + 0.356236i \(0.115940\pi\)
\(524\) −78.8212 199.172i −0.150422 0.380099i
\(525\) −4.36115 + 4.36115i −0.00830696 + 0.00830696i
\(526\) −209.055 + 1009.08i −0.397442 + 1.91841i
\(527\) 169.007i 0.320697i
\(528\) 376.971 + 401.689i 0.713960 + 0.760775i
\(529\) −371.389 −0.702058
\(530\) −129.601 26.8498i −0.244530 0.0506600i
\(531\) −38.8924 38.8924i −0.0732437 0.0732437i
\(532\) −7.00859 17.7099i −0.0131740 0.0332893i
\(533\) −1028.44 1028.44i −1.92952 1.92952i
\(534\) −161.551 245.980i −0.302529 0.460637i
\(535\) −257.342 −0.481014
\(536\) −616.727 + 107.484i −1.15061 + 0.200530i
\(537\) 312.090i 0.581173i
\(538\) 131.201 + 199.769i 0.243868 + 0.371318i
\(539\) −681.606 + 681.606i −1.26457 + 1.26457i
\(540\) 42.6504 + 18.4646i 0.0789823 + 0.0341936i
\(541\) −261.014 + 261.014i −0.482465 + 0.482465i −0.905918 0.423453i \(-0.860818\pi\)
0.423453 + 0.905918i \(0.360818\pi\)
\(542\) −528.243 109.438i −0.974618 0.201915i
\(543\) 288.962i 0.532158i
\(544\) −211.741 + 129.639i −0.389230 + 0.238308i
\(545\) 364.359 0.668550
\(546\) 12.1447 58.6212i 0.0222431 0.107365i
\(547\) −514.948 514.948i −0.941404 0.941404i 0.0569716 0.998376i \(-0.481856\pi\)
−0.998376 + 0.0569716i \(0.981856\pi\)
\(548\) 21.6722 50.0596i 0.0395478 0.0913497i
\(549\) −97.2523 97.2523i −0.177144 0.177144i
\(550\) 166.150 109.121i 0.302091 0.198402i
\(551\) −51.5124 −0.0934889
\(552\) −171.375 + 29.8675i −0.310462 + 0.0541079i
\(553\) 12.8176i 0.0231782i
\(554\) 597.178 392.205i 1.07794 0.707951i
\(555\) −15.6805 + 15.6805i −0.0282532 + 0.0282532i
\(556\) 509.693 201.708i 0.916714 0.362784i
\(557\) 450.359 450.359i 0.808544 0.808544i −0.175869 0.984414i \(-0.556274\pi\)
0.984414 + 0.175869i \(0.0562736\pi\)
\(558\) −26.5143 + 127.981i −0.0475166 + 0.229357i
\(559\) 1980.24i 3.54248i
\(560\) −0.808434 + 25.4667i −0.00144363 + 0.0454762i
\(561\) −267.126 −0.476160
\(562\) 615.236 + 127.460i 1.09473 + 0.226798i
\(563\) 102.842 + 102.842i 0.182668 + 0.182668i 0.792517 0.609849i \(-0.208770\pi\)
−0.609849 + 0.792517i \(0.708770\pi\)
\(564\) −1.72058 + 0.680908i −0.00305067 + 0.00120728i
\(565\) −292.008 292.008i −0.516828 0.516828i
\(566\) −315.225 479.968i −0.556935 0.848000i
\(567\) −6.40956 −0.0113043
\(568\) −489.027 + 695.462i −0.860963 + 1.22441i
\(569\) 236.439i 0.415535i 0.978178 + 0.207767i \(0.0666197\pi\)
−0.978178 + 0.207767i \(0.933380\pi\)
\(570\) 28.4301 + 43.2882i 0.0498774 + 0.0759442i
\(571\) 686.329 686.329i 1.20198 1.20198i 0.228413 0.973564i \(-0.426647\pi\)
0.973564 0.228413i \(-0.0733535\pi\)
\(572\) −766.562 + 1770.65i −1.34014 + 3.09554i
\(573\) 427.164 427.164i 0.745487 0.745487i
\(574\) −83.5945 17.3185i −0.145635 0.0301716i
\(575\) 62.7717i 0.109168i
\(576\) 180.680 64.9514i 0.313681 0.112763i
\(577\) −686.546 −1.18985 −0.594927 0.803780i \(-0.702819\pi\)
−0.594927 + 0.803780i \(0.702819\pi\)
\(578\) −92.8327 + 448.093i −0.160610 + 0.775247i
\(579\) 132.128 + 132.128i 0.228201 + 0.228201i
\(580\) 63.2395 + 27.3781i 0.109034 + 0.0472037i
\(581\) −0.0645621 0.0645621i −0.000111122 0.000111122i
\(582\) −505.400 + 331.928i −0.868384 + 0.570323i
\(583\) −588.288 −1.00907
\(584\) −552.806 388.715i −0.946585 0.665609i
\(585\) 162.784i 0.278263i
\(586\) 767.968 504.373i 1.31052 0.860705i
\(587\) 276.088 276.088i 0.470337 0.470337i −0.431686 0.902024i \(-0.642081\pi\)
0.902024 + 0.431686i \(0.142081\pi\)
\(588\) 123.628 + 312.395i 0.210252 + 0.531284i
\(589\) −102.984 + 102.984i −0.174846 + 0.174846i
\(590\) −16.6334 + 80.2875i −0.0281922 + 0.136080i
\(591\) 263.720i 0.446227i
\(592\) −2.90673 + 91.5654i −0.00491001 + 0.154671i
\(593\) −26.7788 −0.0451582 −0.0225791 0.999745i \(-0.507188\pi\)
−0.0225791 + 0.999745i \(0.507188\pi\)
\(594\) 202.282 + 41.9074i 0.340542 + 0.0705511i
\(595\) −8.73654 8.73654i −0.0146833 0.0146833i
\(596\) 247.063 + 624.300i 0.414535 + 1.04748i
\(597\) −0.0982451 0.0982451i −0.000164565 0.000164565i
\(598\) −334.477 509.280i −0.559326 0.851640i
\(599\) −442.840 −0.739299 −0.369650 0.929171i \(-0.620522\pi\)
−0.369650 + 0.929171i \(0.620522\pi\)
\(600\) −11.8953 68.2532i −0.0198255 0.113755i
\(601\) 418.123i 0.695712i −0.937548 0.347856i \(-0.886910\pi\)
0.937548 0.347856i \(-0.113090\pi\)
\(602\) 63.8069 + 97.1536i 0.105992 + 0.161385i
\(603\) −165.999 + 165.999i −0.275289 + 0.275289i
\(604\) −91.0716 39.4274i −0.150781 0.0652772i
\(605\) 433.440 433.440i 0.716430 0.716430i
\(606\) 73.3939 + 15.2052i 0.121112 + 0.0250911i
\(607\) 128.126i 0.211081i 0.994415 + 0.105541i \(0.0336573\pi\)
−0.994415 + 0.105541i \(0.966343\pi\)
\(608\) 208.020 + 50.0287i 0.342138 + 0.0822840i
\(609\) −9.50371 −0.0156054
\(610\) −41.5926 + 200.763i −0.0681846 + 0.329119i
\(611\) −4.58286 4.58286i −0.00750059 0.00750059i
\(612\) −36.9894 + 85.4402i −0.0604402 + 0.139608i
\(613\) −554.609 554.609i −0.904745 0.904745i 0.0910972 0.995842i \(-0.470963\pi\)
−0.995842 + 0.0910972i \(0.970963\pi\)
\(614\) −59.7358 + 39.2323i −0.0972895 + 0.0638962i
\(615\) 232.131 0.377449
\(616\) 19.4447 + 111.570i 0.0315661 + 0.181121i
\(617\) 1021.91i 1.65626i −0.560533 0.828132i \(-0.689404\pi\)
0.560533 0.828132i \(-0.310596\pi\)
\(618\) 243.854 160.154i 0.394586 0.259150i
\(619\) 362.637 362.637i 0.585844 0.585844i −0.350659 0.936503i \(-0.614043\pi\)
0.936503 + 0.350659i \(0.114043\pi\)
\(620\) 181.164 71.6946i 0.292200 0.115636i
\(621\) −46.1276 + 46.1276i −0.0742795 + 0.0742795i
\(622\) 95.1197 459.132i 0.152926 0.738154i
\(623\) 60.5015i 0.0971131i
\(624\) 460.194 + 490.370i 0.737491 + 0.785849i
\(625\) −25.0000 −0.0400000
\(626\) 1039.29 + 215.314i 1.66021 + 0.343952i
\(627\) 162.773 + 162.773i 0.259605 + 0.259605i
\(628\) 815.061 322.556i 1.29787 0.513623i
\(629\) −31.4123 31.4123i −0.0499400 0.0499400i
\(630\) 5.24517 + 7.98639i 0.00832567 + 0.0126768i
\(631\) 1040.66 1.64922 0.824609 0.565703i \(-0.191395\pi\)
0.824609 + 0.565703i \(0.191395\pi\)
\(632\) −117.779 82.8188i −0.186360 0.131042i
\(633\) 347.993i 0.549752i
\(634\) 20.3329 + 30.9592i 0.0320708 + 0.0488316i
\(635\) −341.604 + 341.604i −0.537959 + 0.537959i
\(636\) −81.4613 + 188.164i −0.128084 + 0.295855i
\(637\) −832.083 + 832.083i −1.30625 + 1.30625i
\(638\) 299.932 + 62.1377i 0.470112 + 0.0973946i
\(639\) 318.819i 0.498935i
\(640\) −228.787 171.978i −0.357480 0.268715i
\(641\) 184.247 0.287437 0.143719 0.989619i \(-0.454094\pi\)
0.143719 + 0.989619i \(0.454094\pi\)
\(642\) −80.8769 + 390.383i −0.125976 + 0.608074i
\(643\) 52.9705 + 52.9705i 0.0823803 + 0.0823803i 0.747096 0.664716i \(-0.231447\pi\)
−0.664716 + 0.747096i \(0.731447\pi\)
\(644\) −32.8198 14.2086i −0.0509624 0.0220630i
\(645\) −223.483 223.483i −0.346486 0.346486i
\(646\) −86.7177 + 56.9530i −0.134238 + 0.0881626i
\(647\) −311.336 −0.481199 −0.240600 0.970624i \(-0.577344\pi\)
−0.240600 + 0.970624i \(0.577344\pi\)
\(648\) 41.4144 58.8969i 0.0639112 0.0908903i
\(649\) 364.443i 0.561545i
\(650\) 202.830 133.212i 0.312047 0.204941i
\(651\) −18.9999 + 18.9999i −0.0291858 + 0.0291858i
\(652\) 319.689 + 807.817i 0.490320 + 1.23898i
\(653\) −177.475 + 177.475i −0.271784 + 0.271784i −0.829818 0.558034i \(-0.811556\pi\)
0.558034 + 0.829818i \(0.311556\pi\)
\(654\) 114.510 552.726i 0.175092 0.845147i
\(655\) 119.742i 0.182813i
\(656\) 699.272 656.242i 1.06596 1.00037i
\(657\) −253.422 −0.385726
\(658\) −0.372510 0.0771739i −0.000566124 0.000117286i
\(659\) 519.478 + 519.478i 0.788283 + 0.788283i 0.981213 0.192930i \(-0.0617990\pi\)
−0.192930 + 0.981213i \(0.561799\pi\)
\(660\) −113.317 286.340i −0.171693 0.433849i
\(661\) 645.148 + 645.148i 0.976018 + 0.976018i 0.999719 0.0237011i \(-0.00754501\pi\)
−0.0237011 + 0.999719i \(0.507545\pi\)
\(662\) 81.3351 + 123.842i 0.122863 + 0.187073i
\(663\) −326.099 −0.491853
\(664\) 1.01042 0.176097i 0.00152171 0.000265207i
\(665\) 10.6472i 0.0160108i
\(666\) 18.8590 + 28.7151i 0.0283169 + 0.0431158i
\(667\) −68.3952 + 68.3952i −0.102542 + 0.102542i
\(668\) −732.781 317.241i −1.09698 0.474912i
\(669\) −281.601 + 281.601i −0.420929 + 0.420929i
\(670\) 342.681 + 70.9942i 0.511464 + 0.105961i
\(671\) 911.307i 1.35813i
\(672\) 38.3783 + 9.22997i 0.0571106 + 0.0137351i
\(673\) 589.163 0.875428 0.437714 0.899114i \(-0.355788\pi\)
0.437714 + 0.899114i \(0.355788\pi\)
\(674\) 60.1429 290.303i 0.0892327 0.430716i
\(675\) −18.3712 18.3712i −0.0272166 0.0272166i
\(676\) −667.224 + 1541.19i −0.987018 + 2.27987i
\(677\) −599.890 599.890i −0.886101 0.886101i 0.108045 0.994146i \(-0.465541\pi\)
−0.994146 + 0.108045i \(0.965541\pi\)
\(678\) −534.741 + 351.199i −0.788704 + 0.517992i
\(679\) −124.309 −0.183076
\(680\) 136.729 23.8295i 0.201073 0.0350433i
\(681\) 158.641i 0.232953i
\(682\) 723.854 475.401i 1.06137 0.697068i
\(683\) 30.3287 30.3287i 0.0444051 0.0444051i −0.684556 0.728961i \(-0.740004\pi\)
0.728961 + 0.684556i \(0.240004\pi\)
\(684\) 74.6023 29.5234i 0.109068 0.0431629i
\(685\) −21.5626 + 21.5626i −0.0314782 + 0.0314782i
\(686\) −28.1706 + 135.976i −0.0410650 + 0.198216i
\(687\) 53.1392i 0.0773496i
\(688\) −1305.02 41.4274i −1.89682 0.0602143i
\(689\) −718.163 −1.04233
\(690\) 95.2234 + 19.7277i 0.138005 + 0.0285909i
\(691\) −166.006 166.006i −0.240240 0.240240i 0.576709 0.816949i \(-0.304337\pi\)
−0.816949 + 0.576709i \(0.804337\pi\)
\(692\) 328.866 130.147i 0.475239 0.188073i
\(693\) 30.0305 + 30.0305i 0.0433341 + 0.0433341i
\(694\) 370.556 + 564.216i 0.533943 + 0.812991i
\(695\) −306.428 −0.440903
\(696\) 61.4069 87.3288i 0.0882282 0.125472i
\(697\) 465.020i 0.667174i
\(698\) −287.802 438.212i −0.412323 0.627811i
\(699\) 204.792 204.792i 0.292978 0.292978i
\(700\) 5.65884 13.0711i 0.00808406 0.0186730i
\(701\) −944.622 + 944.622i −1.34753 + 1.34753i −0.459204 + 0.888331i \(0.651865\pi\)
−0.888331 + 0.459204i \(0.848135\pi\)
\(702\) 246.940 + 51.1592i 0.351766 + 0.0728764i
\(703\) 38.2820i 0.0544552i
\(704\) −1150.85 542.220i −1.63473 0.770199i
\(705\) 1.03441 0.00146725
\(706\) 23.3407 112.663i 0.0330605 0.159579i
\(707\) 10.8960 + 10.8960i 0.0154115 + 0.0154115i
\(708\) 116.567 + 50.4651i 0.164643 + 0.0712783i
\(709\) −13.8364 13.8364i −0.0195154 0.0195154i 0.697282 0.716797i \(-0.254393\pi\)
−0.716797 + 0.697282i \(0.754393\pi\)
\(710\) 397.253 260.901i 0.559512 0.367467i
\(711\) −53.9934 −0.0759401
\(712\) 555.943 + 390.922i 0.780819 + 0.549047i
\(713\) 273.473i 0.383553i
\(714\) −15.9989 + 10.5075i −0.0224074 + 0.0147163i
\(715\) 762.685 762.685i 1.06669 1.06669i
\(716\) 265.216 + 670.170i 0.370413 + 0.935992i
\(717\) −109.787 + 109.787i −0.153120 + 0.153120i
\(718\) 231.012 1115.07i 0.321744 1.55302i
\(719\) 910.813i 1.26678i −0.773834 0.633389i \(-0.781663\pi\)
0.773834 0.633389i \(-0.218337\pi\)
\(720\) −107.277 3.40549i −0.148996 0.00472985i
\(721\) 59.9786 0.0831880
\(722\) −619.442 128.332i −0.857952 0.177745i
\(723\) 138.874 + 138.874i 0.192080 + 0.192080i
\(724\) −245.561 620.505i −0.339173 0.857051i
\(725\) −27.2397 27.2397i −0.0375720 0.0375720i
\(726\) −521.300 793.741i −0.718044 1.09331i
\(727\) 533.203 0.733429 0.366715 0.930333i \(-0.380483\pi\)
0.366715 + 0.930333i \(0.380483\pi\)
\(728\) 23.7375 + 136.202i 0.0326065 + 0.187090i
\(729\) 27.0000i 0.0370370i
\(730\) 207.384 + 315.767i 0.284088 + 0.432557i
\(731\) 447.696 447.696i 0.612443 0.612443i
\(732\) 291.481 + 126.190i 0.398199 + 0.172391i
\(733\) 402.506 402.506i 0.549122 0.549122i −0.377065 0.926187i \(-0.623067\pi\)
0.926187 + 0.377065i \(0.123067\pi\)
\(734\) 252.583 + 52.3283i 0.344118 + 0.0712920i
\(735\) 187.812i 0.255526i
\(736\) 342.622 209.772i 0.465519 0.285016i
\(737\) 1555.50 2.11059
\(738\) 72.9535 352.138i 0.0988530 0.477152i
\(739\) 445.842 + 445.842i 0.603304 + 0.603304i 0.941188 0.337884i \(-0.109711\pi\)
−0.337884 + 0.941188i \(0.609711\pi\)
\(740\) 20.3464 46.9972i 0.0274951 0.0635097i
\(741\) 198.708 + 198.708i 0.268162 + 0.268162i
\(742\) −35.2341 + 23.1405i −0.0474853 + 0.0311866i
\(743\) −807.539 −1.08686 −0.543431 0.839454i \(-0.682875\pi\)
−0.543431 + 0.839454i \(0.682875\pi\)
\(744\) −51.8235 297.354i −0.0696552 0.399670i
\(745\) 375.330i 0.503798i
\(746\) −145.938 + 95.8467i −0.195627 + 0.128481i
\(747\) 0.271965 0.271965i 0.000364077 0.000364077i
\(748\) 573.616 227.005i 0.766866 0.303483i
\(749\) −57.9558 + 57.9558i −0.0773775 + 0.0773775i
\(750\) −7.85694 + 37.9245i −0.0104759 + 0.0505660i
\(751\) 415.595i 0.553388i −0.960958 0.276694i \(-0.910761\pi\)
0.960958 0.276694i \(-0.0892389\pi\)
\(752\) 3.11606 2.92431i 0.00414370 0.00388871i
\(753\) −644.724 −0.856207
\(754\) 366.147 + 75.8558i 0.485606 + 0.100605i
\(755\) 39.2280 + 39.2280i 0.0519576 + 0.0519576i
\(756\) 13.7636 5.44688i 0.0182059 0.00720487i
\(757\) −714.992 714.992i −0.944508 0.944508i 0.0540314 0.998539i \(-0.482793\pi\)
−0.998539 + 0.0540314i \(0.982793\pi\)
\(758\) 332.030 + 505.554i 0.438034 + 0.666958i
\(759\) 432.240 0.569487
\(760\) −97.8362 68.7954i −0.128732 0.0905202i
\(761\) 704.857i 0.926225i −0.886300 0.463112i \(-0.846733\pi\)
0.886300 0.463112i \(-0.153267\pi\)
\(762\) 410.848 + 625.565i 0.539170 + 0.820951i
\(763\) 82.0570 82.0570i 0.107545 0.107545i
\(764\) −554.270 + 1280.28i −0.725484 + 1.67576i
\(765\) 36.8023 36.8023i 0.0481076 0.0481076i
\(766\) −680.142 140.907i −0.887914 0.183952i
\(767\) 444.900i 0.580053i
\(768\) −332.790 + 293.017i −0.433320 + 0.381533i
\(769\) 995.779 1.29490 0.647451 0.762107i \(-0.275835\pi\)
0.647451 + 0.762107i \(0.275835\pi\)
\(770\) 12.8434 61.9935i 0.0166797 0.0805110i
\(771\) 409.349 + 409.349i 0.530933 + 0.530933i
\(772\) −396.011 171.444i −0.512968 0.222078i
\(773\) −620.353 620.353i −0.802526 0.802526i 0.180964 0.983490i \(-0.442078\pi\)
−0.983490 + 0.180964i \(0.942078\pi\)
\(774\) −409.255 + 268.784i −0.528754 + 0.347266i
\(775\) −108.916 −0.140537
\(776\) 803.202 1142.26i 1.03505 1.47199i
\(777\) 7.06279i 0.00908982i
\(778\) −1062.63 + 697.898i −1.36585 + 0.897042i
\(779\) 283.359 283.359i 0.363747 0.363747i
\(780\) −138.334 349.555i −0.177352 0.448148i
\(781\) 1493.76 1493.76i 1.91262 1.91262i
\(782\) −39.5199 + 190.758i −0.0505369 + 0.243936i
\(783\) 40.0340i 0.0511290i
\(784\) −530.950 565.765i −0.677232 0.721639i
\(785\) −490.015 −0.624223
\(786\) 181.647 + 37.6323i 0.231103 + 0.0478782i
\(787\) −183.869 183.869i −0.233633 0.233633i 0.580574 0.814207i \(-0.302828\pi\)
−0.814207 + 0.580574i \(0.802828\pi\)
\(788\) −224.111 566.303i −0.284405 0.718658i
\(789\) −631.056 631.056i −0.799817 0.799817i
\(790\) 44.1848 + 67.2765i 0.0559301 + 0.0851602i
\(791\) −131.525 −0.166277
\(792\) −469.986 + 81.9101i −0.593416 + 0.103422i
\(793\) 1112.49i 1.40289i
\(794\) −401.949 612.015i −0.506233 0.770799i
\(795\) 81.0493 81.0493i 0.101949 0.101949i
\(796\) 0.294457 + 0.127479i 0.000369921 + 0.000160149i
\(797\) −257.392 + 257.392i −0.322951 + 0.322951i −0.849898 0.526947i \(-0.823337\pi\)
0.526947 + 0.849898i \(0.323337\pi\)
\(798\) 16.1516 + 3.34617i 0.0202401 + 0.00419320i
\(799\) 2.07220i 0.00259349i
\(800\) 83.5455 + 136.456i 0.104432 + 0.170570i
\(801\) 254.860 0.318177
\(802\) 213.374 1029.93i 0.266052 1.28420i
\(803\) 1187.35 + 1187.35i 1.47864 + 1.47864i
\(804\) 215.394 497.528i 0.267902 0.618816i
\(805\) 14.1367 + 14.1367i 0.0175612 + 0.0175612i
\(806\) 883.658 580.354i 1.09635 0.720043i
\(807\) −206.981 −0.256482
\(808\) −170.525 + 29.7194i −0.211045 + 0.0367814i
\(809\) 206.640i 0.255427i 0.991811 + 0.127713i \(0.0407638\pi\)
−0.991811 + 0.127713i \(0.959236\pi\)
\(810\) −33.6424 + 22.0951i −0.0415338 + 0.0272779i
\(811\) −304.478 + 304.478i −0.375436 + 0.375436i −0.869452 0.494017i \(-0.835528\pi\)
0.494017 + 0.869452i \(0.335528\pi\)
\(812\) 20.4079 8.07631i 0.0251329 0.00994619i
\(813\) 330.351 330.351i 0.406335 0.406335i
\(814\) 46.1784 222.898i 0.0567302 0.273830i
\(815\) 485.660i 0.595902i
\(816\) 6.82211 214.905i 0.00836043 0.263364i
\(817\) −545.606 −0.667816
\(818\) −743.370 154.006i −0.908766 0.188272i
\(819\) 36.6603 + 36.6603i 0.0447623 + 0.0447623i
\(820\) −498.469 + 197.266i −0.607890 + 0.240569i
\(821\) −60.6328 60.6328i −0.0738523 0.0738523i 0.669216 0.743068i \(-0.266630\pi\)
−0.743068 + 0.669216i \(0.766630\pi\)
\(822\) 25.9334 + 39.4867i 0.0315491 + 0.0480373i
\(823\) −961.097 −1.16780 −0.583899 0.811827i \(-0.698473\pi\)
−0.583899 + 0.811827i \(0.698473\pi\)
\(824\) −387.543 + 551.138i −0.470319 + 0.668857i
\(825\) 172.148i 0.208664i
\(826\) 14.3355 + 21.8274i 0.0173553 + 0.0264255i
\(827\) −204.781 + 204.781i −0.247619 + 0.247619i −0.819993 0.572374i \(-0.806023\pi\)
0.572374 + 0.819993i \(0.306023\pi\)
\(828\) 59.8531 138.252i 0.0722864 0.166971i
\(829\) −541.386 + 541.386i −0.653059 + 0.653059i −0.953728 0.300669i \(-0.902790\pi\)
0.300669 + 0.953728i \(0.402790\pi\)
\(830\) −0.561431 0.116313i −0.000676423 0.000140137i
\(831\) 618.737i 0.744569i
\(832\) −1404.92 661.926i −1.68861 0.795584i
\(833\) 376.237 0.451665
\(834\) −96.3033 + 464.845i −0.115472 + 0.557368i
\(835\) 315.637 + 315.637i 0.378008 + 0.378008i
\(836\) −487.857 211.207i −0.583561 0.252640i
\(837\) −80.0365 80.0365i −0.0956230 0.0956230i
\(838\) 741.354 486.894i 0.884671 0.581020i
\(839\) 1641.31 1.95627 0.978135 0.207969i \(-0.0666854\pi\)
0.978135 + 0.207969i \(0.0666854\pi\)
\(840\) −18.0502 12.6923i −0.0214883 0.0151099i
\(841\) 781.640i 0.929417i
\(842\) −991.993 + 651.504i −1.17814 + 0.773758i
\(843\) −384.754 + 384.754i −0.456411 + 0.456411i
\(844\) −295.727 747.267i −0.350387 0.885388i
\(845\) 663.850 663.850i 0.785621 0.785621i
\(846\) 0.325092 1.56918i 0.000384270 0.00185482i
\(847\) 195.229i 0.230495i
\(848\) 15.0242 473.282i 0.0177173 0.558116i
\(849\) 497.295 0.585742
\(850\) −75.9729 15.7395i −0.0893798 0.0185171i
\(851\) 50.8287 + 50.8287i 0.0597282 + 0.0597282i
\(852\) −270.935 684.621i −0.317998 0.803546i
\(853\) 738.398 + 738.398i 0.865648 + 0.865648i 0.991987 0.126339i \(-0.0403228\pi\)
−0.126339 + 0.991987i \(0.540323\pi\)
\(854\) 35.8465 + 54.5806i 0.0419748 + 0.0639117i
\(855\) −44.8509 −0.0524572
\(856\) −158.078 907.024i −0.184670 1.05961i
\(857\) 1546.29i 1.80431i −0.431416 0.902153i \(-0.641986\pi\)
0.431416 0.902153i \(-0.358014\pi\)
\(858\) −917.284 1396.67i −1.06910 1.62782i
\(859\) −50.1020 + 50.1020i −0.0583260 + 0.0583260i −0.735668 0.677342i \(-0.763132\pi\)
0.677342 + 0.735668i \(0.263132\pi\)
\(860\) 669.817 + 289.982i 0.778857 + 0.337188i
\(861\) 52.2780 52.2780i 0.0607177 0.0607177i
\(862\) −99.2456 20.5610i −0.115134 0.0238527i
\(863\) 566.091i 0.655957i 0.944685 + 0.327978i \(0.106367\pi\)
−0.944685 + 0.327978i \(0.893633\pi\)
\(864\) −38.8809 + 161.667i −0.0450010 + 0.187115i
\(865\) −197.714 −0.228571
\(866\) −169.382 + 817.585i −0.195591 + 0.944094i
\(867\) −280.226 280.226i −0.323214 0.323214i
\(868\) 24.6535 56.9460i 0.0284026 0.0656060i
\(869\) 252.974 + 252.974i 0.291109 + 0.291109i
\(870\) −49.8829 + 32.7612i −0.0573366 + 0.0376566i
\(871\) 1898.91 2.18015
\(872\) 223.815 + 1284.21i 0.256669 + 1.47272i
\(873\) 523.645i 0.599822i
\(874\) 140.319 92.1566i 0.160548 0.105442i
\(875\) −5.63022 + 5.63022i −0.00643454 + 0.00643454i
\(876\) 544.188 215.359i 0.621219 0.245844i
\(877\) −441.097 + 441.097i −0.502961 + 0.502961i −0.912357 0.409396i \(-0.865740\pi\)
0.409396 + 0.912357i \(0.365740\pi\)
\(878\) −123.869 + 597.902i −0.141081 + 0.680981i
\(879\) 795.691i 0.905223i
\(880\) 486.667 + 518.578i 0.553031 + 0.589294i
\(881\) −318.150 −0.361124 −0.180562 0.983564i \(-0.557792\pi\)
−0.180562 + 0.983564i \(0.557792\pi\)
\(882\) −284.907 59.0250i −0.323024 0.0669218i
\(883\) 614.668 + 614.668i 0.696113 + 0.696113i 0.963570 0.267457i \(-0.0861833\pi\)
−0.267457 + 0.963570i \(0.586183\pi\)
\(884\) 700.252 277.121i 0.792140 0.313485i
\(885\) −50.2099 50.2099i −0.0567343 0.0567343i
\(886\) −327.965 499.366i −0.370164 0.563619i
\(887\) −867.460 −0.977971 −0.488985 0.872292i \(-0.662633\pi\)
−0.488985 + 0.872292i \(0.662633\pi\)
\(888\) −64.8994 45.6352i −0.0730849 0.0513910i
\(889\) 153.864i 0.173076i
\(890\) −208.561 317.559i −0.234338 0.356808i
\(891\) −126.502 + 126.502i −0.141978 + 0.141978i
\(892\) 365.394 844.006i 0.409634 0.946195i
\(893\) 1.26269 1.26269i 0.00141399 0.00141399i
\(894\) −569.368 117.958i −0.636876 0.131944i
\(895\) 402.906i 0.450175i
\(896\) −90.2559 + 12.7940i −0.100732 + 0.0142791i
\(897\) 527.666 0.588256
\(898\) 234.319 1131.03i 0.260934 1.25950i
\(899\) −118.673 118.673i −0.132006 0.132006i
\(900\) 55.0615 + 23.8376i 0.0611794 + 0.0264863i
\(901\) 162.363 + 162.363i 0.180203 + 0.180203i
\(902\) −1991.67 + 1308.06i −2.20806 + 1.45017i
\(903\) −100.661 −0.111474
\(904\) 849.833 1208.58i 0.940081 1.33692i
\(905\) 373.048i 0.412208i
\(906\) 71.8366 47.1796i 0.0792898 0.0520747i
\(907\) 585.460 585.460i 0.645491 0.645491i −0.306409 0.951900i \(-0.599127\pi\)
0.951900 + 0.306409i \(0.0991275\pi\)
\(908\) 134.814 + 340.660i 0.148474 + 0.375177i
\(909\) −45.8988 + 45.8988i −0.0504937 + 0.0504937i
\(910\) 15.6788 75.6797i 0.0172294 0.0831645i
\(911\) 314.928i 0.345695i −0.984949 0.172847i \(-0.944703\pi\)
0.984949 0.172847i \(-0.0552967\pi\)
\(912\) −135.109 + 126.795i −0.148146 + 0.139029i
\(913\) −2.54846 −0.00279131
\(914\) 442.818 + 91.7399i 0.484483 + 0.100372i
\(915\) −125.552 125.552i −0.137215 0.137215i
\(916\) 45.1580 + 114.109i 0.0492991 + 0.124573i
\(917\) 26.9670 + 26.9670i 0.0294079 + 0.0294079i
\(918\) −44.2623 67.3946i −0.0482160 0.0734146i
\(919\) −1662.53 −1.80906 −0.904532 0.426405i \(-0.859780\pi\)
−0.904532 + 0.426405i \(0.859780\pi\)
\(920\) −221.244 + 38.5588i −0.240482 + 0.0419118i
\(921\) 61.8922i 0.0672011i
\(922\) 758.796 + 1155.36i 0.822990 + 1.25310i
\(923\) 1823.53 1823.53i 1.97566 1.97566i
\(924\) −90.0065 38.9663i −0.0974096 0.0421713i
\(925\) −20.2435 + 20.2435i −0.0218848 + 0.0218848i
\(926\) −1133.41 234.811i −1.22398 0.253576i
\(927\) 252.657i 0.272554i
\(928\) −57.6502 + 239.710i −0.0621231 + 0.258309i
\(929\) −416.151 −0.447955 −0.223978 0.974594i \(-0.571904\pi\)
−0.223978 + 0.974594i \(0.571904\pi\)
\(930\) −34.2298 + 165.223i −0.0368062 + 0.177659i
\(931\) −229.259 229.259i −0.246251 0.246251i
\(932\) −265.729 + 613.795i −0.285117 + 0.658578i
\(933\) 287.130 + 287.130i 0.307749 + 0.307749i
\(934\) 514.917 338.178i 0.551303 0.362075i
\(935\) −344.858 −0.368832
\(936\) −573.744 + 99.9932i −0.612974 + 0.106830i
\(937\) 251.707i 0.268631i −0.990939 0.134315i \(-0.957116\pi\)
0.990939 0.134315i \(-0.0428835\pi\)
\(938\) 93.1632 61.1862i 0.0993212 0.0652305i
\(939\) −649.950 + 649.950i −0.692172 + 0.692172i
\(940\) −2.22125 + 0.879048i −0.00236304 + 0.000935158i
\(941\) 366.216 366.216i 0.389177 0.389177i −0.485217 0.874394i \(-0.661259\pi\)
0.874394 + 0.485217i \(0.161259\pi\)
\(942\) −154.001 + 743.343i −0.163483 + 0.789112i
\(943\) 752.456i 0.797939i
\(944\) −293.197 9.30748i −0.310590 0.00985962i
\(945\) −8.27470 −0.00875630
\(946\) 3176.80 + 658.147i 3.35814 + 0.695715i
\(947\) −990.634 990.634i −1.04608 1.04608i −0.998886 0.0471906i \(-0.984973\pi\)
−0.0471906 0.998886i \(-0.515027\pi\)
\(948\) 115.943 45.8839i 0.122303 0.0484008i
\(949\) 1449.48 + 1449.48i 1.52738 + 1.52738i
\(950\) 36.7031 + 55.8848i 0.0386348 + 0.0588261i
\(951\) −32.0769 −0.0337296
\(952\) 25.4261 36.1593i 0.0267080 0.0379824i
\(953\) 757.944i 0.795324i 0.917532 + 0.397662i \(0.130178\pi\)
−0.917532 + 0.397662i \(0.869822\pi\)
\(954\) −97.4783 148.422i −0.102178 0.155579i
\(955\) 551.466 551.466i 0.577452 0.577452i
\(956\) 142.455 329.050i 0.149011 0.344194i
\(957\) −187.570 + 187.570i −0.195998 + 0.195998i
\(958\) −354.721 73.4886i −0.370272 0.0767105i
\(959\) 9.71218i 0.0101274i
\(960\) 233.257 83.8520i 0.242976 0.0873458i
\(961\) 486.493 0.506237
\(962\) 56.3731 272.107i 0.0585999 0.282855i
\(963\) −244.136 244.136i −0.253516 0.253516i
\(964\) −416.228 180.197i −0.431772 0.186926i
\(965\) 170.577 + 170.577i 0.176764 + 0.176764i
\(966\) 25.8880 17.0023i 0.0267992 0.0176007i
\(967\) 1492.41 1.54334 0.771670 0.636024i \(-0.219422\pi\)
0.771670 + 0.636024i \(0.219422\pi\)
\(968\) 1793.95 + 1261.45i 1.85325 + 1.30315i
\(969\) 89.8482i 0.0927226i
\(970\) −652.468 + 428.517i −0.672648 + 0.441770i
\(971\) −770.021 + 770.021i −0.793018 + 0.793018i −0.981984 0.188965i \(-0.939487\pi\)
0.188965 + 0.981984i \(0.439487\pi\)
\(972\) 22.9448 + 57.9788i 0.0236057 + 0.0596489i
\(973\) −69.0102 + 69.0102i −0.0709252 + 0.0709252i
\(974\) −201.641 + 973.300i −0.207024 + 0.999281i
\(975\) 210.153i 0.215541i
\(976\) −733.153 23.2738i −0.751182 0.0238461i
\(977\) 607.944 0.622256 0.311128 0.950368i \(-0.399293\pi\)
0.311128 + 0.950368i \(0.399293\pi\)
\(978\) −736.736 152.632i −0.753309 0.156065i
\(979\) −1194.09 1194.09i −1.21970 1.21970i
\(980\) 159.604 + 403.300i 0.162861 + 0.411531i
\(981\) 345.662 + 345.662i 0.352357 + 0.352357i
\(982\) 309.197 + 470.789i 0.314865 + 0.479419i
\(983\) 699.083 0.711173 0.355587 0.934643i \(-0.384281\pi\)
0.355587 + 0.934643i \(0.384281\pi\)
\(984\) 142.591 + 818.165i 0.144910 + 0.831468i
\(985\) 340.461i 0.345646i
\(986\) −65.6295 99.9286i −0.0665613 0.101348i
\(987\) 0.232959 0.232959i 0.000236027 0.000236027i
\(988\) −595.560 257.835i −0.602794 0.260966i
\(989\) −724.424 + 724.424i −0.732482 + 0.732482i
\(990\) 261.145 + 54.1022i 0.263783 + 0.0546487i
\(991\) 968.275i 0.977069i −0.872545 0.488534i \(-0.837532\pi\)
0.872545 0.488534i \(-0.162468\pi\)
\(992\) 363.977 + 594.487i 0.366912 + 0.599282i
\(993\) −128.313 −0.129218
\(994\) 30.7077 148.222i 0.0308930 0.149117i
\(995\) −0.126834 0.126834i −0.000127471 0.000127471i
\(996\) −0.352890 + 0.815126i −0.000354308 + 0.000818399i
\(997\) 871.924 + 871.924i 0.874548 + 0.874548i 0.992964 0.118416i \(-0.0377817\pi\)
−0.118416 + 0.992964i \(0.537782\pi\)
\(998\) 632.499 415.402i 0.633766 0.416235i
\(999\) −29.7517 −0.0297815
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 240.3.bn.a.91.19 64
4.3 odd 2 960.3.bn.a.271.9 64
16.3 odd 4 inner 240.3.bn.a.211.19 yes 64
16.13 even 4 960.3.bn.a.751.9 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
240.3.bn.a.91.19 64 1.1 even 1 trivial
240.3.bn.a.211.19 yes 64 16.3 odd 4 inner
960.3.bn.a.271.9 64 4.3 odd 2
960.3.bn.a.751.9 64 16.13 even 4