Properties

Label 605.2.e.a.362.5
Level $605$
Weight $2$
Character 605.362
Analytic conductor $4.831$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [605,2,Mod(362,605)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(605, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("605.362");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 605 = 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 605.e (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: \(4.83094932229\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 67x^{16} + 1315x^{12} + 9193x^{8} + 16040x^{4} + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 362.5
Root \(-0.125683 + 0.125683i\) of defining polynomial
Character \(\chi\) \(=\) 605.362
Dual form 605.2.e.a.483.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.125683 + 0.125683i) q^{2} +(1.65771 - 1.65771i) q^{3} +1.96841i q^{4} +(2.04266 + 0.909702i) q^{5} +0.416692i q^{6} +(3.15683 - 3.15683i) q^{7} +(-0.498761 - 0.498761i) q^{8} -2.49602i q^{9} +O(q^{10})\) \(q+(-0.125683 + 0.125683i) q^{2} +(1.65771 - 1.65771i) q^{3} +1.96841i q^{4} +(2.04266 + 0.909702i) q^{5} +0.416692i q^{6} +(3.15683 - 3.15683i) q^{7} +(-0.498761 - 0.498761i) q^{8} -2.49602i q^{9} +(-0.371061 + 0.142393i) q^{10} +(3.26305 + 3.26305i) q^{12} +(-1.97128 - 1.97128i) q^{13} +0.793518i q^{14} +(4.89416 - 1.87811i) q^{15} -3.81144 q^{16} +(-2.20398 + 2.20398i) q^{17} +(0.313707 + 0.313707i) q^{18} +1.24889 q^{19} +(-1.79067 + 4.02078i) q^{20} -10.4662i q^{21} +(1.27860 - 1.27860i) q^{23} -1.65360 q^{24} +(3.34488 + 3.71642i) q^{25} +0.495512 q^{26} +(0.835455 + 0.835455i) q^{27} +(6.21392 + 6.21392i) q^{28} -7.47247 q^{29} +(-0.379066 + 0.851158i) q^{30} -5.13483 q^{31} +(1.47655 - 1.47655i) q^{32} -0.554006i q^{34} +(9.32008 - 3.57654i) q^{35} +4.91318 q^{36} +(-1.75014 - 1.75014i) q^{37} +(-0.156964 + 0.156964i) q^{38} -6.53563 q^{39} +(-0.565073 - 1.47252i) q^{40} +10.8036i q^{41} +(1.31542 + 1.31542i) q^{42} +(4.31967 + 4.31967i) q^{43} +(2.27064 - 5.09851i) q^{45} +0.321395i q^{46} +(2.65013 + 2.65013i) q^{47} +(-6.31828 + 6.31828i) q^{48} -12.9311i q^{49} +(-0.887484 - 0.0466955i) q^{50} +7.30714i q^{51} +(3.88028 - 3.88028i) q^{52} +(0.315424 - 0.315424i) q^{53} -0.210005 q^{54} -3.14900 q^{56} +(2.07030 - 2.07030i) q^{57} +(0.939161 - 0.939161i) q^{58} -11.3112i q^{59} +(3.69689 + 9.63370i) q^{60} -1.38079i q^{61} +(0.645360 - 0.645360i) q^{62} +(-7.87950 - 7.87950i) q^{63} -7.25173i q^{64} +(-2.23337 - 5.81993i) q^{65} +(0.721404 + 0.721404i) q^{67} +(-4.33834 - 4.33834i) q^{68} -4.23909i q^{69} +(-0.721865 + 1.62088i) q^{70} +3.52812 q^{71} +(-1.24492 + 1.24492i) q^{72} +(-6.58997 - 6.58997i) q^{73} +0.439926 q^{74} +(11.7056 + 0.615897i) q^{75} +2.45832i q^{76} +(0.821417 - 0.821417i) q^{78} -6.02093 q^{79} +(-7.78547 - 3.46728i) q^{80} +10.2579 q^{81} +(-1.35783 - 1.35783i) q^{82} +(3.45287 + 3.45287i) q^{83} +20.6018 q^{84} +(-6.50695 + 2.49701i) q^{85} -1.08582 q^{86} +(-12.3872 + 12.3872i) q^{87} +2.57764i q^{89} +(0.355415 + 0.926175i) q^{90} -12.4460 q^{91} +(2.51680 + 2.51680i) q^{92} +(-8.51207 + 8.51207i) q^{93} -0.666152 q^{94} +(2.55105 + 1.13612i) q^{95} -4.89541i q^{96} +(-4.62327 - 4.62327i) q^{97} +(1.62522 + 1.62522i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 4 q^{3} + 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 4 q^{3} + 4 q^{5} - 16 q^{12} + 16 q^{15} + 12 q^{16} + 16 q^{20} + 12 q^{23} + 16 q^{25} + 56 q^{26} - 20 q^{27} - 16 q^{31} - 20 q^{36} - 72 q^{37} - 32 q^{38} - 32 q^{42} - 28 q^{45} + 16 q^{47} - 104 q^{48} - 52 q^{53} - 32 q^{56} + 12 q^{58} + 112 q^{60} + 28 q^{67} + 104 q^{70} + 24 q^{71} + 64 q^{75} + 104 q^{78} + 44 q^{80} + 100 q^{81} - 124 q^{82} + 128 q^{86} - 16 q^{92} - 132 q^{93} + 32 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.125683 + 0.125683i −0.0888712 + 0.0888712i −0.750145 0.661274i \(-0.770016\pi\)
0.661274 + 0.750145i \(0.270016\pi\)
\(3\) 1.65771 1.65771i 0.957081 0.957081i −0.0420355 0.999116i \(-0.513384\pi\)
0.999116 + 0.0420355i \(0.0133843\pi\)
\(4\) 1.96841i 0.984204i
\(5\) 2.04266 + 0.909702i 0.913503 + 0.406831i
\(6\) 0.416692i 0.170114i
\(7\) 3.15683 3.15683i 1.19317 1.19317i 0.216996 0.976173i \(-0.430374\pi\)
0.976173 0.216996i \(-0.0696258\pi\)
\(8\) −0.498761 0.498761i −0.176339 0.176339i
\(9\) 2.49602i 0.832007i
\(10\) −0.371061 + 0.142393i −0.117340 + 0.0450285i
\(11\) 0 0
\(12\) 3.26305 + 3.26305i 0.941962 + 0.941962i
\(13\) −1.97128 1.97128i −0.546735 0.546735i 0.378760 0.925495i \(-0.376351\pi\)
−0.925495 + 0.378760i \(0.876351\pi\)
\(14\) 0.793518i 0.212077i
\(15\) 4.89416 1.87811i 1.26367 0.484926i
\(16\) −3.81144 −0.952861
\(17\) −2.20398 + 2.20398i −0.534545 + 0.534545i −0.921921 0.387377i \(-0.873381\pi\)
0.387377 + 0.921921i \(0.373381\pi\)
\(18\) 0.313707 + 0.313707i 0.0739414 + 0.0739414i
\(19\) 1.24889 0.286514 0.143257 0.989685i \(-0.454242\pi\)
0.143257 + 0.989685i \(0.454242\pi\)
\(20\) −1.79067 + 4.02078i −0.400405 + 0.899073i
\(21\) 10.4662i 2.28392i
\(22\) 0 0
\(23\) 1.27860 1.27860i 0.266606 0.266606i −0.561125 0.827731i \(-0.689631\pi\)
0.827731 + 0.561125i \(0.189631\pi\)
\(24\) −1.65360 −0.337540
\(25\) 3.34488 + 3.71642i 0.668977 + 0.743283i
\(26\) 0.495512 0.0971780
\(27\) 0.835455 + 0.835455i 0.160783 + 0.160783i
\(28\) 6.21392 + 6.21392i 1.17432 + 1.17432i
\(29\) −7.47247 −1.38760 −0.693801 0.720167i \(-0.744065\pi\)
−0.693801 + 0.720167i \(0.744065\pi\)
\(30\) −0.379066 + 0.851158i −0.0692076 + 0.155400i
\(31\) −5.13483 −0.922243 −0.461121 0.887337i \(-0.652553\pi\)
−0.461121 + 0.887337i \(0.652553\pi\)
\(32\) 1.47655 1.47655i 0.261020 0.261020i
\(33\) 0 0
\(34\) 0.554006i 0.0950112i
\(35\) 9.32008 3.57654i 1.57538 0.604545i
\(36\) 4.91318 0.818864
\(37\) −1.75014 1.75014i −0.287722 0.287722i 0.548457 0.836179i \(-0.315215\pi\)
−0.836179 + 0.548457i \(0.815215\pi\)
\(38\) −0.156964 + 0.156964i −0.0254629 + 0.0254629i
\(39\) −6.53563 −1.04654
\(40\) −0.565073 1.47252i −0.0893458 0.232826i
\(41\) 10.8036i 1.68724i 0.536938 + 0.843621i \(0.319581\pi\)
−0.536938 + 0.843621i \(0.680419\pi\)
\(42\) 1.31542 + 1.31542i 0.202974 + 0.202974i
\(43\) 4.31967 + 4.31967i 0.658744 + 0.658744i 0.955083 0.296339i \(-0.0957657\pi\)
−0.296339 + 0.955083i \(0.595766\pi\)
\(44\) 0 0
\(45\) 2.27064 5.09851i 0.338486 0.760041i
\(46\) 0.321395i 0.0473871i
\(47\) 2.65013 + 2.65013i 0.386561 + 0.386561i 0.873459 0.486898i \(-0.161872\pi\)
−0.486898 + 0.873459i \(0.661872\pi\)
\(48\) −6.31828 + 6.31828i −0.911965 + 0.911965i
\(49\) 12.9311i 1.84730i
\(50\) −0.887484 0.0466955i −0.125509 0.00660374i
\(51\) 7.30714i 1.02320i
\(52\) 3.88028 3.88028i 0.538099 0.538099i
\(53\) 0.315424 0.315424i 0.0433269 0.0433269i −0.685111 0.728438i \(-0.740247\pi\)
0.728438 + 0.685111i \(0.240247\pi\)
\(54\) −0.210005 −0.0285780
\(55\) 0 0
\(56\) −3.14900 −0.420803
\(57\) 2.07030 2.07030i 0.274217 0.274217i
\(58\) 0.939161 0.939161i 0.123318 0.123318i
\(59\) 11.3112i 1.47259i −0.676662 0.736294i \(-0.736574\pi\)
0.676662 0.736294i \(-0.263426\pi\)
\(60\) 3.69689 + 9.63370i 0.477266 + 1.24371i
\(61\) 1.38079i 0.176793i −0.996085 0.0883963i \(-0.971826\pi\)
0.996085 0.0883963i \(-0.0281742\pi\)
\(62\) 0.645360 0.645360i 0.0819608 0.0819608i
\(63\) −7.87950 7.87950i −0.992724 0.992724i
\(64\) 7.25173i 0.906467i
\(65\) −2.23337 5.81993i −0.277015 0.721873i
\(66\) 0 0
\(67\) 0.721404 + 0.721404i 0.0881335 + 0.0881335i 0.749799 0.661666i \(-0.230150\pi\)
−0.661666 + 0.749799i \(0.730150\pi\)
\(68\) −4.33834 4.33834i −0.526101 0.526101i
\(69\) 4.23909i 0.510326i
\(70\) −0.721865 + 1.62088i −0.0862794 + 0.193733i
\(71\) 3.52812 0.418711 0.209355 0.977840i \(-0.432863\pi\)
0.209355 + 0.977840i \(0.432863\pi\)
\(72\) −1.24492 + 1.24492i −0.146715 + 0.146715i
\(73\) −6.58997 6.58997i −0.771298 0.771298i 0.207036 0.978333i \(-0.433618\pi\)
−0.978333 + 0.207036i \(0.933618\pi\)
\(74\) 0.439926 0.0511404
\(75\) 11.7056 + 0.615897i 1.35165 + 0.0711177i
\(76\) 2.45832i 0.281989i
\(77\) 0 0
\(78\) 0.821417 0.821417i 0.0930072 0.0930072i
\(79\) −6.02093 −0.677407 −0.338704 0.940893i \(-0.609988\pi\)
−0.338704 + 0.940893i \(0.609988\pi\)
\(80\) −7.78547 3.46728i −0.870442 0.387654i
\(81\) 10.2579 1.13977
\(82\) −1.35783 1.35783i −0.149947 0.149947i
\(83\) 3.45287 + 3.45287i 0.379002 + 0.379002i 0.870742 0.491740i \(-0.163639\pi\)
−0.491740 + 0.870742i \(0.663639\pi\)
\(84\) 20.6018 2.24784
\(85\) −6.50695 + 2.49701i −0.705778 + 0.270839i
\(86\) −1.08582 −0.117087
\(87\) −12.3872 + 12.3872i −1.32805 + 1.32805i
\(88\) 0 0
\(89\) 2.57764i 0.273229i 0.990624 + 0.136615i \(0.0436222\pi\)
−0.990624 + 0.136615i \(0.956378\pi\)
\(90\) 0.355415 + 0.926175i 0.0374640 + 0.0976274i
\(91\) −12.4460 −1.30469
\(92\) 2.51680 + 2.51680i 0.262394 + 0.262394i
\(93\) −8.51207 + 8.51207i −0.882660 + 0.882660i
\(94\) −0.666152 −0.0687083
\(95\) 2.55105 + 1.13612i 0.261732 + 0.116563i
\(96\) 4.89541i 0.499635i
\(97\) −4.62327 4.62327i −0.469422 0.469422i 0.432306 0.901727i \(-0.357700\pi\)
−0.901727 + 0.432306i \(0.857700\pi\)
\(98\) 1.62522 + 1.62522i 0.164172 + 0.164172i
\(99\) 0 0
\(100\) −7.31542 + 6.58409i −0.731542 + 0.658409i
\(101\) 12.1812i 1.21208i 0.795435 + 0.606039i \(0.207242\pi\)
−0.795435 + 0.606039i \(0.792758\pi\)
\(102\) −0.918382 0.918382i −0.0909334 0.0909334i
\(103\) −9.08246 + 9.08246i −0.894921 + 0.894921i −0.994981 0.100060i \(-0.968096\pi\)
0.100060 + 0.994981i \(0.468096\pi\)
\(104\) 1.96640i 0.192821i
\(105\) 9.52115 21.3789i 0.929169 2.08637i
\(106\) 0.0792869i 0.00770102i
\(107\) 7.07404 7.07404i 0.683873 0.683873i −0.276998 0.960871i \(-0.589339\pi\)
0.960871 + 0.276998i \(0.0893394\pi\)
\(108\) −1.64452 + 1.64452i −0.158244 + 0.158244i
\(109\) 8.79661 0.842562 0.421281 0.906930i \(-0.361581\pi\)
0.421281 + 0.906930i \(0.361581\pi\)
\(110\) 0 0
\(111\) −5.80247 −0.550746
\(112\) −12.0321 + 12.0321i −1.13692 + 1.13692i
\(113\) −6.95236 + 6.95236i −0.654023 + 0.654023i −0.953959 0.299936i \(-0.903035\pi\)
0.299936 + 0.953959i \(0.403035\pi\)
\(114\) 0.520401i 0.0487400i
\(115\) 3.77487 1.44859i 0.352009 0.135082i
\(116\) 14.7089i 1.36568i
\(117\) −4.92036 + 4.92036i −0.454887 + 0.454887i
\(118\) 1.42162 + 1.42162i 0.130871 + 0.130871i
\(119\) 13.9152i 1.27560i
\(120\) −3.37774 1.50429i −0.308344 0.137322i
\(121\) 0 0
\(122\) 0.173542 + 0.173542i 0.0157118 + 0.0157118i
\(123\) 17.9093 + 17.9093i 1.61483 + 1.61483i
\(124\) 10.1074i 0.907675i
\(125\) 3.45161 + 10.6342i 0.308721 + 0.951153i
\(126\) 1.98064 0.176449
\(127\) −5.46777 + 5.46777i −0.485186 + 0.485186i −0.906783 0.421597i \(-0.861470\pi\)
0.421597 + 0.906783i \(0.361470\pi\)
\(128\) 3.86453 + 3.86453i 0.341579 + 0.341579i
\(129\) 14.3216 1.26094
\(130\) 1.01216 + 0.450769i 0.0887724 + 0.0395350i
\(131\) 19.6002i 1.71248i 0.516578 + 0.856240i \(0.327206\pi\)
−0.516578 + 0.856240i \(0.672794\pi\)
\(132\) 0 0
\(133\) 3.94252 3.94252i 0.341860 0.341860i
\(134\) −0.181336 −0.0156651
\(135\) 0.946531 + 2.46656i 0.0814644 + 0.212288i
\(136\) 2.19852 0.188522
\(137\) −5.79590 5.79590i −0.495177 0.495177i 0.414756 0.909933i \(-0.363867\pi\)
−0.909933 + 0.414756i \(0.863867\pi\)
\(138\) 0.532781 + 0.532781i 0.0453533 + 0.0453533i
\(139\) −12.4159 −1.05310 −0.526550 0.850144i \(-0.676515\pi\)
−0.526550 + 0.850144i \(0.676515\pi\)
\(140\) 7.04008 + 18.3457i 0.594995 + 1.55050i
\(141\) 8.78631 0.739941
\(142\) −0.443424 + 0.443424i −0.0372113 + 0.0372113i
\(143\) 0 0
\(144\) 9.51344i 0.792787i
\(145\) −15.2637 6.79772i −1.26758 0.564520i
\(146\) 1.65649 0.137092
\(147\) −21.4361 21.4361i −1.76802 1.76802i
\(148\) 3.44500 3.44500i 0.283177 0.283177i
\(149\) −1.49550 −0.122516 −0.0612581 0.998122i \(-0.519511\pi\)
−0.0612581 + 0.998122i \(0.519511\pi\)
\(150\) −1.54860 + 1.39379i −0.126443 + 0.113802i
\(151\) 5.93157i 0.482704i −0.970438 0.241352i \(-0.922409\pi\)
0.970438 0.241352i \(-0.0775909\pi\)
\(152\) −0.622896 0.622896i −0.0505235 0.0505235i
\(153\) 5.50119 + 5.50119i 0.444745 + 0.444745i
\(154\) 0 0
\(155\) −10.4887 4.67117i −0.842472 0.375197i
\(156\) 12.8648i 1.03001i
\(157\) −8.26778 8.26778i −0.659841 0.659841i 0.295501 0.955342i \(-0.404513\pi\)
−0.955342 + 0.295501i \(0.904513\pi\)
\(158\) 0.756727 0.756727i 0.0602020 0.0602020i
\(159\) 1.04577i 0.0829346i
\(160\) 4.35932 1.67287i 0.344634 0.132252i
\(161\) 8.07261i 0.636211i
\(162\) −1.28925 + 1.28925i −0.101293 + 0.101293i
\(163\) −4.84865 + 4.84865i −0.379776 + 0.379776i −0.871021 0.491245i \(-0.836542\pi\)
0.491245 + 0.871021i \(0.336542\pi\)
\(164\) −21.2659 −1.66059
\(165\) 0 0
\(166\) −0.867933 −0.0673647
\(167\) 8.83234 8.83234i 0.683467 0.683467i −0.277312 0.960780i \(-0.589444\pi\)
0.960780 + 0.277312i \(0.0894437\pi\)
\(168\) −5.22014 + 5.22014i −0.402743 + 0.402743i
\(169\) 5.22810i 0.402162i
\(170\) 0.503980 1.13164i 0.0386535 0.0867931i
\(171\) 3.11725i 0.238382i
\(172\) −8.50288 + 8.50288i −0.648339 + 0.648339i
\(173\) −16.7036 16.7036i −1.26995 1.26995i −0.946114 0.323834i \(-0.895028\pi\)
−0.323834 0.946114i \(-0.604972\pi\)
\(174\) 3.11372i 0.236050i
\(175\) 22.2913 + 1.17287i 1.68506 + 0.0886606i
\(176\) 0 0
\(177\) −18.7506 18.7506i −1.40938 1.40938i
\(178\) −0.323965 0.323965i −0.0242822 0.0242822i
\(179\) 19.3159i 1.44374i 0.692029 + 0.721870i \(0.256717\pi\)
−0.692029 + 0.721870i \(0.743283\pi\)
\(180\) 10.0359 + 4.46954i 0.748035 + 0.333140i
\(181\) 13.4648 1.00083 0.500417 0.865785i \(-0.333180\pi\)
0.500417 + 0.865785i \(0.333180\pi\)
\(182\) 1.56425 1.56425i 0.115950 0.115950i
\(183\) −2.28896 2.28896i −0.169205 0.169205i
\(184\) −1.27543 −0.0940257
\(185\) −1.98283 5.16705i −0.145781 0.379889i
\(186\) 2.13964i 0.156886i
\(187\) 0 0
\(188\) −5.21654 + 5.21654i −0.380455 + 0.380455i
\(189\) 5.27477 0.383683
\(190\) −0.463413 + 0.177833i −0.0336195 + 0.0129013i
\(191\) −13.3527 −0.966168 −0.483084 0.875574i \(-0.660484\pi\)
−0.483084 + 0.875574i \(0.660484\pi\)
\(192\) −12.0213 12.0213i −0.867562 0.867562i
\(193\) 2.28334 + 2.28334i 0.164358 + 0.164358i 0.784494 0.620136i \(-0.212923\pi\)
−0.620136 + 0.784494i \(0.712923\pi\)
\(194\) 1.16213 0.0834361
\(195\) −13.3500 5.94548i −0.956017 0.425765i
\(196\) 25.4537 1.81812
\(197\) 3.61891 3.61891i 0.257837 0.257837i −0.566337 0.824174i \(-0.691640\pi\)
0.824174 + 0.566337i \(0.191640\pi\)
\(198\) 0 0
\(199\) 7.26740i 0.515173i −0.966255 0.257586i \(-0.917073\pi\)
0.966255 0.257586i \(-0.0829272\pi\)
\(200\) 0.185307 3.52190i 0.0131032 0.249036i
\(201\) 2.39176 0.168702
\(202\) −1.53097 1.53097i −0.107719 0.107719i
\(203\) −23.5893 + 23.5893i −1.65564 + 1.65564i
\(204\) −14.3834 −1.00704
\(205\) −9.82808 + 22.0681i −0.686423 + 1.54130i
\(206\) 2.28302i 0.159065i
\(207\) −3.19140 3.19140i −0.221818 0.221818i
\(208\) 7.51343 + 7.51343i 0.520962 + 0.520962i
\(209\) 0 0
\(210\) 1.49031 + 3.88360i 0.102841 + 0.267994i
\(211\) 14.3789i 0.989886i −0.868925 0.494943i \(-0.835189\pi\)
0.868925 0.494943i \(-0.164811\pi\)
\(212\) 0.620884 + 0.620884i 0.0426425 + 0.0426425i
\(213\) 5.84861 5.84861i 0.400740 0.400740i
\(214\) 1.77817i 0.121553i
\(215\) 4.89399 + 12.7532i 0.333767 + 0.869763i
\(216\) 0.833384i 0.0567046i
\(217\) −16.2098 + 16.2098i −1.10039 + 1.10039i
\(218\) −1.10558 + 1.10558i −0.0748795 + 0.0748795i
\(219\) −21.8485 −1.47639
\(220\) 0 0
\(221\) 8.68934 0.584508
\(222\) 0.729271 0.729271i 0.0489455 0.0489455i
\(223\) 7.68134 7.68134i 0.514381 0.514381i −0.401485 0.915866i \(-0.631506\pi\)
0.915866 + 0.401485i \(0.131506\pi\)
\(224\) 9.32245i 0.622883i
\(225\) 9.27625 8.34889i 0.618417 0.556593i
\(226\) 1.74758i 0.116248i
\(227\) 10.9700 10.9700i 0.728106 0.728106i −0.242137 0.970242i \(-0.577848\pi\)
0.970242 + 0.242137i \(0.0778482\pi\)
\(228\) 4.07519 + 4.07519i 0.269886 + 0.269886i
\(229\) 20.6756i 1.36628i −0.730286 0.683142i \(-0.760613\pi\)
0.730286 0.683142i \(-0.239387\pi\)
\(230\) −0.292374 + 0.656500i −0.0192786 + 0.0432883i
\(231\) 0 0
\(232\) 3.72697 + 3.72697i 0.244688 + 0.244688i
\(233\) 13.0750 + 13.0750i 0.856571 + 0.856571i 0.990932 0.134362i \(-0.0428984\pi\)
−0.134362 + 0.990932i \(0.542898\pi\)
\(234\) 1.23681i 0.0808527i
\(235\) 3.00247 + 7.82413i 0.195860 + 0.510390i
\(236\) 22.2650 1.44933
\(237\) −9.98096 + 9.98096i −0.648333 + 0.648333i
\(238\) −1.74890 1.74890i −0.113364 0.113364i
\(239\) 16.6078 1.07427 0.537134 0.843497i \(-0.319507\pi\)
0.537134 + 0.843497i \(0.319507\pi\)
\(240\) −18.6538 + 7.15831i −1.20410 + 0.462067i
\(241\) 13.5493i 0.872789i −0.899755 0.436395i \(-0.856255\pi\)
0.899755 0.436395i \(-0.143745\pi\)
\(242\) 0 0
\(243\) 14.4984 14.4984i 0.930070 0.930070i
\(244\) 2.71796 0.174000
\(245\) 11.7635 26.4138i 0.751540 1.68752i
\(246\) −4.50178 −0.287023
\(247\) −2.46191 2.46191i −0.156647 0.156647i
\(248\) 2.56105 + 2.56105i 0.162627 + 0.162627i
\(249\) 11.4477 0.725471
\(250\) −1.77035 0.902730i −0.111966 0.0570936i
\(251\) −6.59073 −0.416003 −0.208002 0.978128i \(-0.566696\pi\)
−0.208002 + 0.978128i \(0.566696\pi\)
\(252\) 15.5101 15.5101i 0.977043 0.977043i
\(253\) 0 0
\(254\) 1.37441i 0.0862381i
\(255\) −6.64732 + 14.9260i −0.416272 + 0.934701i
\(256\) 13.5321 0.845753
\(257\) 11.1970 + 11.1970i 0.698451 + 0.698451i 0.964076 0.265626i \(-0.0855785\pi\)
−0.265626 + 0.964076i \(0.585578\pi\)
\(258\) −1.79997 + 1.79997i −0.112061 + 0.112061i
\(259\) −11.0498 −0.686601
\(260\) 11.4560 4.39618i 0.710470 0.272640i
\(261\) 18.6514i 1.15449i
\(262\) −2.46341 2.46341i −0.152190 0.152190i
\(263\) −21.0043 21.0043i −1.29518 1.29518i −0.931541 0.363637i \(-0.881535\pi\)
−0.363637 0.931541i \(-0.618465\pi\)
\(264\) 0 0
\(265\) 0.931246 0.357361i 0.0572060 0.0219525i
\(266\) 0.991014i 0.0607630i
\(267\) 4.27298 + 4.27298i 0.261502 + 0.261502i
\(268\) −1.42002 + 1.42002i −0.0867413 + 0.0867413i
\(269\) 4.29801i 0.262054i 0.991379 + 0.131027i \(0.0418275\pi\)
−0.991379 + 0.131027i \(0.958173\pi\)
\(270\) −0.428967 0.191042i −0.0261061 0.0116264i
\(271\) 20.8238i 1.26495i −0.774579 0.632477i \(-0.782038\pi\)
0.774579 0.632477i \(-0.217962\pi\)
\(272\) 8.40036 8.40036i 0.509347 0.509347i
\(273\) −20.6319 + 20.6319i −1.24870 + 1.24870i
\(274\) 1.45689 0.0880140
\(275\) 0 0
\(276\) 8.34425 0.502265
\(277\) −6.87337 + 6.87337i −0.412981 + 0.412981i −0.882776 0.469795i \(-0.844328\pi\)
0.469795 + 0.882776i \(0.344328\pi\)
\(278\) 1.56046 1.56046i 0.0935903 0.0935903i
\(279\) 12.8166i 0.767312i
\(280\) −6.43233 2.86466i −0.384405 0.171196i
\(281\) 0.853512i 0.0509163i 0.999676 + 0.0254581i \(0.00810445\pi\)
−0.999676 + 0.0254581i \(0.991896\pi\)
\(282\) −1.10429 + 1.10429i −0.0657594 + 0.0657594i
\(283\) 6.87072 + 6.87072i 0.408422 + 0.408422i 0.881188 0.472766i \(-0.156744\pi\)
−0.472766 + 0.881188i \(0.656744\pi\)
\(284\) 6.94478i 0.412097i
\(285\) 6.11225 2.34555i 0.362059 0.138938i
\(286\) 0 0
\(287\) 34.1052 + 34.1052i 2.01316 + 2.01316i
\(288\) −3.68551 3.68551i −0.217171 0.217171i
\(289\) 7.28491i 0.428524i
\(290\) 2.77274 1.06403i 0.162821 0.0624817i
\(291\) −15.3281 −0.898549
\(292\) 12.9717 12.9717i 0.759114 0.759114i
\(293\) 18.8718 + 18.8718i 1.10250 + 1.10250i 0.994108 + 0.108395i \(0.0345710\pi\)
0.108395 + 0.994108i \(0.465429\pi\)
\(294\) 5.38829 0.314251
\(295\) 10.2898 23.1048i 0.599095 1.34521i
\(296\) 1.74581i 0.101473i
\(297\) 0 0
\(298\) 0.187959 0.187959i 0.0108882 0.0108882i
\(299\) −5.04094 −0.291525
\(300\) −1.21234 + 23.0414i −0.0699943 + 1.33030i
\(301\) 27.2729 1.57199
\(302\) 0.745497 + 0.745497i 0.0428985 + 0.0428985i
\(303\) 20.1930 + 20.1930i 1.16006 + 1.16006i
\(304\) −4.76006 −0.273008
\(305\) 1.25611 2.82049i 0.0719247 0.161501i
\(306\) −1.38281 −0.0790500
\(307\) 4.08294 4.08294i 0.233026 0.233026i −0.580929 0.813954i \(-0.697311\pi\)
0.813954 + 0.580929i \(0.197311\pi\)
\(308\) 0 0
\(309\) 30.1122i 1.71302i
\(310\) 1.90533 0.731163i 0.108216 0.0415272i
\(311\) −0.766768 −0.0434794 −0.0217397 0.999764i \(-0.506921\pi\)
−0.0217397 + 0.999764i \(0.506921\pi\)
\(312\) 3.25972 + 3.25972i 0.184545 + 0.184545i
\(313\) 18.9656 18.9656i 1.07200 1.07200i 0.0748001 0.997199i \(-0.476168\pi\)
0.997199 0.0748001i \(-0.0238319\pi\)
\(314\) 2.07824 0.117282
\(315\) −8.92710 23.2631i −0.502985 1.31073i
\(316\) 11.8516i 0.666707i
\(317\) 13.4304 + 13.4304i 0.754329 + 0.754329i 0.975284 0.220955i \(-0.0709174\pi\)
−0.220955 + 0.975284i \(0.570917\pi\)
\(318\) 0.131435 + 0.131435i 0.00737050 + 0.00737050i
\(319\) 0 0
\(320\) 6.59692 14.8128i 0.368779 0.828060i
\(321\) 23.4534i 1.30904i
\(322\) 1.01459 + 1.01459i 0.0565408 + 0.0565408i
\(323\) −2.75253 + 2.75253i −0.153155 + 0.153155i
\(324\) 20.1918i 1.12177i
\(325\) 0.732399 13.9198i 0.0406262 0.772132i
\(326\) 1.21878i 0.0675022i
\(327\) 14.5822 14.5822i 0.806400 0.806400i
\(328\) 5.38842 5.38842i 0.297526 0.297526i
\(329\) 16.7320 0.922465
\(330\) 0 0
\(331\) −0.0204452 −0.00112377 −0.000561885 1.00000i \(-0.500179\pi\)
−0.000561885 1.00000i \(0.500179\pi\)
\(332\) −6.79666 + 6.79666i −0.373015 + 0.373015i
\(333\) −4.36839 + 4.36839i −0.239386 + 0.239386i
\(334\) 2.22015i 0.121481i
\(335\) 0.817317 + 2.12984i 0.0446548 + 0.116366i
\(336\) 39.8914i 2.17625i
\(337\) 11.1779 11.1779i 0.608899 0.608899i −0.333760 0.942658i \(-0.608317\pi\)
0.942658 + 0.333760i \(0.108317\pi\)
\(338\) 0.657083 + 0.657083i 0.0357406 + 0.0357406i
\(339\) 23.0500i 1.25191i
\(340\) −4.91513 12.8083i −0.266561 0.694629i
\(341\) 0 0
\(342\) 0.391784 + 0.391784i 0.0211853 + 0.0211853i
\(343\) −18.7235 18.7235i −1.01097 1.01097i
\(344\) 4.30897i 0.232324i
\(345\) 3.85631 8.65900i 0.207617 0.466185i
\(346\) 4.19870 0.225724
\(347\) −15.4800 + 15.4800i −0.831008 + 0.831008i −0.987655 0.156647i \(-0.949932\pi\)
0.156647 + 0.987655i \(0.449932\pi\)
\(348\) −24.3831 24.3831i −1.30707 1.30707i
\(349\) −27.9856 −1.49804 −0.749018 0.662549i \(-0.769474\pi\)
−0.749018 + 0.662549i \(0.769474\pi\)
\(350\) −2.94904 + 2.65422i −0.157633 + 0.141874i
\(351\) 3.29383i 0.175812i
\(352\) 0 0
\(353\) −9.36952 + 9.36952i −0.498689 + 0.498689i −0.911030 0.412340i \(-0.864711\pi\)
0.412340 + 0.911030i \(0.364711\pi\)
\(354\) 4.71327 0.250507
\(355\) 7.20673 + 3.20954i 0.382494 + 0.170345i
\(356\) −5.07384 −0.268913
\(357\) 23.0674 + 23.0674i 1.22086 + 1.22086i
\(358\) −2.42768 2.42768i −0.128307 0.128307i
\(359\) −1.69815 −0.0896252 −0.0448126 0.998995i \(-0.514269\pi\)
−0.0448126 + 0.998995i \(0.514269\pi\)
\(360\) −3.67544 + 1.41043i −0.193713 + 0.0743363i
\(361\) −17.4403 −0.917910
\(362\) −1.69230 + 1.69230i −0.0889453 + 0.0889453i
\(363\) 0 0
\(364\) 24.4988i 1.28408i
\(365\) −7.46613 19.4559i −0.390795 1.01837i
\(366\) 0.575366 0.0300748
\(367\) 15.1500 + 15.1500i 0.790825 + 0.790825i 0.981628 0.190803i \(-0.0611092\pi\)
−0.190803 + 0.981628i \(0.561109\pi\)
\(368\) −4.87330 + 4.87330i −0.254038 + 0.254038i
\(369\) 26.9661 1.40380
\(370\) 0.898617 + 0.400202i 0.0467169 + 0.0208055i
\(371\) 1.99148i 0.103393i
\(372\) −16.7552 16.7552i −0.868718 0.868718i
\(373\) −6.29327 6.29327i −0.325853 0.325853i 0.525154 0.851007i \(-0.324008\pi\)
−0.851007 + 0.525154i \(0.824008\pi\)
\(374\) 0 0
\(375\) 23.3502 + 11.9067i 1.20580 + 0.614858i
\(376\) 2.64356i 0.136331i
\(377\) 14.7303 + 14.7303i 0.758651 + 0.758651i
\(378\) −0.662948 + 0.662948i −0.0340984 + 0.0340984i
\(379\) 32.3401i 1.66120i −0.556871 0.830599i \(-0.687998\pi\)
0.556871 0.830599i \(-0.312002\pi\)
\(380\) −2.23634 + 5.02150i −0.114722 + 0.257597i
\(381\) 18.1280i 0.928724i
\(382\) 1.67821 1.67821i 0.0858645 0.0858645i
\(383\) 16.2896 16.2896i 0.832358 0.832358i −0.155481 0.987839i \(-0.549693\pi\)
0.987839 + 0.155481i \(0.0496926\pi\)
\(384\) 12.8125 0.653838
\(385\) 0 0
\(386\) −0.573952 −0.0292134
\(387\) 10.7820 10.7820i 0.548079 0.548079i
\(388\) 9.10047 9.10047i 0.462007 0.462007i
\(389\) 14.3543i 0.727792i −0.931440 0.363896i \(-0.881446\pi\)
0.931440 0.363896i \(-0.118554\pi\)
\(390\) 2.42512 0.930627i 0.122801 0.0471241i
\(391\) 5.63601i 0.285025i
\(392\) −6.44953 + 6.44953i −0.325750 + 0.325750i
\(393\) 32.4915 + 32.4915i 1.63898 + 1.63898i
\(394\) 0.909671i 0.0458286i
\(395\) −12.2987 5.47725i −0.618814 0.275590i
\(396\) 0 0
\(397\) −8.05942 8.05942i −0.404491 0.404491i 0.475321 0.879812i \(-0.342332\pi\)
−0.879812 + 0.475321i \(0.842332\pi\)
\(398\) 0.913388 + 0.913388i 0.0457840 + 0.0457840i
\(399\) 13.0711i 0.654375i
\(400\) −12.7488 14.1649i −0.637442 0.708246i
\(401\) −22.3236 −1.11479 −0.557395 0.830248i \(-0.688199\pi\)
−0.557395 + 0.830248i \(0.688199\pi\)
\(402\) −0.300603 + 0.300603i −0.0149927 + 0.0149927i
\(403\) 10.1222 + 10.1222i 0.504222 + 0.504222i
\(404\) −23.9776 −1.19293
\(405\) 20.9534 + 9.33168i 1.04119 + 0.463695i
\(406\) 5.92954i 0.294278i
\(407\) 0 0
\(408\) 3.64452 3.64452i 0.180430 0.180430i
\(409\) 2.81860 0.139371 0.0696855 0.997569i \(-0.477800\pi\)
0.0696855 + 0.997569i \(0.477800\pi\)
\(410\) −1.53836 4.00880i −0.0759741 0.197981i
\(411\) −19.2159 −0.947849
\(412\) −17.8780 17.8780i −0.880785 0.880785i
\(413\) −35.7074 35.7074i −1.75704 1.75704i
\(414\) 0.802209 0.0394264
\(415\) 3.91194 + 10.1941i 0.192030 + 0.500409i
\(416\) −5.82141 −0.285418
\(417\) −20.5819 + 20.5819i −1.00790 + 1.00790i
\(418\) 0 0
\(419\) 24.7639i 1.20980i −0.796303 0.604898i \(-0.793214\pi\)
0.796303 0.604898i \(-0.206786\pi\)
\(420\) 42.0824 + 18.7415i 2.05341 + 0.914491i
\(421\) 28.6112 1.39443 0.697213 0.716864i \(-0.254423\pi\)
0.697213 + 0.716864i \(0.254423\pi\)
\(422\) 1.80718 + 1.80718i 0.0879724 + 0.0879724i
\(423\) 6.61478 6.61478i 0.321621 0.321621i
\(424\) −0.314643 −0.0152804
\(425\) −15.5630 0.818856i −0.754916 0.0397203i
\(426\) 1.47014i 0.0712285i
\(427\) −4.35893 4.35893i −0.210943 0.210943i
\(428\) 13.9246 + 13.9246i 0.673070 + 0.673070i
\(429\) 0 0
\(430\) −2.21795 0.987771i −0.106959 0.0476346i
\(431\) 33.8869i 1.63228i 0.577857 + 0.816138i \(0.303889\pi\)
−0.577857 + 0.816138i \(0.696111\pi\)
\(432\) −3.18429 3.18429i −0.153204 0.153204i
\(433\) −1.88692 + 1.88692i −0.0906795 + 0.0906795i −0.750991 0.660312i \(-0.770424\pi\)
0.660312 + 0.750991i \(0.270424\pi\)
\(434\) 4.07458i 0.195586i
\(435\) −36.5714 + 14.0341i −1.75347 + 0.672884i
\(436\) 17.3153i 0.829253i
\(437\) 1.59682 1.59682i 0.0763864 0.0763864i
\(438\) 2.74599 2.74599i 0.131208 0.131208i
\(439\) 25.1409 1.19991 0.599956 0.800033i \(-0.295185\pi\)
0.599956 + 0.800033i \(0.295185\pi\)
\(440\) 0 0
\(441\) −32.2763 −1.53697
\(442\) −1.09210 + 1.09210i −0.0519460 + 0.0519460i
\(443\) 8.85103 8.85103i 0.420525 0.420525i −0.464859 0.885385i \(-0.653895\pi\)
0.885385 + 0.464859i \(0.153895\pi\)
\(444\) 11.4216i 0.542046i
\(445\) −2.34488 + 5.26522i −0.111158 + 0.249596i
\(446\) 1.93083i 0.0914273i
\(447\) −2.47911 + 2.47911i −0.117258 + 0.117258i
\(448\) −22.8925 22.8925i −1.08157 1.08157i
\(449\) 12.1995i 0.575731i −0.957671 0.287865i \(-0.907054\pi\)
0.957671 0.287865i \(-0.0929455\pi\)
\(450\) −0.116553 + 2.21518i −0.00549436 + 0.104425i
\(451\) 0 0
\(452\) −13.6851 13.6851i −0.643692 0.643692i
\(453\) −9.83284 9.83284i −0.461987 0.461987i
\(454\) 2.75749i 0.129415i
\(455\) −25.4229 11.3221i −1.19184 0.530790i
\(456\) −2.06516 −0.0967102
\(457\) 21.3621 21.3621i 0.999277 0.999277i −0.000722482 1.00000i \(-0.500230\pi\)
1.00000 0.000722482i \(0.000229973\pi\)
\(458\) 2.59857 + 2.59857i 0.121423 + 0.121423i
\(459\) −3.68266 −0.171892
\(460\) 2.85141 + 7.43049i 0.132948 + 0.346448i
\(461\) 16.7546i 0.780340i −0.920743 0.390170i \(-0.872416\pi\)
0.920743 0.390170i \(-0.127584\pi\)
\(462\) 0 0
\(463\) −15.7524 + 15.7524i −0.732077 + 0.732077i −0.971031 0.238954i \(-0.923195\pi\)
0.238954 + 0.971031i \(0.423195\pi\)
\(464\) 28.4809 1.32219
\(465\) −25.1307 + 9.64377i −1.16541 + 0.447219i
\(466\) −3.28660 −0.152249
\(467\) 22.8580 + 22.8580i 1.05774 + 1.05774i 0.998228 + 0.0595134i \(0.0189549\pi\)
0.0595134 + 0.998228i \(0.481045\pi\)
\(468\) −9.68527 9.68527i −0.447702 0.447702i
\(469\) 4.55469 0.210316
\(470\) −1.36072 0.606000i −0.0627653 0.0279527i
\(471\) −27.4112 −1.26304
\(472\) −5.64156 + 5.64156i −0.259674 + 0.259674i
\(473\) 0 0
\(474\) 2.50887i 0.115236i
\(475\) 4.17738 + 4.64139i 0.191671 + 0.212961i
\(476\) −27.3908 −1.25545
\(477\) −0.787305 0.787305i −0.0360482 0.0360482i
\(478\) −2.08732 + 2.08732i −0.0954716 + 0.0954716i
\(479\) 19.0743 0.871526 0.435763 0.900061i \(-0.356479\pi\)
0.435763 + 0.900061i \(0.356479\pi\)
\(480\) 4.45336 9.99963i 0.203267 0.456418i
\(481\) 6.90005i 0.314615i
\(482\) 1.70292 + 1.70292i 0.0775658 + 0.0775658i
\(483\) −13.3821 13.3821i −0.608905 0.608905i
\(484\) 0 0
\(485\) −5.23794 13.6495i −0.237843 0.619794i
\(486\) 3.64439i 0.165313i
\(487\) −19.5034 19.5034i −0.883785 0.883785i 0.110132 0.993917i \(-0.464873\pi\)
−0.993917 + 0.110132i \(0.964873\pi\)
\(488\) −0.688686 + 0.688686i −0.0311753 + 0.0311753i
\(489\) 16.0753i 0.726952i
\(490\) 1.84130 + 4.79823i 0.0831813 + 0.216762i
\(491\) 37.3349i 1.68490i 0.538775 + 0.842449i \(0.318887\pi\)
−0.538775 + 0.842449i \(0.681113\pi\)
\(492\) −35.2528 + 35.2528i −1.58932 + 1.58932i
\(493\) 16.4692 16.4692i 0.741735 0.741735i
\(494\) 0.618839 0.0278429
\(495\) 0 0
\(496\) 19.5711 0.878769
\(497\) 11.1377 11.1377i 0.499592 0.499592i
\(498\) −1.43878 + 1.43878i −0.0644734 + 0.0644734i
\(499\) 14.1177i 0.631993i 0.948760 + 0.315996i \(0.102339\pi\)
−0.948760 + 0.315996i \(0.897661\pi\)
\(500\) −20.9325 + 6.79417i −0.936128 + 0.303845i
\(501\) 29.2830i 1.30827i
\(502\) 0.828342 0.828342i 0.0369707 0.0369707i
\(503\) −8.84744 8.84744i −0.394488 0.394488i 0.481796 0.876284i \(-0.339985\pi\)
−0.876284 + 0.481796i \(0.839985\pi\)
\(504\) 7.85997i 0.350111i
\(505\) −11.0813 + 24.8821i −0.493111 + 1.10724i
\(506\) 0 0
\(507\) −8.66669 8.66669i −0.384901 0.384901i
\(508\) −10.7628 10.7628i −0.477522 0.477522i
\(509\) 2.12688i 0.0942725i −0.998888 0.0471363i \(-0.984991\pi\)
0.998888 0.0471363i \(-0.0150095\pi\)
\(510\) −1.04048 2.71139i −0.0460734 0.120063i
\(511\) −41.6068 −1.84058
\(512\) −9.42980 + 9.42980i −0.416742 + 0.416742i
\(513\) 1.04339 + 1.04339i 0.0460667 + 0.0460667i
\(514\) −2.81455 −0.124144
\(515\) −26.8147 + 10.2900i −1.18160 + 0.453432i
\(516\) 28.1907i 1.24102i
\(517\) 0 0
\(518\) 1.38877 1.38877i 0.0610191 0.0610191i
\(519\) −55.3794 −2.43089
\(520\) −1.78883 + 4.01667i −0.0784456 + 0.176143i
\(521\) 24.8668 1.08944 0.544718 0.838619i \(-0.316637\pi\)
0.544718 + 0.838619i \(0.316637\pi\)
\(522\) −2.34416 2.34416i −0.102601 0.102601i
\(523\) 13.6144 + 13.6144i 0.595318 + 0.595318i 0.939063 0.343745i \(-0.111696\pi\)
−0.343745 + 0.939063i \(0.611696\pi\)
\(524\) −38.5812 −1.68543
\(525\) 38.8968 35.0083i 1.69760 1.52789i
\(526\) 5.27975 0.230208
\(527\) 11.3171 11.3171i 0.492980 0.492980i
\(528\) 0 0
\(529\) 19.7304i 0.857843i
\(530\) −0.0721275 + 0.161956i −0.00313302 + 0.00703491i
\(531\) −28.2329 −1.22520
\(532\) 7.76049 + 7.76049i 0.336460 + 0.336460i
\(533\) 21.2970 21.2970i 0.922475 0.922475i
\(534\) −1.07408 −0.0464800
\(535\) 20.8851 8.01455i 0.902941 0.346499i
\(536\) 0.719616i 0.0310827i
\(537\) 32.0202 + 32.0202i 1.38178 + 1.38178i
\(538\) −0.540186 0.540186i −0.0232891 0.0232891i
\(539\) 0 0
\(540\) −4.85520 + 1.86316i −0.208934 + 0.0801776i
\(541\) 33.4198i 1.43683i 0.695616 + 0.718414i \(0.255132\pi\)
−0.695616 + 0.718414i \(0.744868\pi\)
\(542\) 2.61719 + 2.61719i 0.112418 + 0.112418i
\(543\) 22.3208 22.3208i 0.957879 0.957879i
\(544\) 6.50860i 0.279054i
\(545\) 17.9684 + 8.00229i 0.769683 + 0.342781i
\(546\) 5.18614i 0.221946i
\(547\) 20.4901 20.4901i 0.876093 0.876093i −0.117035 0.993128i \(-0.537339\pi\)
0.993128 + 0.117035i \(0.0373390\pi\)
\(548\) 11.4087 11.4087i 0.487355 0.487355i
\(549\) −3.44649 −0.147093
\(550\) 0 0
\(551\) −9.33227 −0.397568
\(552\) −2.11429 + 2.11429i −0.0899902 + 0.0899902i
\(553\) −19.0070 + 19.0070i −0.808261 + 0.808261i
\(554\) 1.72773i 0.0734042i
\(555\) −11.8524 5.27852i −0.503108 0.224061i
\(556\) 24.4395i 1.03647i
\(557\) 13.6444 13.6444i 0.578131 0.578131i −0.356257 0.934388i \(-0.615947\pi\)
0.934388 + 0.356257i \(0.115947\pi\)
\(558\) −1.61083 1.61083i −0.0681919 0.0681919i
\(559\) 17.0306i 0.720317i
\(560\) −35.5230 + 13.6318i −1.50112 + 0.576047i
\(561\) 0 0
\(562\) −0.107272 0.107272i −0.00452499 0.00452499i
\(563\) −0.755686 0.755686i −0.0318484 0.0318484i 0.691003 0.722852i \(-0.257169\pi\)
−0.722852 + 0.691003i \(0.757169\pi\)
\(564\) 17.2950i 0.728252i
\(565\) −20.5258 + 7.87670i −0.863529 + 0.331375i
\(566\) −1.72706 −0.0725939
\(567\) 32.3826 32.3826i 1.35994 1.35994i
\(568\) −1.75969 1.75969i −0.0738348 0.0738348i
\(569\) 7.88940 0.330741 0.165371 0.986232i \(-0.447118\pi\)
0.165371 + 0.986232i \(0.447118\pi\)
\(570\) −0.473410 + 1.06300i −0.0198290 + 0.0445242i
\(571\) 12.2418i 0.512302i 0.966637 + 0.256151i \(0.0824544\pi\)
−0.966637 + 0.256151i \(0.917546\pi\)
\(572\) 0 0
\(573\) −22.1350 + 22.1350i −0.924701 + 0.924701i
\(574\) −8.57287 −0.357825
\(575\) 9.02855 + 0.475043i 0.376517 + 0.0198106i
\(576\) −18.1005 −0.754186
\(577\) 32.8802 + 32.8802i 1.36882 + 1.36882i 0.862124 + 0.506697i \(0.169134\pi\)
0.506697 + 0.862124i \(0.330866\pi\)
\(578\) −0.915589 0.915589i −0.0380835 0.0380835i
\(579\) 7.57022 0.314608
\(580\) 13.3807 30.0451i 0.555603 1.24756i
\(581\) 21.8002 0.904426
\(582\) 1.92648 1.92648i 0.0798551 0.0798551i
\(583\) 0 0
\(584\) 6.57364i 0.272019i
\(585\) −14.5267 + 5.57453i −0.600603 + 0.230479i
\(586\) −4.74372 −0.195961
\(587\) −3.86005 3.86005i −0.159321 0.159321i 0.622945 0.782266i \(-0.285936\pi\)
−0.782266 + 0.622945i \(0.785936\pi\)
\(588\) 42.1949 42.1949i 1.74009 1.74009i
\(589\) −6.41282 −0.264236
\(590\) 1.61063 + 4.19713i 0.0663085 + 0.172793i
\(591\) 11.9982i 0.493541i
\(592\) 6.67057 + 6.67057i 0.274159 + 0.274159i
\(593\) 28.4741 + 28.4741i 1.16929 + 1.16929i 0.982376 + 0.186913i \(0.0598483\pi\)
0.186913 + 0.982376i \(0.440152\pi\)
\(594\) 0 0
\(595\) −12.6587 + 28.4239i −0.518955 + 1.16527i
\(596\) 2.94376i 0.120581i
\(597\) −12.0473 12.0473i −0.493062 0.493062i
\(598\) 0.633560 0.633560i 0.0259082 0.0259082i
\(599\) 6.94646i 0.283825i −0.989879 0.141912i \(-0.954675\pi\)
0.989879 0.141912i \(-0.0453251\pi\)
\(600\) −5.53111 6.14548i −0.225807 0.250888i
\(601\) 24.2943i 0.990985i −0.868612 0.495493i \(-0.834988\pi\)
0.868612 0.495493i \(-0.165012\pi\)
\(602\) −3.42774 + 3.42774i −0.139704 + 0.139704i
\(603\) 1.80064 1.80064i 0.0733277 0.0733277i
\(604\) 11.6757 0.475079
\(605\) 0 0
\(606\) −5.07582 −0.206191
\(607\) −2.84537 + 2.84537i −0.115490 + 0.115490i −0.762490 0.647000i \(-0.776023\pi\)
0.647000 + 0.762490i \(0.276023\pi\)
\(608\) 1.84405 1.84405i 0.0747861 0.0747861i
\(609\) 78.2085i 3.16917i
\(610\) 0.196615 + 0.512358i 0.00796071 + 0.0207448i
\(611\) 10.4483i 0.422693i
\(612\) −10.8286 + 10.8286i −0.437719 + 0.437719i
\(613\) 32.5918 + 32.5918i 1.31637 + 1.31637i 0.916628 + 0.399742i \(0.130900\pi\)
0.399742 + 0.916628i \(0.369100\pi\)
\(614\) 1.02631i 0.0414185i
\(615\) 20.2904 + 52.8747i 0.818188 + 2.13211i
\(616\) 0 0
\(617\) 6.94955 + 6.94955i 0.279778 + 0.279778i 0.833021 0.553242i \(-0.186610\pi\)
−0.553242 + 0.833021i \(0.686610\pi\)
\(618\) −3.78459 3.78459i −0.152238 0.152238i
\(619\) 20.8324i 0.837324i −0.908142 0.418662i \(-0.862499\pi\)
0.908142 0.418662i \(-0.137501\pi\)
\(620\) 9.19476 20.6460i 0.369270 0.829164i
\(621\) 2.13642 0.0857315
\(622\) 0.0963696 0.0963696i 0.00386407 0.00386407i
\(623\) 8.13715 + 8.13715i 0.326008 + 0.326008i
\(624\) 24.9102 0.997206
\(625\) −2.62352 + 24.8620i −0.104941 + 0.994478i
\(626\) 4.76730i 0.190540i
\(627\) 0 0
\(628\) 16.2744 16.2744i 0.649418 0.649418i
\(629\) 7.71458 0.307600
\(630\) 4.04576 + 1.80179i 0.161187 + 0.0717850i
\(631\) −30.3096 −1.20661 −0.603304 0.797511i \(-0.706149\pi\)
−0.603304 + 0.797511i \(0.706149\pi\)
\(632\) 3.00300 + 3.00300i 0.119453 + 0.119453i
\(633\) −23.8361 23.8361i −0.947401 0.947401i
\(634\) −3.37595 −0.134076
\(635\) −16.1428 + 6.19472i −0.640608 + 0.245830i
\(636\) 2.05849 0.0816246
\(637\) −25.4909 + 25.4909i −1.00998 + 1.00998i
\(638\) 0 0
\(639\) 8.80625i 0.348370i
\(640\) 4.37833 + 11.4095i 0.173069 + 0.450999i
\(641\) −33.8177 −1.33572 −0.667859 0.744288i \(-0.732789\pi\)
−0.667859 + 0.744288i \(0.732789\pi\)
\(642\) 2.94769 + 2.94769i 0.116336 + 0.116336i
\(643\) −8.93302 + 8.93302i −0.352284 + 0.352284i −0.860959 0.508675i \(-0.830136\pi\)
0.508675 + 0.860959i \(0.330136\pi\)
\(644\) 15.8902 0.626161
\(645\) 29.2540 + 13.0284i 1.15188 + 0.512991i
\(646\) 0.691891i 0.0272221i
\(647\) 6.53948 + 6.53948i 0.257094 + 0.257094i 0.823871 0.566777i \(-0.191810\pi\)
−0.566777 + 0.823871i \(0.691810\pi\)
\(648\) −5.11626 5.11626i −0.200986 0.200986i
\(649\) 0 0
\(650\) 1.65743 + 1.84153i 0.0650098 + 0.0722308i
\(651\) 53.7423i 2.10633i
\(652\) −9.54412 9.54412i −0.373777 0.373777i
\(653\) −2.95335 + 2.95335i −0.115573 + 0.115573i −0.762528 0.646955i \(-0.776042\pi\)
0.646955 + 0.762528i \(0.276042\pi\)
\(654\) 3.66548i 0.143331i
\(655\) −17.8304 + 40.0365i −0.696691 + 1.56436i
\(656\) 41.1774i 1.60771i
\(657\) −16.4487 + 16.4487i −0.641725 + 0.641725i
\(658\) −2.10293 + 2.10293i −0.0819806 + 0.0819806i
\(659\) −16.5191 −0.643494 −0.321747 0.946826i \(-0.604270\pi\)
−0.321747 + 0.946826i \(0.604270\pi\)
\(660\) 0 0
\(661\) 35.6112 1.38512 0.692558 0.721362i \(-0.256484\pi\)
0.692558 + 0.721362i \(0.256484\pi\)
\(662\) 0.00256961 0.00256961i 9.98707e−5 9.98707e-5i
\(663\) 14.4044 14.4044i 0.559422 0.559422i
\(664\) 3.44431i 0.133665i
\(665\) 11.6397 4.46669i 0.451369 0.173211i
\(666\) 1.09806i 0.0425491i
\(667\) −9.55427 + 9.55427i −0.369943 + 0.369943i
\(668\) 17.3857 + 17.3857i 0.672671 + 0.672671i
\(669\) 25.4669i 0.984608i
\(670\) −0.370407 0.164962i −0.0143101 0.00637304i
\(671\) 0 0
\(672\) −15.4539 15.4539i −0.596149 0.596149i
\(673\) 4.53251 + 4.53251i 0.174716 + 0.174716i 0.789048 0.614332i \(-0.210574\pi\)
−0.614332 + 0.789048i \(0.710574\pi\)
\(674\) 2.80974i 0.108227i
\(675\) −0.310400 + 5.89940i −0.0119473 + 0.227068i
\(676\) 10.2910 0.395809
\(677\) 19.5446 19.5446i 0.751162 0.751162i −0.223534 0.974696i \(-0.571760\pi\)
0.974696 + 0.223534i \(0.0717595\pi\)
\(678\) −2.89699 2.89699i −0.111258 0.111258i
\(679\) −29.1897 −1.12020
\(680\) 4.49082 + 2.00000i 0.172215 + 0.0766965i
\(681\) 36.3703i 1.39371i
\(682\) 0 0
\(683\) −5.39890 + 5.39890i −0.206583 + 0.206583i −0.802814 0.596230i \(-0.796665\pi\)
0.596230 + 0.802814i \(0.296665\pi\)
\(684\) 6.13601 0.234616
\(685\) −6.56648 17.1116i −0.250892 0.653800i
\(686\) 4.70644 0.179693
\(687\) −34.2742 34.2742i −1.30764 1.30764i
\(688\) −16.4642 16.4642i −0.627692 0.627692i
\(689\) −1.24358 −0.0473766
\(690\) 0.603616 + 1.57296i 0.0229793 + 0.0598815i
\(691\) −25.3818 −0.965570 −0.482785 0.875739i \(-0.660375\pi\)
−0.482785 + 0.875739i \(0.660375\pi\)
\(692\) 32.8794 32.8794i 1.24989 1.24989i
\(693\) 0 0
\(694\) 3.89113i 0.147705i
\(695\) −25.3613 11.2947i −0.962011 0.428434i
\(696\) 12.3565 0.468372
\(697\) −23.8110 23.8110i −0.901906 0.901906i
\(698\) 3.51731 3.51731i 0.133132 0.133132i
\(699\) 43.3491 1.63961
\(700\) −2.30869 + 43.8784i −0.0872601 + 1.65845i
\(701\) 31.0378i 1.17228i −0.810210 0.586140i \(-0.800647\pi\)
0.810210 0.586140i \(-0.199353\pi\)
\(702\) 0.413978 + 0.413978i 0.0156246 + 0.0156246i
\(703\) −2.18573 2.18573i −0.0824364 0.0824364i
\(704\) 0 0
\(705\) 17.9474 + 7.99293i 0.675938 + 0.301031i
\(706\) 2.35518i 0.0886382i
\(707\) 38.4540 + 38.4540i 1.44621 + 1.44621i
\(708\) 36.9089 36.9089i 1.38712 1.38712i
\(709\) 49.7760i 1.86938i 0.355467 + 0.934689i \(0.384322\pi\)
−0.355467 + 0.934689i \(0.615678\pi\)
\(710\) −1.30915 + 0.502379i −0.0491314 + 0.0188539i
\(711\) 15.0284i 0.563607i
\(712\) 1.28562 1.28562i 0.0481808 0.0481808i
\(713\) −6.56537 + 6.56537i −0.245875 + 0.245875i
\(714\) −5.79835 −0.216998
\(715\) 0 0
\(716\) −38.0216 −1.42093
\(717\) 27.5309 27.5309i 1.02816 1.02816i
\(718\) 0.213429 0.213429i 0.00796510 0.00796510i
\(719\) 36.4841i 1.36063i 0.732921 + 0.680314i \(0.238157\pi\)
−0.732921 + 0.680314i \(0.761843\pi\)
\(720\) −8.65440 + 19.4327i −0.322530 + 0.724213i
\(721\) 57.3435i 2.13558i
\(722\) 2.19194 2.19194i 0.0815757 0.0815757i
\(723\) −22.4609 22.4609i −0.835330 0.835330i
\(724\) 26.5043i 0.985025i
\(725\) −24.9945 27.7708i −0.928273 1.03138i
\(726\) 0 0
\(727\) −17.4528 17.4528i −0.647287 0.647287i 0.305050 0.952336i \(-0.401327\pi\)
−0.952336 + 0.305050i \(0.901327\pi\)
\(728\) 6.20757 + 6.20757i 0.230068 + 0.230068i
\(729\) 17.2944i 0.640532i
\(730\) 3.38364 + 1.50692i 0.125234 + 0.0557734i
\(731\) −19.0410 −0.704256
\(732\) 4.50560 4.50560i 0.166532 0.166532i
\(733\) −6.58997 6.58997i −0.243406 0.243406i 0.574852 0.818258i \(-0.305060\pi\)
−0.818258 + 0.574852i \(0.805060\pi\)
\(734\) −3.80820 −0.140563
\(735\) −24.2860 63.2869i −0.895804 2.33437i
\(736\) 3.77583i 0.139179i
\(737\) 0 0
\(738\) −3.38917 + 3.38917i −0.124757 + 0.124757i
\(739\) 36.2605 1.33387 0.666933 0.745118i \(-0.267607\pi\)
0.666933 + 0.745118i \(0.267607\pi\)
\(740\) 10.1709 3.90302i 0.373888 0.143478i
\(741\) −8.16227 −0.299848
\(742\) 0.250295 + 0.250295i 0.00918862 + 0.00918862i
\(743\) −29.6603 29.6603i −1.08813 1.08813i −0.995721 0.0924088i \(-0.970543\pi\)
−0.0924088 0.995721i \(-0.529457\pi\)
\(744\) 8.49097 0.311294
\(745\) −3.05479 1.36046i −0.111919 0.0498435i
\(746\) 1.58191 0.0579180
\(747\) 8.61843 8.61843i 0.315332 0.315332i
\(748\) 0 0
\(749\) 44.6630i 1.63195i
\(750\) −4.43119 + 1.43826i −0.161804 + 0.0525178i
\(751\) −18.2399 −0.665584 −0.332792 0.943000i \(-0.607991\pi\)
−0.332792 + 0.943000i \(0.607991\pi\)
\(752\) −10.1008 10.1008i −0.368339 0.368339i
\(753\) −10.9255 + 10.9255i −0.398149 + 0.398149i
\(754\) −3.70270 −0.134844
\(755\) 5.39596 12.1162i 0.196379 0.440952i
\(756\) 10.3829i 0.377622i
\(757\) 13.9623 + 13.9623i 0.507468 + 0.507468i 0.913748 0.406281i \(-0.133174\pi\)
−0.406281 + 0.913748i \(0.633174\pi\)
\(758\) 4.06459 + 4.06459i 0.147633 + 0.147633i
\(759\) 0 0
\(760\) −0.705712 1.83901i −0.0255989 0.0667080i
\(761\) 44.1709i 1.60119i −0.599203 0.800597i \(-0.704516\pi\)
0.599203 0.800597i \(-0.295484\pi\)
\(762\) −2.27837 2.27837i −0.0825368 0.0825368i
\(763\) 27.7694 27.7694i 1.00532 1.00532i
\(764\) 26.2836i 0.950907i
\(765\) 6.23259 + 16.2415i 0.225340 + 0.587212i
\(766\) 4.09464i 0.147945i
\(767\) −22.2975 + 22.2975i −0.805115 + 0.805115i
\(768\) 22.4323 22.4323i 0.809454 0.809454i
\(769\) −19.2821 −0.695332 −0.347666 0.937618i \(-0.613026\pi\)
−0.347666 + 0.937618i \(0.613026\pi\)
\(770\) 0 0
\(771\) 37.1229 1.33695
\(772\) −4.49453 + 4.49453i −0.161762 + 0.161762i
\(773\) −20.3097 + 20.3097i −0.730490 + 0.730490i −0.970717 0.240227i \(-0.922778\pi\)
0.240227 + 0.970717i \(0.422778\pi\)
\(774\) 2.71022i 0.0974170i
\(775\) −17.1754 19.0832i −0.616959 0.685488i
\(776\) 4.61181i 0.165554i
\(777\) −18.3174 + 18.3174i −0.657133 + 0.657133i
\(778\) 1.80409 + 1.80409i 0.0646797 + 0.0646797i
\(779\) 13.4925i 0.483419i
\(780\) 11.7031 26.2783i 0.419039 0.940915i
\(781\) 0 0
\(782\) −0.708350 0.708350i −0.0253305 0.0253305i
\(783\) −6.24291 6.24291i −0.223103 0.223103i
\(784\) 49.2862i 1.76022i
\(785\) −9.36701 24.4095i −0.334323 0.871211i
\(786\) −8.16726 −0.291317
\(787\) −30.2941 + 30.2941i −1.07987 + 1.07987i −0.0833458 + 0.996521i \(0.526561\pi\)
−0.996521 + 0.0833458i \(0.973439\pi\)
\(788\) 7.12350 + 7.12350i 0.253764 + 0.253764i
\(789\) −69.6380 −2.47918
\(790\) 2.23413 0.857336i 0.0794868 0.0305027i
\(791\) 43.8948i 1.56072i
\(792\) 0 0
\(793\) −2.72193 + 2.72193i −0.0966587 + 0.0966587i
\(794\) 2.02586 0.0718952
\(795\) 0.951336 2.13614i 0.0337404 0.0757611i
\(796\) 14.3052 0.507035
\(797\) −5.70581 5.70581i −0.202110 0.202110i 0.598793 0.800904i \(-0.295647\pi\)
−0.800904 + 0.598793i \(0.795647\pi\)
\(798\) 1.64282 + 1.64282i 0.0581551 + 0.0581551i
\(799\) −11.6817 −0.413268
\(800\) 10.4264 + 0.548591i 0.368629 + 0.0193956i
\(801\) 6.43383 0.227328
\(802\) 2.80570 2.80570i 0.0990727 0.0990727i
\(803\) 0 0
\(804\) 4.70796i 0.166037i
\(805\) 7.34368 16.4896i 0.258831 0.581181i
\(806\) −2.54437 −0.0896217
\(807\) 7.12486 + 7.12486i 0.250807 + 0.250807i
\(808\) 6.07552 6.07552i 0.213736 0.213736i
\(809\) −25.7993 −0.907054 −0.453527 0.891243i \(-0.649834\pi\)
−0.453527 + 0.891243i \(0.649834\pi\)
\(810\) −3.80632 + 1.46066i −0.133740 + 0.0513223i
\(811\) 5.32931i 0.187137i 0.995613 + 0.0935687i \(0.0298275\pi\)
−0.995613 + 0.0935687i \(0.970173\pi\)
\(812\) −46.4333 46.4333i −1.62949 1.62949i
\(813\) −34.5198 34.5198i −1.21066 1.21066i
\(814\) 0 0
\(815\) −14.3150 + 5.49329i −0.501431 + 0.192422i
\(816\) 27.8508i 0.974972i
\(817\) 5.39479 + 5.39479i 0.188740 + 0.188740i
\(818\) −0.354250 + 0.354250i −0.0123861 + 0.0123861i
\(819\) 31.0654i 1.08551i
\(820\) −43.4390 19.3457i −1.51696 0.675580i
\(821\) 1.07893i 0.0376548i −0.999823 0.0188274i \(-0.994007\pi\)
0.999823 0.0188274i \(-0.00599330\pi\)
\(822\) 2.41511 2.41511i 0.0842365 0.0842365i
\(823\) −28.2971 + 28.2971i −0.986374 + 0.986374i −0.999908 0.0135342i \(-0.995692\pi\)
0.0135342 + 0.999908i \(0.495692\pi\)
\(824\) 9.05995 0.315618
\(825\) 0 0
\(826\) 8.97561 0.312301
\(827\) −2.04606 + 2.04606i −0.0711485 + 0.0711485i −0.741786 0.670637i \(-0.766021\pi\)
0.670637 + 0.741786i \(0.266021\pi\)
\(828\) 6.28198 6.28198i 0.218314 0.218314i
\(829\) 40.5134i 1.40709i −0.710651 0.703545i \(-0.751600\pi\)
0.710651 0.703545i \(-0.248400\pi\)
\(830\) −1.77289 0.789561i −0.0615379 0.0274061i
\(831\) 22.7882i 0.790512i
\(832\) −14.2952 + 14.2952i −0.495597 + 0.495597i
\(833\) 28.5000 + 28.5000i 0.987465 + 0.987465i
\(834\) 5.17359i 0.179147i
\(835\) 26.0762 10.0066i 0.902406 0.346294i
\(836\) 0 0
\(837\) −4.28992 4.28992i −0.148281 0.148281i
\(838\) 3.11240 + 3.11240i 0.107516 + 0.107516i
\(839\) 42.0635i 1.45219i −0.687593 0.726096i \(-0.741333\pi\)
0.687593 0.726096i \(-0.258667\pi\)
\(840\) −15.4117 + 5.91417i −0.531755 + 0.204058i
\(841\) 26.8378 0.925440
\(842\) −3.59594 + 3.59594i −0.123924 + 0.123924i
\(843\) 1.41488 + 1.41488i 0.0487310 + 0.0487310i
\(844\) 28.3036 0.974250
\(845\) 4.75602 10.6792i 0.163612 0.367376i
\(846\) 1.66273i 0.0571658i
\(847\) 0 0
\(848\) −1.20222 + 1.20222i −0.0412845 + 0.0412845i
\(849\) 22.7794 0.781785
\(850\) 2.05892 1.85308i 0.0706203 0.0635603i
\(851\) −4.47545 −0.153417
\(852\) 11.5124 + 11.5124i 0.394410 + 0.394410i
\(853\) 19.2871 + 19.2871i 0.660379 + 0.660379i 0.955469 0.295091i \(-0.0953499\pi\)
−0.295091 + 0.955469i \(0.595350\pi\)
\(854\) 1.09568 0.0374936
\(855\) 2.83577 6.36746i 0.0969812 0.217763i
\(856\) −7.05651 −0.241186
\(857\) 23.4018 23.4018i 0.799391 0.799391i −0.183608 0.982999i \(-0.558778\pi\)
0.982999 + 0.183608i \(0.0587778\pi\)
\(858\) 0 0
\(859\) 31.9233i 1.08921i 0.838693 + 0.544605i \(0.183321\pi\)
−0.838693 + 0.544605i \(0.816679\pi\)
\(860\) −25.1035 + 9.63336i −0.856024 + 0.328495i
\(861\) 113.073 3.85352
\(862\) −4.25901 4.25901i −0.145062 0.145062i
\(863\) 20.4630 20.4630i 0.696569 0.696569i −0.267100 0.963669i \(-0.586065\pi\)
0.963669 + 0.267100i \(0.0860654\pi\)
\(864\) 2.46719 0.0839355
\(865\) −18.9243 49.3149i −0.643447 1.67676i
\(866\) 0.474306i 0.0161176i
\(867\) 12.0763 + 12.0763i 0.410132 + 0.410132i
\(868\) −31.9074 31.9074i −1.08301 1.08301i
\(869\) 0 0
\(870\) 2.83256 6.36025i 0.0960326 0.215633i
\(871\) 2.84418i 0.0963714i
\(872\) −4.38740 4.38740i −0.148576 0.148576i
\(873\) −11.5398 + 11.5398i −0.390562 + 0.390562i
\(874\) 0.401386i 0.0135771i
\(875\) 44.4665 + 22.6742i 1.50324 + 0.766529i
\(876\) 43.0068i 1.45307i
\(877\) 1.40135 1.40135i 0.0473204 0.0473204i −0.683051 0.730371i \(-0.739347\pi\)
0.730371 + 0.683051i \(0.239347\pi\)
\(878\) −3.15979 + 3.15979i −0.106638 + 0.106638i
\(879\) 62.5680 2.11037
\(880\) 0 0
\(881\) 25.3007 0.852401 0.426201 0.904629i \(-0.359852\pi\)
0.426201 + 0.904629i \(0.359852\pi\)
\(882\) 4.05658 4.05658i 0.136592 0.136592i
\(883\) 2.89490 2.89490i 0.0974212 0.0974212i −0.656716 0.754138i \(-0.728055\pi\)
0.754138 + 0.656716i \(0.228055\pi\)
\(884\) 17.1042i 0.575275i
\(885\) −21.2436 55.3586i −0.714096 1.86086i
\(886\) 2.22485i 0.0747452i
\(887\) −14.1709 + 14.1709i −0.475813 + 0.475813i −0.903790 0.427977i \(-0.859227\pi\)
0.427977 + 0.903790i \(0.359227\pi\)
\(888\) 2.89404 + 2.89404i 0.0971178 + 0.0971178i
\(889\) 34.5216i 1.15782i
\(890\) −0.367037 0.956460i −0.0123031 0.0320606i
\(891\) 0 0
\(892\) 15.1200 + 15.1200i 0.506256 + 0.506256i
\(893\) 3.30971 + 3.30971i 0.110755 + 0.110755i
\(894\) 0.623164i 0.0208417i
\(895\) −17.5717 + 39.4558i −0.587359 + 1.31886i
\(896\) 24.3993 0.815123
\(897\) −8.35644 + 8.35644i −0.279013 + 0.279013i
\(898\) 1.53327 + 1.53327i 0.0511659 + 0.0511659i
\(899\) 38.3698 1.27971
\(900\) 16.4340 + 18.2594i 0.547801 + 0.608648i
\(901\) 1.39038i 0.0463203i
\(902\) 0 0
\(903\) 45.2107 45.2107i 1.50452 1.50452i
\(904\) 6.93513 0.230659
\(905\) 27.5040 + 12.2490i 0.914265 + 0.407171i
\(906\) 2.47164 0.0821147
\(907\) 8.81403 + 8.81403i 0.292665 + 0.292665i 0.838132 0.545467i \(-0.183648\pi\)
−0.545467 + 0.838132i \(0.683648\pi\)
\(908\) 21.5935 + 21.5935i 0.716604 + 0.716604i
\(909\) 30.4046 1.00846
\(910\) 4.61822 1.77222i 0.153092 0.0587485i
\(911\) 31.0467 1.02862 0.514311 0.857604i \(-0.328048\pi\)
0.514311 + 0.857604i \(0.328048\pi\)
\(912\) −7.89082 + 7.89082i −0.261291 + 0.261291i
\(913\) 0 0
\(914\) 5.36970i 0.177614i
\(915\) −2.59328 6.75783i −0.0857313 0.223407i
\(916\) 40.6980 1.34470
\(917\) 61.8745 + 61.8745i 2.04328 + 2.04328i
\(918\) 0.462847 0.462847i 0.0152762 0.0152762i
\(919\) 22.0347 0.726859 0.363429 0.931622i \(-0.381606\pi\)
0.363429 + 0.931622i \(0.381606\pi\)
\(920\) −2.60526 1.16026i −0.0858928 0.0382526i
\(921\) 13.5367i 0.446049i
\(922\) 2.10577 + 2.10577i 0.0693497 + 0.0693497i
\(923\) −6.95491 6.95491i −0.228924 0.228924i
\(924\) 0 0
\(925\) 0.650239 12.3583i 0.0213797 0.406338i
\(926\) 3.95962i 0.130121i
\(927\) 22.6700 + 22.6700i 0.744580 + 0.744580i
\(928\) −11.0335 + 11.0335i −0.362193 + 0.362193i
\(929\) 19.8981i 0.652835i 0.945226 + 0.326417i \(0.105841\pi\)
−0.945226 + 0.326417i \(0.894159\pi\)
\(930\) 1.94644 4.37055i 0.0638262 0.143316i
\(931\) 16.1495i 0.529278i
\(932\) −25.7369 + 25.7369i −0.843040 + 0.843040i
\(933\) −1.27108 + 1.27108i −0.0416133 + 0.0416133i
\(934\) −5.74571 −0.188005
\(935\) 0 0
\(936\) 4.90816 0.160428
\(937\) 8.24405 8.24405i 0.269321 0.269321i −0.559505 0.828827i \(-0.689009\pi\)
0.828827 + 0.559505i \(0.189009\pi\)
\(938\) −0.572447 + 0.572447i −0.0186911 + 0.0186911i
\(939\) 62.8790i 2.05198i
\(940\) −15.4011 + 5.91009i −0.502328 + 0.192766i
\(941\) 0.127366i 0.00415202i 0.999998 + 0.00207601i \(0.000660816\pi\)
−0.999998 + 0.00207601i \(0.999339\pi\)
\(942\) 3.44512 3.44512i 0.112248 0.112248i
\(943\) 13.8135 + 13.8135i 0.449829 + 0.449829i
\(944\) 43.1118i 1.40317i
\(945\) 10.7745 + 4.79847i 0.350496 + 0.156094i
\(946\) 0 0
\(947\) 41.6247 + 41.6247i 1.35262 + 1.35262i 0.882718 + 0.469903i \(0.155711\pi\)
0.469903 + 0.882718i \(0.344289\pi\)
\(948\) −19.6466 19.6466i −0.638092 0.638092i
\(949\) 25.9814i 0.843391i
\(950\) −1.10837 0.0583174i −0.0359602 0.00189207i
\(951\) 44.5276 1.44391
\(952\) 6.94035 6.94035i 0.224938 0.224938i
\(953\) −29.8434 29.8434i −0.966723 0.966723i 0.0327407 0.999464i \(-0.489576\pi\)
−0.999464 + 0.0327407i \(0.989576\pi\)
\(954\) 0.197902 0.00640730
\(955\) −27.2750 12.1470i −0.882598 0.393068i
\(956\) 32.6909i 1.05730i
\(957\) 0 0
\(958\) −2.39731 + 2.39731i −0.0774536 + 0.0774536i
\(959\) −36.5933 −1.18166
\(960\) −13.6196 35.4911i −0.439569 1.14547i
\(961\) −4.63353 −0.149469
\(962\) −0.867218 0.867218i −0.0279602 0.0279602i
\(963\) −17.6569 17.6569i −0.568987 0.568987i
\(964\) 26.6706 0.859002
\(965\) 2.58691 + 6.74122i 0.0832756 + 0.217008i
\(966\) 3.36379 0.108228
\(967\) 1.28318 1.28318i 0.0412643 0.0412643i −0.686174 0.727438i \(-0.740711\pi\)
0.727438 + 0.686174i \(0.240711\pi\)
\(968\) 0 0
\(969\) 9.12579i 0.293163i
\(970\) 2.37383 + 1.05719i 0.0762192 + 0.0339444i
\(971\) −35.0831 −1.12587 −0.562934 0.826502i \(-0.690328\pi\)
−0.562934 + 0.826502i \(0.690328\pi\)
\(972\) 28.5387 + 28.5387i 0.915378 + 0.915378i
\(973\) −39.1947 + 39.1947i −1.25653 + 1.25653i
\(974\) 4.90250 0.157086
\(975\) −21.8609 24.2891i −0.700110 0.777875i
\(976\) 5.26282i 0.168459i
\(977\) −36.6633 36.6633i −1.17296 1.17296i −0.981500 0.191461i \(-0.938677\pi\)
−0.191461 0.981500i \(-0.561323\pi\)
\(978\) −2.02039 2.02039i −0.0646051 0.0646051i
\(979\) 0 0
\(980\) 51.9931 + 23.1553i 1.66086 + 0.739669i
\(981\) 21.9565i 0.701017i
\(982\) −4.69235 4.69235i −0.149739 0.149739i
\(983\) 0.552530 0.552530i 0.0176230 0.0176230i −0.698240 0.715863i \(-0.746033\pi\)
0.715863 + 0.698240i \(0.246033\pi\)
\(984\) 17.8649i 0.569513i
\(985\) 10.6843 4.10006i 0.340431 0.130639i
\(986\) 4.13979i 0.131838i
\(987\) 27.7368 27.7368i 0.882874 0.882874i
\(988\) 4.84604 4.84604i 0.154173 0.154173i
\(989\) 11.0462 0.351250
\(990\) 0 0
\(991\) −27.7886 −0.882735 −0.441368 0.897326i \(-0.645507\pi\)
−0.441368 + 0.897326i \(0.645507\pi\)
\(992\) −7.58186 + 7.58186i −0.240724 + 0.240724i
\(993\) −0.0338922 + 0.0338922i −0.00107554 + 0.00107554i
\(994\) 2.79963i 0.0887987i
\(995\) 6.61117 14.8448i 0.209588 0.470612i
\(996\) 22.5338i 0.714011i
\(997\) 33.4795 33.4795i 1.06031 1.06031i 0.0622463 0.998061i \(-0.480174\pi\)
0.998061 0.0622463i \(-0.0198264\pi\)
\(998\) −1.77435 1.77435i −0.0561660 0.0561660i
\(999\) 2.92433i 0.0925217i
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 605.2.e.a.362.5 20
5.3 odd 4 inner 605.2.e.a.483.6 yes 20
11.2 odd 10 605.2.m.f.282.5 80
11.3 even 5 605.2.m.f.112.6 80
11.4 even 5 605.2.m.f.457.5 80
11.5 even 5 605.2.m.f.602.6 80
11.6 odd 10 605.2.m.f.602.5 80
11.7 odd 10 605.2.m.f.457.6 80
11.8 odd 10 605.2.m.f.112.5 80
11.9 even 5 605.2.m.f.282.6 80
11.10 odd 2 inner 605.2.e.a.362.6 yes 20
55.3 odd 20 605.2.m.f.233.6 80
55.8 even 20 605.2.m.f.233.5 80
55.13 even 20 605.2.m.f.403.6 80
55.18 even 20 605.2.m.f.578.6 80
55.28 even 20 605.2.m.f.118.6 80
55.38 odd 20 605.2.m.f.118.5 80
55.43 even 4 inner 605.2.e.a.483.5 yes 20
55.48 odd 20 605.2.m.f.578.5 80
55.53 odd 20 605.2.m.f.403.5 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.e.a.362.5 20 1.1 even 1 trivial
605.2.e.a.362.6 yes 20 11.10 odd 2 inner
605.2.e.a.483.5 yes 20 55.43 even 4 inner
605.2.e.a.483.6 yes 20 5.3 odd 4 inner
605.2.m.f.112.5 80 11.8 odd 10
605.2.m.f.112.6 80 11.3 even 5
605.2.m.f.118.5 80 55.38 odd 20
605.2.m.f.118.6 80 55.28 even 20
605.2.m.f.233.5 80 55.8 even 20
605.2.m.f.233.6 80 55.3 odd 20
605.2.m.f.282.5 80 11.2 odd 10
605.2.m.f.282.6 80 11.9 even 5
605.2.m.f.403.5 80 55.53 odd 20
605.2.m.f.403.6 80 55.13 even 20
605.2.m.f.457.5 80 11.4 even 5
605.2.m.f.457.6 80 11.7 odd 10
605.2.m.f.578.5 80 55.48 odd 20
605.2.m.f.578.6 80 55.18 even 20
605.2.m.f.602.5 80 11.6 odd 10
605.2.m.f.602.6 80 11.5 even 5