Properties

Label 605.2.e.a.483.7
Level $605$
Weight $2$
Character 605.483
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 483.7
Root \(0.895288 + 0.895288i\) of defining polynomial
Character \(\chi\) \(=\) 605.483
Dual form 605.2.e.a.362.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.895288 + 0.895288i) q^{2} +(-1.60711 - 1.60711i) q^{3} -0.396917i q^{4} +(-0.452009 + 2.18991i) q^{5} -2.87765i q^{6} +(-1.81197 - 1.81197i) q^{7} +(2.14593 - 2.14593i) q^{8} +2.16559i q^{9} +O(q^{10})\) \(q+(0.895288 + 0.895288i) q^{2} +(-1.60711 - 1.60711i) q^{3} -0.396917i q^{4} +(-0.452009 + 2.18991i) q^{5} -2.87765i q^{6} +(-1.81197 - 1.81197i) q^{7} +(2.14593 - 2.14593i) q^{8} +2.16559i q^{9} +(-2.36528 + 1.55592i) q^{10} +(-0.637889 + 0.637889i) q^{12} +(-3.52344 + 3.52344i) q^{13} -3.24447i q^{14} +(4.24584 - 2.79299i) q^{15} +3.04862 q^{16} +(-0.212794 - 0.212794i) q^{17} +(-1.93883 + 1.93883i) q^{18} -6.08244 q^{19} +(0.869212 + 0.179410i) q^{20} +5.82406i q^{21} +(-5.07364 - 5.07364i) q^{23} -6.89749 q^{24} +(-4.59138 - 1.97971i) q^{25} -6.30899 q^{26} +(-1.34098 + 1.34098i) q^{27} +(-0.719202 + 0.719202i) q^{28} -3.98426 q^{29} +(6.30178 + 1.30072i) q^{30} +7.59403 q^{31} +(-1.56247 - 1.56247i) q^{32} -0.381023i q^{34} +(4.78707 - 3.14902i) q^{35} +0.859562 q^{36} +(-4.56304 + 4.56304i) q^{37} +(-5.44554 - 5.44554i) q^{38} +11.3251 q^{39} +(3.72941 + 5.66937i) q^{40} +2.42532i q^{41} +(-5.21422 + 5.21422i) q^{42} +(-1.43561 + 1.43561i) q^{43} +(-4.74245 - 0.978869i) q^{45} -9.08474i q^{46} +(2.49745 - 2.49745i) q^{47} +(-4.89947 - 4.89947i) q^{48} -0.433531i q^{49} +(-2.33819 - 5.88302i) q^{50} +0.683965i q^{51} +(1.39851 + 1.39851i) q^{52} +(-6.21422 - 6.21422i) q^{53} -2.40113 q^{54} -7.77673 q^{56} +(9.77514 + 9.77514i) q^{57} +(-3.56706 - 3.56706i) q^{58} -1.17470i q^{59} +(-1.10859 - 1.68525i) q^{60} -0.0929527i q^{61} +(6.79885 + 6.79885i) q^{62} +(3.92399 - 3.92399i) q^{63} -8.89496i q^{64} +(-6.12337 - 9.30862i) q^{65} +(7.07364 - 7.07364i) q^{67} +(-0.0844615 + 0.0844615i) q^{68} +16.3078i q^{69} +(7.10509 + 1.46653i) q^{70} +11.2433 q^{71} +(4.64722 + 4.64722i) q^{72} +(2.80629 - 2.80629i) q^{73} -8.17047 q^{74} +(4.19722 + 10.5605i) q^{75} +2.41423i q^{76} +(10.1392 + 10.1392i) q^{78} -2.35834 q^{79} +(-1.37800 + 6.67620i) q^{80} +10.8070 q^{81} +(-2.17136 + 2.17136i) q^{82} +(-5.86965 + 5.86965i) q^{83} +2.31167 q^{84} +(0.562183 - 0.369813i) q^{85} -2.57056 q^{86} +(6.40314 + 6.40314i) q^{87} -2.55325i q^{89} +(-3.36949 - 5.12223i) q^{90} +12.7687 q^{91} +(-2.01382 + 2.01382i) q^{92} +(-12.2044 - 12.2044i) q^{93} +4.47188 q^{94} +(2.74932 - 13.3200i) q^{95} +5.02211i q^{96} +(5.32387 - 5.32387i) q^{97} +(0.388135 - 0.388135i) 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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).

\(n\) \(122\) \(486\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.895288 + 0.895288i 0.633065 + 0.633065i 0.948835 0.315771i \(-0.102263\pi\)
−0.315771 + 0.948835i \(0.602263\pi\)
\(3\) −1.60711 1.60711i −0.927864 0.927864i 0.0697033 0.997568i \(-0.477795\pi\)
−0.997568 + 0.0697033i \(0.977795\pi\)
\(4\) 0.396917i 0.198459i
\(5\) −0.452009 + 2.18991i −0.202145 + 0.979356i
\(6\) 2.87765i 1.17480i
\(7\) −1.81197 1.81197i −0.684860 0.684860i 0.276231 0.961091i \(-0.410915\pi\)
−0.961091 + 0.276231i \(0.910915\pi\)
\(8\) 2.14593 2.14593i 0.758702 0.758702i
\(9\) 2.16559i 0.721865i
\(10\) −2.36528 + 1.55592i −0.747966 + 0.492025i
\(11\) 0 0
\(12\) −0.637889 + 0.637889i −0.184143 + 0.184143i
\(13\) −3.52344 + 3.52344i −0.977226 + 0.977226i −0.999746 0.0225204i \(-0.992831\pi\)
0.0225204 + 0.999746i \(0.492831\pi\)
\(14\) 3.24447i 0.867121i
\(15\) 4.24584 2.79299i 1.09627 0.721147i
\(16\) 3.04862 0.762155
\(17\) −0.212794 0.212794i −0.0516100 0.0516100i 0.680831 0.732441i \(-0.261619\pi\)
−0.732441 + 0.680831i \(0.761619\pi\)
\(18\) −1.93883 + 1.93883i −0.456987 + 0.456987i
\(19\) −6.08244 −1.39541 −0.697704 0.716386i \(-0.745795\pi\)
−0.697704 + 0.716386i \(0.745795\pi\)
\(20\) 0.869212 + 0.179410i 0.194362 + 0.0401174i
\(21\) 5.82406i 1.27091i
\(22\) 0 0
\(23\) −5.07364 5.07364i −1.05793 1.05793i −0.998216 0.0597111i \(-0.980982\pi\)
−0.0597111 0.998216i \(-0.519018\pi\)
\(24\) −6.89749 −1.40794
\(25\) −4.59138 1.97971i −0.918275 0.395943i
\(26\) −6.30899 −1.23729
\(27\) −1.34098 + 1.34098i −0.258072 + 0.258072i
\(28\) −0.719202 + 0.719202i −0.135916 + 0.135916i
\(29\) −3.98426 −0.739859 −0.369930 0.929060i \(-0.620618\pi\)
−0.369930 + 0.929060i \(0.620618\pi\)
\(30\) 6.30178 + 1.30072i 1.15054 + 0.237479i
\(31\) 7.59403 1.36393 0.681964 0.731386i \(-0.261126\pi\)
0.681964 + 0.731386i \(0.261126\pi\)
\(32\) −1.56247 1.56247i −0.276208 0.276208i
\(33\) 0 0
\(34\) 0.381023i 0.0653449i
\(35\) 4.78707 3.14902i 0.809163 0.532281i
\(36\) 0.859562 0.143260
\(37\) −4.56304 + 4.56304i −0.750159 + 0.750159i −0.974509 0.224350i \(-0.927974\pi\)
0.224350 + 0.974509i \(0.427974\pi\)
\(38\) −5.44554 5.44554i −0.883383 0.883383i
\(39\) 11.3251 1.81347
\(40\) 3.72941 + 5.66937i 0.589671 + 0.896406i
\(41\) 2.42532i 0.378771i 0.981903 + 0.189385i \(0.0606496\pi\)
−0.981903 + 0.189385i \(0.939350\pi\)
\(42\) −5.21422 + 5.21422i −0.804571 + 0.804571i
\(43\) −1.43561 + 1.43561i −0.218928 + 0.218928i −0.808047 0.589119i \(-0.799475\pi\)
0.589119 + 0.808047i \(0.299475\pi\)
\(44\) 0 0
\(45\) −4.74245 0.978869i −0.706963 0.145921i
\(46\) 9.08474i 1.33947i
\(47\) 2.49745 2.49745i 0.364291 0.364291i −0.501099 0.865390i \(-0.667071\pi\)
0.865390 + 0.501099i \(0.167071\pi\)
\(48\) −4.89947 4.89947i −0.707177 0.707177i
\(49\) 0.433531i 0.0619330i
\(50\) −2.33819 5.88302i −0.330670 0.831985i
\(51\) 0.683965i 0.0957742i
\(52\) 1.39851 + 1.39851i 0.193939 + 0.193939i
\(53\) −6.21422 6.21422i −0.853588 0.853588i 0.136985 0.990573i \(-0.456259\pi\)
−0.990573 + 0.136985i \(0.956259\pi\)
\(54\) −2.40113 −0.326752
\(55\) 0 0
\(56\) −7.77673 −1.03921
\(57\) 9.77514 + 9.77514i 1.29475 + 1.29475i
\(58\) −3.56706 3.56706i −0.468379 0.468379i
\(59\) 1.17470i 0.152933i −0.997072 0.0764664i \(-0.975636\pi\)
0.997072 0.0764664i \(-0.0243638\pi\)
\(60\) −1.10859 1.68525i −0.143118 0.217565i
\(61\) 0.0929527i 0.0119014i −0.999982 0.00595069i \(-0.998106\pi\)
0.999982 0.00595069i \(-0.00189417\pi\)
\(62\) 6.79885 + 6.79885i 0.863454 + 0.863454i
\(63\) 3.92399 3.92399i 0.494377 0.494377i
\(64\) 8.89496i 1.11187i
\(65\) −6.12337 9.30862i −0.759511 1.15459i
\(66\) 0 0
\(67\) 7.07364 7.07364i 0.864183 0.864183i −0.127638 0.991821i \(-0.540740\pi\)
0.991821 + 0.127638i \(0.0407397\pi\)
\(68\) −0.0844615 + 0.0844615i −0.0102425 + 0.0102425i
\(69\) 16.3078i 1.96323i
\(70\) 7.10509 + 1.46653i 0.849220 + 0.175284i
\(71\) 11.2433 1.33433 0.667165 0.744910i \(-0.267508\pi\)
0.667165 + 0.744910i \(0.267508\pi\)
\(72\) 4.64722 + 4.64722i 0.547680 + 0.547680i
\(73\) 2.80629 2.80629i 0.328451 0.328451i −0.523546 0.851997i \(-0.675391\pi\)
0.851997 + 0.523546i \(0.175391\pi\)
\(74\) −8.17047 −0.949798
\(75\) 4.19722 + 10.5605i 0.484653 + 1.21942i
\(76\) 2.41423i 0.276931i
\(77\) 0 0
\(78\) 10.1392 + 10.1392i 1.14804 + 1.14804i
\(79\) −2.35834 −0.265334 −0.132667 0.991161i \(-0.542354\pi\)
−0.132667 + 0.991161i \(0.542354\pi\)
\(80\) −1.37800 + 6.67620i −0.154066 + 0.746421i
\(81\) 10.8070 1.20078
\(82\) −2.17136 + 2.17136i −0.239786 + 0.239786i
\(83\) −5.86965 + 5.86965i −0.644278 + 0.644278i −0.951604 0.307327i \(-0.900566\pi\)
0.307327 + 0.951604i \(0.400566\pi\)
\(84\) 2.31167 0.252224
\(85\) 0.562183 0.369813i 0.0609773 0.0401119i
\(86\) −2.57056 −0.277191
\(87\) 6.40314 + 6.40314i 0.686489 + 0.686489i
\(88\) 0 0
\(89\) 2.55325i 0.270644i −0.990802 0.135322i \(-0.956793\pi\)
0.990802 0.135322i \(-0.0432069\pi\)
\(90\) −3.36949 5.12223i −0.355175 0.539930i
\(91\) 12.7687 1.33853
\(92\) −2.01382 + 2.01382i −0.209955 + 0.209955i
\(93\) −12.2044 12.2044i −1.26554 1.26554i
\(94\) 4.47188 0.461239
\(95\) 2.74932 13.3200i 0.282074 1.36660i
\(96\) 5.02211i 0.512567i
\(97\) 5.32387 5.32387i 0.540557 0.540557i −0.383135 0.923692i \(-0.625156\pi\)
0.923692 + 0.383135i \(0.125156\pi\)
\(98\) 0.388135 0.388135i 0.0392076 0.0392076i
\(99\) 0 0
\(100\) −0.785783 + 1.82240i −0.0785783 + 0.182240i
\(101\) 16.0361i 1.59565i 0.602887 + 0.797826i \(0.294017\pi\)
−0.602887 + 0.797826i \(0.705983\pi\)
\(102\) −0.612346 + 0.612346i −0.0606313 + 0.0606313i
\(103\) 1.01770 + 1.01770i 0.100277 + 0.100277i 0.755465 0.655188i \(-0.227411\pi\)
−0.655188 + 0.755465i \(0.727411\pi\)
\(104\) 15.1221i 1.48285i
\(105\) −12.7542 2.63253i −1.24468 0.256909i
\(106\) 11.1270i 1.08075i
\(107\) −7.90751 7.90751i −0.764448 0.764448i 0.212675 0.977123i \(-0.431782\pi\)
−0.977123 + 0.212675i \(0.931782\pi\)
\(108\) 0.532258 + 0.532258i 0.0512166 + 0.0512166i
\(109\) 16.2607 1.55749 0.778746 0.627339i \(-0.215856\pi\)
0.778746 + 0.627339i \(0.215856\pi\)
\(110\) 0 0
\(111\) 14.6666 1.39209
\(112\) −5.52401 5.52401i −0.521970 0.521970i
\(113\) −1.35809 1.35809i −0.127758 0.127758i 0.640337 0.768094i \(-0.278795\pi\)
−0.768094 + 0.640337i \(0.778795\pi\)
\(114\) 17.5031i 1.63932i
\(115\) 13.4041 8.81746i 1.24994 0.822232i
\(116\) 1.58142i 0.146831i
\(117\) −7.63034 7.63034i −0.705425 0.705425i
\(118\) 1.05169 1.05169i 0.0968164 0.0968164i
\(119\) 0.771151i 0.0706913i
\(120\) 3.11773 15.1049i 0.284608 1.37888i
\(121\) 0 0
\(122\) 0.0832195 0.0832195i 0.00753434 0.00753434i
\(123\) 3.89775 3.89775i 0.351448 0.351448i
\(124\) 3.01420i 0.270683i
\(125\) 6.41073 9.15983i 0.573393 0.819280i
\(126\) 7.02621 0.625945
\(127\) −1.78209 1.78209i −0.158135 0.158135i 0.623605 0.781740i \(-0.285667\pi\)
−0.781740 + 0.623605i \(0.785667\pi\)
\(128\) 4.83862 4.83862i 0.427678 0.427678i
\(129\) 4.61435 0.406271
\(130\) 2.85172 13.8161i 0.250112 1.21175i
\(131\) 13.8354i 1.20880i −0.796680 0.604401i \(-0.793412\pi\)
0.796680 0.604401i \(-0.206588\pi\)
\(132\) 0 0
\(133\) 11.0212 + 11.0212i 0.955659 + 0.955659i
\(134\) 12.6659 1.09417
\(135\) −2.33048 3.54275i −0.200576 0.304912i
\(136\) −0.913281 −0.0783132
\(137\) −1.38713 + 1.38713i −0.118510 + 0.118510i −0.763875 0.645364i \(-0.776706\pi\)
0.645364 + 0.763875i \(0.276706\pi\)
\(138\) −14.6002 + 14.6002i −1.24285 + 1.24285i
\(139\) −8.66388 −0.734861 −0.367430 0.930051i \(-0.619762\pi\)
−0.367430 + 0.930051i \(0.619762\pi\)
\(140\) −1.24990 1.90007i −0.105636 0.160585i
\(141\) −8.02735 −0.676025
\(142\) 10.0660 + 10.0660i 0.844717 + 0.844717i
\(143\) 0 0
\(144\) 6.60208i 0.550173i
\(145\) 1.80092 8.72516i 0.149559 0.724585i
\(146\) 5.02488 0.415862
\(147\) −0.696731 + 0.696731i −0.0574654 + 0.0574654i
\(148\) 1.81115 + 1.81115i 0.148876 + 0.148876i
\(149\) −8.51526 −0.697598 −0.348799 0.937198i \(-0.613410\pi\)
−0.348799 + 0.937198i \(0.613410\pi\)
\(150\) −5.69693 + 13.2124i −0.465152 + 1.07879i
\(151\) 6.89254i 0.560907i 0.959868 + 0.280454i \(0.0904849\pi\)
−0.959868 + 0.280454i \(0.909515\pi\)
\(152\) −13.0525 + 13.0525i −1.05870 + 1.05870i
\(153\) 0.460825 0.460825i 0.0372555 0.0372555i
\(154\) 0 0
\(155\) −3.43257 + 16.6302i −0.275711 + 1.33577i
\(156\) 4.49513i 0.359898i
\(157\) 3.85613 3.85613i 0.307753 0.307753i −0.536284 0.844037i \(-0.680173\pi\)
0.844037 + 0.536284i \(0.180173\pi\)
\(158\) −2.11140 2.11140i −0.167974 0.167974i
\(159\) 19.9738i 1.58403i
\(160\) 4.12791 2.71541i 0.326340 0.214672i
\(161\) 18.3866i 1.44906i
\(162\) 9.67537 + 9.67537i 0.760169 + 0.760169i
\(163\) −1.58417 1.58417i −0.124082 0.124082i 0.642339 0.766421i \(-0.277964\pi\)
−0.766421 + 0.642339i \(0.777964\pi\)
\(164\) 0.962651 0.0751704
\(165\) 0 0
\(166\) −10.5101 −0.815738
\(167\) −5.94876 5.94876i −0.460329 0.460329i 0.438435 0.898763i \(-0.355533\pi\)
−0.898763 + 0.438435i \(0.855533\pi\)
\(168\) 12.4980 + 12.4980i 0.964245 + 0.964245i
\(169\) 11.8292i 0.909941i
\(170\) 0.834405 + 0.172226i 0.0639959 + 0.0132091i
\(171\) 13.1721i 1.00730i
\(172\) 0.569817 + 0.569817i 0.0434482 + 0.0434482i
\(173\) 9.76335 9.76335i 0.742294 0.742294i −0.230725 0.973019i \(-0.574110\pi\)
0.973019 + 0.230725i \(0.0741098\pi\)
\(174\) 11.4653i 0.869184i
\(175\) 4.73225 + 11.9066i 0.357725 + 0.900056i
\(176\) 0 0
\(177\) −1.88787 + 1.88787i −0.141901 + 0.141901i
\(178\) 2.28589 2.28589i 0.171335 0.171335i
\(179\) 6.88939i 0.514937i 0.966287 + 0.257468i \(0.0828883\pi\)
−0.966287 + 0.257468i \(0.917112\pi\)
\(180\) −0.388530 + 1.88236i −0.0289593 + 0.140303i
\(181\) −23.2695 −1.72961 −0.864805 0.502108i \(-0.832558\pi\)
−0.864805 + 0.502108i \(0.832558\pi\)
\(182\) 11.4317 + 11.4317i 0.847374 + 0.847374i
\(183\) −0.149385 + 0.149385i −0.0110429 + 0.0110429i
\(184\) −21.7754 −1.60530
\(185\) −7.93009 12.0552i −0.583032 0.886313i
\(186\) 21.8530i 1.60234i
\(187\) 0 0
\(188\) −0.991282 0.991282i −0.0722967 0.0722967i
\(189\) 4.85963 0.353486
\(190\) 14.3867 9.46379i 1.04372 0.686575i
\(191\) 7.53352 0.545106 0.272553 0.962141i \(-0.412132\pi\)
0.272553 + 0.962141i \(0.412132\pi\)
\(192\) −14.2952 + 14.2952i −1.03167 + 1.03167i
\(193\) −17.8684 + 17.8684i −1.28619 + 1.28619i −0.349112 + 0.937081i \(0.613517\pi\)
−0.937081 + 0.349112i \(0.886483\pi\)
\(194\) 9.53280 0.684416
\(195\) −5.11905 + 24.8009i −0.366583 + 1.77603i
\(196\) −0.172076 −0.0122911
\(197\) −10.3579 10.3579i −0.737967 0.737967i 0.234217 0.972184i \(-0.424747\pi\)
−0.972184 + 0.234217i \(0.924747\pi\)
\(198\) 0 0
\(199\) 8.62950i 0.611729i −0.952075 0.305865i \(-0.901055\pi\)
0.952075 0.305865i \(-0.0989455\pi\)
\(200\) −14.1011 + 5.60445i −0.997099 + 0.396294i
\(201\) −22.7362 −1.60369
\(202\) −14.3569 + 14.3569i −1.01015 + 1.01015i
\(203\) 7.21936 + 7.21936i 0.506700 + 0.506700i
\(204\) 0.271477 0.0190072
\(205\) −5.31122 1.09627i −0.370952 0.0765665i
\(206\) 1.82227i 0.126964i
\(207\) 10.9874 10.9874i 0.763680 0.763680i
\(208\) −10.7416 + 10.7416i −0.744798 + 0.744798i
\(209\) 0 0
\(210\) −9.06177 13.7755i −0.625322 0.950601i
\(211\) 16.9115i 1.16423i −0.813105 0.582117i \(-0.802225\pi\)
0.813105 0.582117i \(-0.197775\pi\)
\(212\) −2.46653 + 2.46653i −0.169402 + 0.169402i
\(213\) −18.0691 18.0691i −1.23808 1.23808i
\(214\) 14.1590i 0.967890i
\(215\) −2.49494 3.79275i −0.170153 0.258663i
\(216\) 5.75530i 0.391599i
\(217\) −13.7602 13.7602i −0.934100 0.934100i
\(218\) 14.5580 + 14.5580i 0.985993 + 0.985993i
\(219\) −9.02002 −0.609517
\(220\) 0 0
\(221\) 1.49953 0.100869
\(222\) 13.1308 + 13.1308i 0.881284 + 0.881284i
\(223\) 5.32716 + 5.32716i 0.356733 + 0.356733i 0.862607 0.505874i \(-0.168830\pi\)
−0.505874 + 0.862607i \(0.668830\pi\)
\(224\) 5.66229i 0.378328i
\(225\) 4.28726 9.94306i 0.285817 0.662871i
\(226\) 2.43176i 0.161758i
\(227\) −4.15249 4.15249i −0.275610 0.275610i 0.555744 0.831354i \(-0.312434\pi\)
−0.831354 + 0.555744i \(0.812434\pi\)
\(228\) 3.87992 3.87992i 0.256954 0.256954i
\(229\) 23.9755i 1.58435i 0.610295 + 0.792174i \(0.291051\pi\)
−0.610295 + 0.792174i \(0.708949\pi\)
\(230\) 19.8947 + 4.10639i 1.31182 + 0.270767i
\(231\) 0 0
\(232\) −8.54996 + 8.54996i −0.561332 + 0.561332i
\(233\) −10.1914 + 10.1914i −0.667661 + 0.667661i −0.957174 0.289513i \(-0.906507\pi\)
0.289513 + 0.957174i \(0.406507\pi\)
\(234\) 13.6627i 0.893159i
\(235\) 4.34031 + 6.59805i 0.283131 + 0.430410i
\(236\) −0.466259 −0.0303509
\(237\) 3.79011 + 3.79011i 0.246194 + 0.246194i
\(238\) −0.690403 + 0.690403i −0.0447522 + 0.0447522i
\(239\) 15.1177 0.977885 0.488942 0.872316i \(-0.337383\pi\)
0.488942 + 0.872316i \(0.337383\pi\)
\(240\) 12.9440 8.51477i 0.835530 0.549626i
\(241\) 3.12966i 0.201599i 0.994907 + 0.100800i \(0.0321401\pi\)
−0.994907 + 0.100800i \(0.967860\pi\)
\(242\) 0 0
\(243\) −13.3451 13.3451i −0.856086 0.856086i
\(244\) −0.0368945 −0.00236193
\(245\) 0.949392 + 0.195960i 0.0606544 + 0.0125194i
\(246\) 6.97922 0.444979
\(247\) 21.4311 21.4311i 1.36363 1.36363i
\(248\) 16.2963 16.2963i 1.03481 1.03481i
\(249\) 18.8663 1.19560
\(250\) 13.9401 2.46124i 0.881652 0.155662i
\(251\) −6.19727 −0.391168 −0.195584 0.980687i \(-0.562660\pi\)
−0.195584 + 0.980687i \(0.562660\pi\)
\(252\) −1.55750 1.55750i −0.0981133 0.0981133i
\(253\) 0 0
\(254\) 3.19096i 0.200219i
\(255\) −1.49782 0.309158i −0.0937970 0.0193602i
\(256\) −9.12601 −0.570375
\(257\) −0.957737 + 0.957737i −0.0597420 + 0.0597420i −0.736347 0.676605i \(-0.763451\pi\)
0.676605 + 0.736347i \(0.263451\pi\)
\(258\) 4.13117 + 4.13117i 0.257196 + 0.257196i
\(259\) 16.5362 1.02751
\(260\) −3.69475 + 2.43047i −0.229139 + 0.150732i
\(261\) 8.62830i 0.534078i
\(262\) 12.3867 12.3867i 0.765250 0.765250i
\(263\) −6.97161 + 6.97161i −0.429888 + 0.429888i −0.888590 0.458702i \(-0.848314\pi\)
0.458702 + 0.888590i \(0.348314\pi\)
\(264\) 0 0
\(265\) 16.4174 10.7997i 1.00851 0.663418i
\(266\) 19.7343i 1.20999i
\(267\) −4.10335 + 4.10335i −0.251121 + 0.251121i
\(268\) −2.80765 2.80765i −0.171505 0.171505i
\(269\) 13.5535i 0.826369i −0.910647 0.413184i \(-0.864416\pi\)
0.910647 0.413184i \(-0.135584\pi\)
\(270\) 1.08533 5.25824i 0.0660511 0.320006i
\(271\) 5.38948i 0.327388i −0.986511 0.163694i \(-0.947659\pi\)
0.986511 0.163694i \(-0.0523409\pi\)
\(272\) −0.648727 0.648727i −0.0393349 0.0393349i
\(273\) −20.5207 20.5207i −1.24197 1.24197i
\(274\) −2.48376 −0.150049
\(275\) 0 0
\(276\) 6.47284 0.389619
\(277\) −20.1679 20.1679i −1.21177 1.21177i −0.970444 0.241328i \(-0.922417\pi\)
−0.241328 0.970444i \(-0.577583\pi\)
\(278\) −7.75667 7.75667i −0.465214 0.465214i
\(279\) 16.4456i 0.984572i
\(280\) 3.51515 17.0303i 0.210071 1.01776i
\(281\) 11.4142i 0.680912i −0.940260 0.340456i \(-0.889419\pi\)
0.940260 0.340456i \(-0.110581\pi\)
\(282\) −7.18679 7.18679i −0.427967 0.427967i
\(283\) 1.31371 1.31371i 0.0780921 0.0780921i −0.666982 0.745074i \(-0.732414\pi\)
0.745074 + 0.666982i \(0.232414\pi\)
\(284\) 4.46264i 0.264809i
\(285\) −25.8251 + 16.9882i −1.52975 + 1.00629i
\(286\) 0 0
\(287\) 4.39460 4.39460i 0.259405 0.259405i
\(288\) 3.38367 3.38367i 0.199385 0.199385i
\(289\) 16.9094i 0.994673i
\(290\) 9.42388 6.19919i 0.553389 0.364029i
\(291\) −17.1121 −1.00313
\(292\) −1.11387 1.11387i −0.0651840 0.0651840i
\(293\) 12.6589 12.6589i 0.739540 0.739540i −0.232949 0.972489i \(-0.574837\pi\)
0.972489 + 0.232949i \(0.0748374\pi\)
\(294\) −1.24755 −0.0727586
\(295\) 2.57248 + 0.530975i 0.149776 + 0.0309146i
\(296\) 19.5839i 1.13829i
\(297\) 0 0
\(298\) −7.62362 7.62362i −0.441624 0.441624i
\(299\) 35.7533 2.06767
\(300\) 4.19163 1.66595i 0.242004 0.0961837i
\(301\) 5.20255 0.299870
\(302\) −6.17081 + 6.17081i −0.355090 + 0.355090i
\(303\) 25.7718 25.7718i 1.48055 1.48055i
\(304\) −18.5431 −1.06352
\(305\) 0.203558 + 0.0420155i 0.0116557 + 0.00240580i
\(306\) 0.825142 0.0471702
\(307\) 9.10688 + 9.10688i 0.519757 + 0.519757i 0.917498 0.397741i \(-0.130206\pi\)
−0.397741 + 0.917498i \(0.630206\pi\)
\(308\) 0 0
\(309\) 3.27111i 0.186087i
\(310\) −17.9620 + 11.8157i −1.02017 + 0.671086i
\(311\) −18.8540 −1.06911 −0.534557 0.845133i \(-0.679521\pi\)
−0.534557 + 0.845133i \(0.679521\pi\)
\(312\) 24.3029 24.3029i 1.37588 1.37588i
\(313\) 6.78679 + 6.78679i 0.383612 + 0.383612i 0.872402 0.488790i \(-0.162561\pi\)
−0.488790 + 0.872402i \(0.662561\pi\)
\(314\) 6.90470 0.389655
\(315\) 6.81949 + 10.3669i 0.384235 + 0.584106i
\(316\) 0.936066i 0.0526578i
\(317\) −9.33298 + 9.33298i −0.524192 + 0.524192i −0.918835 0.394642i \(-0.870868\pi\)
0.394642 + 0.918835i \(0.370868\pi\)
\(318\) −17.8823 + 17.8823i −1.00279 + 1.00279i
\(319\) 0 0
\(320\) 19.4791 + 4.02060i 1.08892 + 0.224759i
\(321\) 25.4165i 1.41861i
\(322\) −16.4613 + 16.4613i −0.917351 + 0.917351i
\(323\) 1.29430 + 1.29430i 0.0720170 + 0.0720170i
\(324\) 4.28948i 0.238304i
\(325\) 23.1528 9.20203i 1.28429 0.510437i
\(326\) 2.83658i 0.157104i
\(327\) −26.1327 26.1327i −1.44514 1.44514i
\(328\) 5.20457 + 5.20457i 0.287374 + 0.287374i
\(329\) −9.05061 −0.498976
\(330\) 0 0
\(331\) −12.7005 −0.698084 −0.349042 0.937107i \(-0.613493\pi\)
−0.349042 + 0.937107i \(0.613493\pi\)
\(332\) 2.32977 + 2.32977i 0.127862 + 0.127862i
\(333\) −9.88169 9.88169i −0.541513 0.541513i
\(334\) 10.6517i 0.582835i
\(335\) 12.2933 + 18.6880i 0.671652 + 1.02103i
\(336\) 17.7554i 0.968635i
\(337\) 11.0394 + 11.0394i 0.601356 + 0.601356i 0.940672 0.339316i \(-0.110196\pi\)
−0.339316 + 0.940672i \(0.610196\pi\)
\(338\) 10.5906 10.5906i 0.576052 0.576052i
\(339\) 4.36518i 0.237084i
\(340\) −0.146785 0.223140i −0.00796055 0.0121015i
\(341\) 0 0
\(342\) 11.7928 11.7928i 0.637683 0.637683i
\(343\) −13.4693 + 13.4693i −0.727276 + 0.727276i
\(344\) 6.16143i 0.332202i
\(345\) −35.7125 7.37126i −1.92270 0.396855i
\(346\) 17.4820 0.939840
\(347\) −1.68836 1.68836i −0.0906360 0.0906360i 0.660335 0.750971i \(-0.270414\pi\)
−0.750971 + 0.660335i \(0.770414\pi\)
\(348\) 2.54152 2.54152i 0.136240 0.136240i
\(349\) 35.3076 1.88997 0.944987 0.327107i \(-0.106074\pi\)
0.944987 + 0.327107i \(0.106074\pi\)
\(350\) −6.42313 + 14.8966i −0.343331 + 0.796256i
\(351\) 9.44972i 0.504389i
\(352\) 0 0
\(353\) −0.0520523 0.0520523i −0.00277046 0.00277046i 0.705720 0.708491i \(-0.250624\pi\)
−0.708491 + 0.705720i \(0.750624\pi\)
\(354\) −3.38038 −0.179665
\(355\) −5.08206 + 24.6217i −0.269728 + 1.30678i
\(356\) −1.01343 −0.0537116
\(357\) 1.23932 1.23932i 0.0655920 0.0655920i
\(358\) −6.16799 + 6.16799i −0.325988 + 0.325988i
\(359\) −16.2236 −0.856250 −0.428125 0.903719i \(-0.640826\pi\)
−0.428125 + 0.903719i \(0.640826\pi\)
\(360\) −12.2776 + 8.07639i −0.647084 + 0.425663i
\(361\) 17.9961 0.947163
\(362\) −20.8329 20.8329i −1.09495 1.09495i
\(363\) 0 0
\(364\) 5.06813i 0.265642i
\(365\) 4.87704 + 7.41398i 0.255276 + 0.388065i
\(366\) −0.267485 −0.0139817
\(367\) −9.29959 + 9.29959i −0.485435 + 0.485435i −0.906862 0.421427i \(-0.861529\pi\)
0.421427 + 0.906862i \(0.361529\pi\)
\(368\) −15.4676 15.4676i −0.806305 0.806305i
\(369\) −5.25226 −0.273421
\(370\) 3.69313 17.8926i 0.191997 0.930190i
\(371\) 22.5199i 1.16918i
\(372\) −4.84415 + 4.84415i −0.251157 + 0.251157i
\(373\) 18.8004 18.8004i 0.973446 0.973446i −0.0262108 0.999656i \(-0.508344\pi\)
0.999656 + 0.0262108i \(0.00834413\pi\)
\(374\) 0 0
\(375\) −25.0236 + 4.41810i −1.29221 + 0.228150i
\(376\) 10.7187i 0.552776i
\(377\) 14.0383 14.0383i 0.723010 0.723010i
\(378\) 4.35077 + 4.35077i 0.223779 + 0.223779i
\(379\) 13.5195i 0.694448i 0.937782 + 0.347224i \(0.112876\pi\)
−0.937782 + 0.347224i \(0.887124\pi\)
\(380\) −5.28693 1.09125i −0.271214 0.0559801i
\(381\) 5.72801i 0.293455i
\(382\) 6.74467 + 6.74467i 0.345087 + 0.345087i
\(383\) 12.9136 + 12.9136i 0.659855 + 0.659855i 0.955346 0.295490i \(-0.0954830\pi\)
−0.295490 + 0.955346i \(0.595483\pi\)
\(384\) −15.5524 −0.793654
\(385\) 0 0
\(386\) −31.9947 −1.62849
\(387\) −3.10894 3.10894i −0.158036 0.158036i
\(388\) −2.11314 2.11314i −0.107278 0.107278i
\(389\) 17.6678i 0.895793i 0.894085 + 0.447896i \(0.147827\pi\)
−0.894085 + 0.447896i \(0.852173\pi\)
\(390\) −26.7870 + 17.6209i −1.35641 + 0.892270i
\(391\) 2.15928i 0.109199i
\(392\) −0.930328 0.930328i −0.0469886 0.0469886i
\(393\) −22.2349 + 22.2349i −1.12160 + 1.12160i
\(394\) 18.5465i 0.934362i
\(395\) 1.06599 5.16454i 0.0536359 0.259856i
\(396\) 0 0
\(397\) −11.7203 + 11.7203i −0.588223 + 0.588223i −0.937150 0.348927i \(-0.886546\pi\)
0.348927 + 0.937150i \(0.386546\pi\)
\(398\) 7.72589 7.72589i 0.387264 0.387264i
\(399\) 35.4245i 1.77344i
\(400\) −13.9974 6.03540i −0.699868 0.301770i
\(401\) −21.8570 −1.09149 −0.545744 0.837952i \(-0.683753\pi\)
−0.545744 + 0.837952i \(0.683753\pi\)
\(402\) −20.3555 20.3555i −1.01524 1.01524i
\(403\) −26.7571 + 26.7571i −1.33287 + 1.33287i
\(404\) 6.36501 0.316671
\(405\) −4.88485 + 23.6663i −0.242730 + 1.17599i
\(406\) 12.9268i 0.641548i
\(407\) 0 0
\(408\) 1.46774 + 1.46774i 0.0726641 + 0.0726641i
\(409\) −20.1955 −0.998602 −0.499301 0.866429i \(-0.666410\pi\)
−0.499301 + 0.866429i \(0.666410\pi\)
\(410\) −3.77360 5.73655i −0.186365 0.283308i
\(411\) 4.45853 0.219923
\(412\) 0.403943 0.403943i 0.0199009 0.0199009i
\(413\) −2.12852 + 2.12852i −0.104738 + 0.104738i
\(414\) 19.6739 0.966918
\(415\) −10.2008 15.5071i −0.500740 0.761214i
\(416\) 11.0105 0.539835
\(417\) 13.9238 + 13.9238i 0.681851 + 0.681851i
\(418\) 0 0
\(419\) 11.1391i 0.544179i −0.962272 0.272090i \(-0.912285\pi\)
0.962272 0.272090i \(-0.0877148\pi\)
\(420\) −1.04490 + 5.06234i −0.0509857 + 0.247017i
\(421\) 29.9049 1.45748 0.728738 0.684793i \(-0.240107\pi\)
0.728738 + 0.684793i \(0.240107\pi\)
\(422\) 15.1406 15.1406i 0.737035 0.737035i
\(423\) 5.40847 + 5.40847i 0.262969 + 0.262969i
\(424\) −26.6706 −1.29524
\(425\) 0.555745 + 1.39829i 0.0269576 + 0.0678268i
\(426\) 32.3542i 1.56757i
\(427\) −0.168428 + 0.168428i −0.00815078 + 0.00815078i
\(428\) −3.13863 + 3.13863i −0.151711 + 0.151711i
\(429\) 0 0
\(430\) 1.16192 5.62929i 0.0560327 0.271469i
\(431\) 38.0839i 1.83444i −0.398386 0.917218i \(-0.630430\pi\)
0.398386 0.917218i \(-0.369570\pi\)
\(432\) −4.08814 + 4.08814i −0.196691 + 0.196691i
\(433\) −2.71048 2.71048i −0.130257 0.130257i 0.638972 0.769230i \(-0.279360\pi\)
−0.769230 + 0.638972i \(0.779360\pi\)
\(434\) 24.6386i 1.18269i
\(435\) −16.9166 + 11.1280i −0.811087 + 0.533547i
\(436\) 6.45415i 0.309098i
\(437\) 30.8601 + 30.8601i 1.47624 + 1.47624i
\(438\) −8.07552 8.07552i −0.385863 0.385863i
\(439\) 17.8832 0.853518 0.426759 0.904365i \(-0.359655\pi\)
0.426759 + 0.904365i \(0.359655\pi\)
\(440\) 0 0
\(441\) 0.938852 0.0447072
\(442\) 1.34251 + 1.34251i 0.0638568 + 0.0638568i
\(443\) −1.27317 1.27317i −0.0604903 0.0604903i 0.676215 0.736705i \(-0.263619\pi\)
−0.736705 + 0.676215i \(0.763619\pi\)
\(444\) 5.82143i 0.276273i
\(445\) 5.59138 + 1.15409i 0.265057 + 0.0547092i
\(446\) 9.53870i 0.451670i
\(447\) 13.6850 + 13.6850i 0.647276 + 0.647276i
\(448\) −16.1174 + 16.1174i −0.761476 + 0.761476i
\(449\) 14.4932i 0.683974i −0.939705 0.341987i \(-0.888900\pi\)
0.939705 0.341987i \(-0.111100\pi\)
\(450\) 12.7402 5.06357i 0.600581 0.238699i
\(451\) 0 0
\(452\) −0.539048 + 0.539048i −0.0253547 + 0.0253547i
\(453\) 11.0771 11.0771i 0.520446 0.520446i
\(454\) 7.43534i 0.348958i
\(455\) −5.77158 + 27.9623i −0.270576 + 1.31089i
\(456\) 41.9536 1.96466
\(457\) 27.2363 + 27.2363i 1.27406 + 1.27406i 0.943939 + 0.330121i \(0.107090\pi\)
0.330121 + 0.943939i \(0.392910\pi\)
\(458\) −21.4650 + 21.4650i −1.00299 + 1.00299i
\(459\) 0.570704 0.0266382
\(460\) −3.49980 5.32033i −0.163179 0.248062i
\(461\) 19.2825i 0.898077i 0.893512 + 0.449038i \(0.148233\pi\)
−0.893512 + 0.449038i \(0.851767\pi\)
\(462\) 0 0
\(463\) 13.7252 + 13.7252i 0.637863 + 0.637863i 0.950028 0.312165i \(-0.101054\pi\)
−0.312165 + 0.950028i \(0.601054\pi\)
\(464\) −12.1465 −0.563888
\(465\) 32.2431 21.2100i 1.49524 0.983592i
\(466\) −18.2485 −0.845344
\(467\) −25.7033 + 25.7033i −1.18941 + 1.18941i −0.212174 + 0.977232i \(0.568054\pi\)
−0.977232 + 0.212174i \(0.931946\pi\)
\(468\) −3.02861 + 3.02861i −0.139998 + 0.139998i
\(469\) −25.6344 −1.18369
\(470\) −2.02133 + 9.79299i −0.0932370 + 0.451717i
\(471\) −12.3944 −0.571106
\(472\) −2.52083 2.52083i −0.116030 0.116030i
\(473\) 0 0
\(474\) 6.78648i 0.311713i
\(475\) 27.9268 + 12.0415i 1.28137 + 0.552502i
\(476\) 0.306083 0.0140293
\(477\) 13.4575 13.4575i 0.616176 0.616176i
\(478\) 13.5347 + 13.5347i 0.619064 + 0.619064i
\(479\) −8.51668 −0.389137 −0.194569 0.980889i \(-0.562331\pi\)
−0.194569 + 0.980889i \(0.562331\pi\)
\(480\) −10.9980 2.27004i −0.501986 0.103613i
\(481\) 32.1552i 1.46615i
\(482\) −2.80195 + 2.80195i −0.127625 + 0.127625i
\(483\) 29.5492 29.5492i 1.34454 1.34454i
\(484\) 0 0
\(485\) 9.25234 + 14.0652i 0.420127 + 0.638669i
\(486\) 23.8953i 1.08391i
\(487\) −3.08581 + 3.08581i −0.139831 + 0.139831i −0.773557 0.633726i \(-0.781525\pi\)
0.633726 + 0.773557i \(0.281525\pi\)
\(488\) −0.199470 0.199470i −0.00902959 0.00902959i
\(489\) 5.09187i 0.230262i
\(490\) 0.674539 + 1.02542i 0.0304726 + 0.0463238i
\(491\) 17.4116i 0.785776i 0.919586 + 0.392888i \(0.128524\pi\)
−0.919586 + 0.392888i \(0.871476\pi\)
\(492\) −1.54708 1.54708i −0.0697479 0.0697479i
\(493\) 0.847826 + 0.847826i 0.0381841 + 0.0381841i
\(494\) 38.3740 1.72653
\(495\) 0 0
\(496\) 23.1513 1.03953
\(497\) −20.3724 20.3724i −0.913829 0.913829i
\(498\) 16.8908 + 16.8908i 0.756895 + 0.756895i
\(499\) 7.90395i 0.353829i 0.984226 + 0.176915i \(0.0566117\pi\)
−0.984226 + 0.176915i \(0.943388\pi\)
\(500\) −3.63570 2.54453i −0.162593 0.113795i
\(501\) 19.1206i 0.854245i
\(502\) −5.54834 5.54834i −0.247635 0.247635i
\(503\) −26.6750 + 26.6750i −1.18938 + 1.18938i −0.212140 + 0.977239i \(0.568043\pi\)
−0.977239 + 0.212140i \(0.931957\pi\)
\(504\) 16.8412i 0.750169i
\(505\) −35.1176 7.24847i −1.56271 0.322553i
\(506\) 0 0
\(507\) −19.0109 + 19.0109i −0.844302 + 0.844302i
\(508\) −0.707341 + 0.707341i −0.0313832 + 0.0313832i
\(509\) 41.0367i 1.81892i 0.415793 + 0.909459i \(0.363504\pi\)
−0.415793 + 0.909459i \(0.636496\pi\)
\(510\) −1.06419 1.61777i −0.0471233 0.0716358i
\(511\) −10.1698 −0.449887
\(512\) −17.8476 17.8476i −0.788762 0.788762i
\(513\) 8.15643 8.15643i 0.360115 0.360115i
\(514\) −1.71490 −0.0756411
\(515\) −2.68868 + 1.76866i −0.118477 + 0.0779364i
\(516\) 1.83152i 0.0806280i
\(517\) 0 0
\(518\) 14.8046 + 14.8046i 0.650479 + 0.650479i
\(519\) −31.3815 −1.37750
\(520\) −33.1160 6.83534i −1.45223 0.299749i
\(521\) −35.5162 −1.55599 −0.777996 0.628269i \(-0.783764\pi\)
−0.777996 + 0.628269i \(0.783764\pi\)
\(522\) 7.72482 7.72482i 0.338106 0.338106i
\(523\) 23.8121 23.8121i 1.04123 1.04123i 0.0421189 0.999113i \(-0.486589\pi\)
0.999113 0.0421189i \(-0.0134108\pi\)
\(524\) −5.49150 −0.239897
\(525\) 11.5300 26.7405i 0.503210 1.16705i
\(526\) −12.4832 −0.544293
\(527\) −1.61596 1.61596i −0.0703923 0.0703923i
\(528\) 0 0
\(529\) 28.4836i 1.23842i
\(530\) 24.3672 + 5.02952i 1.05844 + 0.218468i
\(531\) 2.54392 0.110397
\(532\) 4.37451 4.37451i 0.189659 0.189659i
\(533\) −8.54546 8.54546i −0.370145 0.370145i
\(534\) −7.34736 −0.317951
\(535\) 20.8910 13.7424i 0.903195 0.594137i
\(536\) 30.3591i 1.31131i
\(537\) 11.0720 11.0720i 0.477792 0.477792i
\(538\) 12.1343 12.1343i 0.523145 0.523145i
\(539\) 0 0
\(540\) −1.40618 + 0.925009i −0.0605124 + 0.0398061i
\(541\) 12.8744i 0.553515i −0.960940 0.276758i \(-0.910740\pi\)
0.960940 0.276758i \(-0.0892599\pi\)
\(542\) 4.82514 4.82514i 0.207258 0.207258i
\(543\) 37.3966 + 37.3966i 1.60484 + 1.60484i
\(544\) 0.664967i 0.0285102i
\(545\) −7.34998 + 35.6094i −0.314839 + 1.52534i
\(546\) 36.7439i 1.57250i
\(547\) 15.3187 + 15.3187i 0.654980 + 0.654980i 0.954188 0.299208i \(-0.0967224\pi\)
−0.299208 + 0.954188i \(0.596722\pi\)
\(548\) 0.550575 + 0.550575i 0.0235194 + 0.0235194i
\(549\) 0.201298 0.00859119
\(550\) 0 0
\(551\) 24.2340 1.03241
\(552\) 34.9954 + 34.9954i 1.48950 + 1.48950i
\(553\) 4.27324 + 4.27324i 0.181717 + 0.181717i
\(554\) 36.1122i 1.53426i
\(555\) −6.62944 + 32.1185i −0.281404 + 1.36335i
\(556\) 3.43884i 0.145839i
\(557\) −12.5950 12.5950i −0.533666 0.533666i 0.387995 0.921661i \(-0.373168\pi\)
−0.921661 + 0.387995i \(0.873168\pi\)
\(558\) −14.7235 + 14.7235i −0.623297 + 0.623297i
\(559\) 10.1165i 0.427884i
\(560\) 14.5940 9.60016i 0.616708 0.405681i
\(561\) 0 0
\(562\) 10.2190 10.2190i 0.431061 0.431061i
\(563\) −19.8779 + 19.8779i −0.837752 + 0.837752i −0.988563 0.150811i \(-0.951812\pi\)
0.150811 + 0.988563i \(0.451812\pi\)
\(564\) 3.18619i 0.134163i
\(565\) 3.58795 2.36021i 0.150946 0.0992948i
\(566\) 2.35230 0.0988747
\(567\) −19.5819 19.5819i −0.822364 0.822364i
\(568\) 24.1273 24.1273i 1.01236 1.01236i
\(569\) −26.1664 −1.09695 −0.548476 0.836167i \(-0.684792\pi\)
−0.548476 + 0.836167i \(0.684792\pi\)
\(570\) −38.3302 7.91158i −1.60548 0.331380i
\(571\) 27.6158i 1.15568i −0.816149 0.577842i \(-0.803895\pi\)
0.816149 0.577842i \(-0.196105\pi\)
\(572\) 0 0
\(573\) −12.1072 12.1072i −0.505785 0.505785i
\(574\) 7.86887 0.328440
\(575\) 13.2506 + 33.3393i 0.552589 + 1.39035i
\(576\) 19.2629 0.802620
\(577\) 20.9132 20.9132i 0.870629 0.870629i −0.121912 0.992541i \(-0.538902\pi\)
0.992541 + 0.121912i \(0.0389024\pi\)
\(578\) 15.1388 15.1388i 0.629692 0.629692i
\(579\) 57.4328 2.38683
\(580\) −3.46317 0.714818i −0.143800 0.0296812i
\(581\) 21.2712 0.882480
\(582\) −15.3203 15.3203i −0.635045 0.635045i
\(583\) 0 0
\(584\) 12.0442i 0.498393i
\(585\) 20.1587 13.2607i 0.833460 0.548264i
\(586\) 22.6667 0.936353
\(587\) 5.11085 5.11085i 0.210947 0.210947i −0.593723 0.804670i \(-0.702342\pi\)
0.804670 + 0.593723i \(0.202342\pi\)
\(588\) 0.276545 + 0.276545i 0.0114045 + 0.0114045i
\(589\) −46.1902 −1.90324
\(590\) 1.82774 + 2.77849i 0.0752467 + 0.114389i
\(591\) 33.2924i 1.36947i
\(592\) −13.9110 + 13.9110i −0.571738 + 0.571738i
\(593\) −7.89832 + 7.89832i −0.324345 + 0.324345i −0.850431 0.526086i \(-0.823659\pi\)
0.526086 + 0.850431i \(0.323659\pi\)
\(594\) 0 0
\(595\) −1.68875 0.348567i −0.0692319 0.0142899i
\(596\) 3.37986i 0.138444i
\(597\) −13.8685 + 13.8685i −0.567602 + 0.567602i
\(598\) 32.0095 + 32.0095i 1.30897 + 1.30897i
\(599\) 16.3481i 0.667964i −0.942579 0.333982i \(-0.891608\pi\)
0.942579 0.333982i \(-0.108392\pi\)
\(600\) 31.6690 + 13.6551i 1.29288 + 0.557466i
\(601\) 32.5519i 1.32782i −0.747813 0.663909i \(-0.768896\pi\)
0.747813 0.663909i \(-0.231104\pi\)
\(602\) 4.65778 + 4.65778i 0.189837 + 0.189837i
\(603\) 15.3186 + 15.3186i 0.623823 + 0.623823i
\(604\) 2.73577 0.111317
\(605\) 0 0
\(606\) 46.1463 1.87457
\(607\) 14.9647 + 14.9647i 0.607399 + 0.607399i 0.942266 0.334867i \(-0.108691\pi\)
−0.334867 + 0.942266i \(0.608691\pi\)
\(608\) 9.50362 + 9.50362i 0.385423 + 0.385423i
\(609\) 23.2046i 0.940298i
\(610\) 0.144627 + 0.219859i 0.00585577 + 0.00890182i
\(611\) 17.5992i 0.711989i
\(612\) −0.182909 0.182909i −0.00739367 0.00739367i
\(613\) 21.1838 21.1838i 0.855607 0.855607i −0.135210 0.990817i \(-0.543171\pi\)
0.990817 + 0.135210i \(0.0431710\pi\)
\(614\) 16.3066i 0.658079i
\(615\) 6.77388 + 10.2975i 0.273149 + 0.415236i
\(616\) 0 0
\(617\) 16.8977 16.8977i 0.680276 0.680276i −0.279786 0.960062i \(-0.590264\pi\)
0.960062 + 0.279786i \(0.0902636\pi\)
\(618\) 2.92859 2.92859i 0.117805 0.117805i
\(619\) 6.97674i 0.280419i 0.990122 + 0.140209i \(0.0447776\pi\)
−0.990122 + 0.140209i \(0.955222\pi\)
\(620\) 6.60082 + 1.36245i 0.265095 + 0.0547172i
\(621\) 13.6073 0.546042
\(622\) −16.8798 16.8798i −0.676818 0.676818i
\(623\) −4.62641 + 4.62641i −0.185353 + 0.185353i
\(624\) 34.5259 1.38214
\(625\) 17.1615 + 18.1792i 0.686458 + 0.727169i
\(626\) 12.1523i 0.485702i
\(627\) 0 0
\(628\) −1.53057 1.53057i −0.0610762 0.0610762i
\(629\) 1.94197 0.0774314
\(630\) −3.17591 + 15.3867i −0.126531 + 0.613022i
\(631\) 17.3689 0.691445 0.345723 0.938337i \(-0.387634\pi\)
0.345723 + 0.938337i \(0.387634\pi\)
\(632\) −5.06084 + 5.06084i −0.201309 + 0.201309i
\(633\) −27.1786 + 27.1786i −1.08025 + 1.08025i
\(634\) −16.7114 −0.663695
\(635\) 4.70812 3.09708i 0.186836 0.122904i
\(636\) 7.92796 0.314364
\(637\) 1.52752 + 1.52752i 0.0605225 + 0.0605225i
\(638\) 0 0
\(639\) 24.3483i 0.963206i
\(640\) 8.40902 + 12.7832i 0.332396 + 0.505301i
\(641\) −27.8829 −1.10131 −0.550653 0.834734i \(-0.685621\pi\)
−0.550653 + 0.834734i \(0.685621\pi\)
\(642\) −22.7551 + 22.7551i −0.898070 + 0.898070i
\(643\) −11.8044 11.8044i −0.465519 0.465519i 0.434940 0.900459i \(-0.356770\pi\)
−0.900459 + 0.434940i \(0.856770\pi\)
\(644\) 7.29795 0.287579
\(645\) −2.08573 + 10.1050i −0.0821255 + 0.397884i
\(646\) 2.31755i 0.0911828i
\(647\) 14.0447 14.0447i 0.552153 0.552153i −0.374908 0.927062i \(-0.622326\pi\)
0.927062 + 0.374908i \(0.122326\pi\)
\(648\) 23.1911 23.1911i 0.911031 0.911031i
\(649\) 0 0
\(650\) 28.9669 + 12.4900i 1.13618 + 0.489898i
\(651\) 44.2281i 1.73344i
\(652\) −0.628785 + 0.628785i −0.0246251 + 0.0246251i
\(653\) 26.2218 + 26.2218i 1.02614 + 1.02614i 0.999649 + 0.0264889i \(0.00843267\pi\)
0.0264889 + 0.999649i \(0.491567\pi\)
\(654\) 46.7926i 1.82974i
\(655\) 30.2982 + 6.25372i 1.18385 + 0.244353i
\(656\) 7.39388i 0.288682i
\(657\) 6.07729 + 6.07729i 0.237098 + 0.237098i
\(658\) −8.10291 8.10291i −0.315884 0.315884i
\(659\) −25.1740 −0.980641 −0.490320 0.871542i \(-0.663120\pi\)
−0.490320 + 0.871542i \(0.663120\pi\)
\(660\) 0 0
\(661\) −25.7739 −1.00249 −0.501244 0.865306i \(-0.667124\pi\)
−0.501244 + 0.865306i \(0.667124\pi\)
\(662\) −11.3706 11.3706i −0.441932 0.441932i
\(663\) −2.40991 2.40991i −0.0935931 0.0935931i
\(664\) 25.1917i 0.977629i
\(665\) −29.1171 + 19.1537i −1.12911 + 0.742749i
\(666\) 17.6939i 0.685626i
\(667\) 20.2147 + 20.2147i 0.782717 + 0.782717i
\(668\) −2.36116 + 2.36116i −0.0913562 + 0.0913562i
\(669\) 17.1227i 0.662000i
\(670\) −5.72510 + 27.7371i −0.221180 + 1.07158i
\(671\) 0 0
\(672\) 9.09992 9.09992i 0.351037 0.351037i
\(673\) 15.9996 15.9996i 0.616740 0.616740i −0.327954 0.944694i \(-0.606359\pi\)
0.944694 + 0.327954i \(0.106359\pi\)
\(674\) 19.7670i 0.761395i
\(675\) 8.81170 3.50218i 0.339162 0.134799i
\(676\) −4.69523 −0.180586
\(677\) 19.8094 + 19.8094i 0.761336 + 0.761336i 0.976564 0.215228i \(-0.0690495\pi\)
−0.215228 + 0.976564i \(0.569050\pi\)
\(678\) −3.90809 + 3.90809i −0.150089 + 0.150089i
\(679\) −19.2934 −0.740413
\(680\) 0.412811 2.00000i 0.0158306 0.0766965i
\(681\) 13.3470i 0.511458i
\(682\) 0 0
\(683\) −27.8670 27.8670i −1.06630 1.06630i −0.997640 0.0686610i \(-0.978127\pi\)
−0.0686610 0.997640i \(-0.521873\pi\)
\(684\) −5.22824 −0.199907
\(685\) −2.41068 3.66467i −0.0921075 0.140020i
\(686\) −24.1179 −0.920825
\(687\) 38.5313 38.5313i 1.47006 1.47006i
\(688\) −4.37662 + 4.37662i −0.166857 + 0.166857i
\(689\) 43.7908 1.66830
\(690\) −25.3736 38.5724i −0.965955 1.46843i
\(691\) −46.7547 −1.77863 −0.889317 0.457291i \(-0.848820\pi\)
−0.889317 + 0.457291i \(0.848820\pi\)
\(692\) −3.87524 3.87524i −0.147315 0.147315i
\(693\) 0 0
\(694\) 3.02314i 0.114757i
\(695\) 3.91615 18.9731i 0.148548 0.719690i
\(696\) 27.4814 1.04168
\(697\) 0.516092 0.516092i 0.0195484 0.0195484i
\(698\) 31.6105 + 31.6105i 1.19648 + 1.19648i
\(699\) 32.7574 1.23900
\(700\) 4.72594 1.87831i 0.178624 0.0709935i
\(701\) 22.9748i 0.867748i 0.900974 + 0.433874i \(0.142854\pi\)
−0.900974 + 0.433874i \(0.857146\pi\)
\(702\) 8.46022 8.46022i 0.319310 0.319310i
\(703\) 27.7544 27.7544i 1.04678 1.04678i
\(704\) 0 0
\(705\) 3.62844 17.5791i 0.136655 0.662069i
\(706\) 0.0932036i 0.00350776i
\(707\) 29.0569 29.0569i 1.09280 1.09280i
\(708\) 0.749328 + 0.749328i 0.0281615 + 0.0281615i
\(709\) 10.9351i 0.410675i −0.978691 0.205338i \(-0.934171\pi\)
0.978691 0.205338i \(-0.0658292\pi\)
\(710\) −26.5934 + 17.4936i −0.998033 + 0.656523i
\(711\) 5.10721i 0.191535i
\(712\) −5.47910 5.47910i −0.205338 0.205338i
\(713\) −38.5294 38.5294i −1.44294 1.44294i
\(714\) 2.21910 0.0830479
\(715\) 0 0
\(716\) 2.73452 0.102194
\(717\) −24.2958 24.2958i −0.907345 0.907345i
\(718\) −14.5248 14.5248i −0.542062 0.542062i
\(719\) 45.7653i 1.70676i −0.521291 0.853379i \(-0.674549\pi\)
0.521291 0.853379i \(-0.325451\pi\)
\(720\) −14.4579 2.98420i −0.538815 0.111215i
\(721\) 3.68809i 0.137352i
\(722\) 16.1117 + 16.1117i 0.599615 + 0.599615i
\(723\) 5.02971 5.02971i 0.187057 0.187057i
\(724\) 9.23608i 0.343256i
\(725\) 18.2932 + 7.88770i 0.679394 + 0.292942i
\(726\) 0 0
\(727\) −36.0611 + 36.0611i −1.33743 + 1.33743i −0.438893 + 0.898539i \(0.644629\pi\)
−0.898539 + 0.438893i \(0.855371\pi\)
\(728\) 27.4008 27.4008i 1.01554 1.01554i
\(729\) 10.4730i 0.387887i
\(730\) −2.27129 + 11.0040i −0.0840642 + 0.407277i
\(731\) 0.610976 0.0225978
\(732\) 0.0592935 + 0.0592935i 0.00219155 + 0.00219155i
\(733\) 2.80629 2.80629i 0.103653 0.103653i −0.653379 0.757031i \(-0.726649\pi\)
0.757031 + 0.653379i \(0.226649\pi\)
\(734\) −16.6516 −0.614623
\(735\) −1.21085 1.84070i −0.0446627 0.0678954i
\(736\) 15.8548i 0.584416i
\(737\) 0 0
\(738\) −4.70228 4.70228i −0.173093 0.173093i
\(739\) −1.57253 −0.0578465 −0.0289232 0.999582i \(-0.509208\pi\)
−0.0289232 + 0.999582i \(0.509208\pi\)
\(740\) −4.78490 + 3.14759i −0.175897 + 0.115708i
\(741\) −68.8842 −2.53053
\(742\) −20.1618 + 20.1618i −0.740165 + 0.740165i
\(743\) 30.1633 30.1633i 1.10658 1.10658i 0.112988 0.993596i \(-0.463958\pi\)
0.993596 0.112988i \(-0.0360423\pi\)
\(744\) −52.3797 −1.92033
\(745\) 3.84898 18.6476i 0.141016 0.683196i
\(746\) 33.6635 1.23251
\(747\) −12.7113 12.7113i −0.465081 0.465081i
\(748\) 0 0
\(749\) 28.6563i 1.04708i
\(750\) −26.3588 18.4479i −0.962487 0.673620i
\(751\) 39.3563 1.43613 0.718066 0.695975i \(-0.245028\pi\)
0.718066 + 0.695975i \(0.245028\pi\)
\(752\) 7.61379 7.61379i 0.277646 0.277646i
\(753\) 9.95968 + 9.95968i 0.362951 + 0.362951i
\(754\) 25.1367 0.915423
\(755\) −15.0940 3.11549i −0.549328 0.113384i
\(756\) 1.92887i 0.0701524i
\(757\) 10.8518 10.8518i 0.394417 0.394417i −0.481842 0.876258i \(-0.660032\pi\)
0.876258 + 0.481842i \(0.160032\pi\)
\(758\) −12.1038 + 12.1038i −0.439631 + 0.439631i
\(759\) 0 0
\(760\) −22.6839 34.4836i −0.822832 1.25085i
\(761\) 3.99343i 0.144762i 0.997377 + 0.0723808i \(0.0230597\pi\)
−0.997377 + 0.0723808i \(0.976940\pi\)
\(762\) −5.12822 + 5.12822i −0.185776 + 0.185776i
\(763\) −29.4639 29.4639i −1.06666 1.06666i
\(764\) 2.99018i 0.108181i
\(765\) 0.800866 + 1.21746i 0.0289554 + 0.0440173i
\(766\) 23.1228i 0.835462i
\(767\) 4.13898 + 4.13898i 0.149450 + 0.149450i
\(768\) 14.6665 + 14.6665i 0.529231 + 0.529231i
\(769\) −43.6566 −1.57430 −0.787148 0.616764i \(-0.788443\pi\)
−0.787148 + 0.616764i \(0.788443\pi\)
\(770\) 0 0
\(771\) 3.07838 0.110865
\(772\) 7.09226 + 7.09226i 0.255256 + 0.255256i
\(773\) −3.55842 3.55842i −0.127987 0.127987i 0.640211 0.768199i \(-0.278847\pi\)
−0.768199 + 0.640211i \(0.778847\pi\)
\(774\) 5.56680i 0.200094i
\(775\) −34.8670 15.0340i −1.25246 0.540038i
\(776\) 22.8493i 0.820244i
\(777\) −26.5754 26.5754i −0.953388 0.953388i
\(778\) −15.8178 + 15.8178i −0.567095 + 0.567095i
\(779\) 14.7519i 0.528540i
\(780\) 9.84390 + 2.03184i 0.352468 + 0.0727515i
\(781\) 0 0
\(782\) −1.93317 + 1.93317i −0.0691302 + 0.0691302i
\(783\) 5.34281 5.34281i 0.190937 0.190937i
\(784\) 1.32167i 0.0472026i
\(785\) 6.70156 + 10.1876i 0.239189 + 0.363610i
\(786\) −39.8134 −1.42010
\(787\) −29.9760 29.9760i −1.06853 1.06853i −0.997472 0.0710579i \(-0.977362\pi\)
−0.0710579 0.997472i \(-0.522638\pi\)
\(788\) −4.11122 + 4.11122i −0.146456 + 0.146456i
\(789\) 22.4083 0.797755
\(790\) 5.57813 3.66939i 0.198461 0.130551i
\(791\) 4.92162i 0.174993i
\(792\) 0 0
\(793\) 0.327513 + 0.327513i 0.0116303 + 0.0116303i
\(794\) −20.9860 −0.744766
\(795\) −43.7408 9.02836i −1.55133 0.320203i
\(796\) −3.42520 −0.121403
\(797\) 32.2937 32.2937i 1.14390 1.14390i 0.156170 0.987730i \(-0.450085\pi\)
0.987730 0.156170i \(-0.0499149\pi\)
\(798\) 31.7152 31.7152i 1.12270 1.12270i
\(799\) −1.06288 −0.0376021
\(800\) 4.08064 + 10.2671i 0.144272 + 0.362998i
\(801\) 5.52930 0.195368
\(802\) −19.5683 19.5683i −0.690982 0.690982i
\(803\) 0 0
\(804\) 9.02440i 0.318266i
\(805\) −40.2648 8.31089i −1.41915 0.292920i
\(806\) −47.9106 −1.68758
\(807\) −21.7819 + 21.7819i −0.766758 + 0.766758i
\(808\) 34.4124 + 34.4124i 1.21062 + 1.21062i
\(809\) −31.8280 −1.11901 −0.559507 0.828825i \(-0.689010\pi\)
−0.559507 + 0.828825i \(0.689010\pi\)
\(810\) −25.5615 + 16.8148i −0.898139 + 0.590811i
\(811\) 31.7003i 1.11315i 0.830798 + 0.556574i \(0.187884\pi\)
−0.830798 + 0.556574i \(0.812116\pi\)
\(812\) 2.86549 2.86549i 0.100559 0.100559i
\(813\) −8.66148 + 8.66148i −0.303772 + 0.303772i
\(814\) 0 0
\(815\) 4.18524 2.75312i 0.146603 0.0964377i
\(816\) 2.08515i 0.0729948i
\(817\) 8.73199 8.73199i 0.305494 0.305494i
\(818\) −18.0808 18.0808i −0.632179 0.632179i
\(819\) 27.6519i 0.966235i
\(820\) −0.435127 + 2.10811i −0.0151953 + 0.0736185i
\(821\) 31.0257i 1.08280i 0.840764 + 0.541402i \(0.182106\pi\)
−0.840764 + 0.541402i \(0.817894\pi\)
\(822\) 3.99167 + 3.99167i 0.139225 + 0.139225i
\(823\) 28.4141 + 28.4141i 0.990453 + 0.990453i 0.999955 0.00950231i \(-0.00302472\pi\)
−0.00950231 + 0.999955i \(0.503025\pi\)
\(824\) 4.36783 0.152161
\(825\) 0 0
\(826\) −3.81128 −0.132611
\(827\) 1.98953 + 1.98953i 0.0691826 + 0.0691826i 0.740851 0.671669i \(-0.234422\pi\)
−0.671669 + 0.740851i \(0.734422\pi\)
\(828\) −4.36111 4.36111i −0.151559 0.151559i
\(829\) 27.9016i 0.969062i −0.874774 0.484531i \(-0.838990\pi\)
0.874774 0.484531i \(-0.161010\pi\)
\(830\) 4.75064 23.0160i 0.164897 0.798898i
\(831\) 64.8240i 2.24872i
\(832\) 31.3409 + 31.3409i 1.08655 + 1.08655i
\(833\) −0.0922526 + 0.0922526i −0.00319636 + 0.00319636i
\(834\) 24.9316i 0.863311i
\(835\) 15.7161 10.3383i 0.543878 0.357772i
\(836\) 0 0
\(837\) −10.1834 + 10.1834i −0.351991 + 0.351991i
\(838\) 9.97269 9.97269i 0.344501 0.344501i
\(839\) 43.1638i 1.49018i −0.666964 0.745090i \(-0.732406\pi\)
0.666964 0.745090i \(-0.267594\pi\)
\(840\) −33.0188 + 21.7203i −1.13926 + 0.749422i
\(841\) −13.1256 −0.452609
\(842\) 26.7735 + 26.7735i 0.922676 + 0.922676i
\(843\) −18.3438 + 18.3438i −0.631794 + 0.631794i
\(844\) −6.71246 −0.231052
\(845\) 25.9049 + 5.34692i 0.891156 + 0.183940i
\(846\) 9.68428i 0.332952i
\(847\) 0 0
\(848\) −18.9448 18.9448i −0.650567 0.650567i
\(849\) −4.22256 −0.144918
\(850\) −0.754317 + 1.74942i −0.0258729 + 0.0600046i
\(851\) 46.3024 1.58723
\(852\) −7.17195 + 7.17195i −0.245707 + 0.245707i
\(853\) 4.64124 4.64124i 0.158913 0.158913i −0.623172 0.782085i \(-0.714156\pi\)
0.782085 + 0.623172i \(0.214156\pi\)
\(854\) −0.301582 −0.0103199
\(855\) 28.8457 + 5.95391i 0.986501 + 0.203619i
\(856\) −33.9380 −1.15998
\(857\) 16.3855 + 16.3855i 0.559717 + 0.559717i 0.929227 0.369510i \(-0.120474\pi\)
−0.369510 + 0.929227i \(0.620474\pi\)
\(858\) 0 0
\(859\) 44.6723i 1.52420i −0.647461 0.762099i \(-0.724169\pi\)
0.647461 0.762099i \(-0.275831\pi\)
\(860\) −1.50541 + 0.990283i −0.0513340 + 0.0337684i
\(861\) −14.1252 −0.481386
\(862\) 34.0960 34.0960i 1.16132 1.16132i
\(863\) −8.43404 8.43404i −0.287098 0.287098i 0.548834 0.835932i \(-0.315072\pi\)
−0.835932 + 0.548834i \(0.815072\pi\)
\(864\) 4.19048 0.142563
\(865\) 16.9677 + 25.7939i 0.576919 + 0.877020i
\(866\) 4.85331i 0.164922i
\(867\) −27.1753 + 27.1753i −0.922922 + 0.922922i
\(868\) −5.46164 + 5.46164i −0.185380 + 0.185380i
\(869\) 0 0
\(870\) −25.1080 5.18243i −0.851240 0.175701i
\(871\) 49.8471i 1.68900i
\(872\) 34.8943 34.8943i 1.18167 1.18167i
\(873\) 11.5294 + 11.5294i 0.390210 + 0.390210i
\(874\) 55.2574i 1.86911i
\(875\) −28.2134 + 4.98128i −0.953787 + 0.168398i
\(876\) 3.58020i 0.120964i
\(877\) 11.2634 + 11.2634i 0.380337 + 0.380337i 0.871224 0.490886i \(-0.163327\pi\)
−0.490886 + 0.871224i \(0.663327\pi\)
\(878\) 16.0106 + 16.0106i 0.540332 + 0.540332i
\(879\) −40.6884 −1.37239
\(880\) 0 0
\(881\) −35.9869 −1.21243 −0.606214 0.795301i \(-0.707313\pi\)
−0.606214 + 0.795301i \(0.707313\pi\)
\(882\) 0.840543 + 0.840543i 0.0283026 + 0.0283026i
\(883\) −11.4964 11.4964i −0.386886 0.386886i 0.486689 0.873575i \(-0.338204\pi\)
−0.873575 + 0.486689i \(0.838204\pi\)
\(884\) 0.595190i 0.0200184i
\(885\) −3.28092 4.98759i −0.110287 0.167656i
\(886\) 2.27971i 0.0765885i
\(887\) −22.0357 22.0357i −0.739886 0.739886i 0.232670 0.972556i \(-0.425254\pi\)
−0.972556 + 0.232670i \(0.925254\pi\)
\(888\) 31.4735 31.4735i 1.05618 1.05618i
\(889\) 6.45817i 0.216600i
\(890\) 3.97265 + 6.03914i 0.133163 + 0.202432i
\(891\) 0 0
\(892\) 2.11444 2.11444i 0.0707968 0.0707968i
\(893\) −15.1906 + 15.1906i −0.508334 + 0.508334i
\(894\) 24.5040i 0.819535i
\(895\) −15.0871 3.11407i −0.504306 0.104092i
\(896\) −17.5349 −0.585799
\(897\) −57.4594 57.4594i −1.91851 1.91851i
\(898\) 12.9756 12.9756i 0.433000 0.433000i
\(899\) −30.2566 −1.00911
\(900\) −3.94657 1.70169i −0.131552 0.0567229i
\(901\) 2.64469i 0.0881074i
\(902\) 0 0
\(903\) −8.36106 8.36106i −0.278239 0.278239i
\(904\) −5.82872 −0.193860
\(905\) 10.5180 50.9581i 0.349631 1.69390i
\(906\) 19.8343 0.658952
\(907\) −24.4871 + 24.4871i −0.813081 + 0.813081i −0.985095 0.172013i \(-0.944973\pi\)
0.172013 + 0.985095i \(0.444973\pi\)
\(908\) −1.64819 + 1.64819i −0.0546972 + 0.0546972i
\(909\) −34.7277 −1.15185
\(910\) −30.2016 + 19.8671i −1.00117 + 0.658588i
\(911\) −30.6831 −1.01658 −0.508288 0.861187i \(-0.669722\pi\)
−0.508288 + 0.861187i \(0.669722\pi\)
\(912\) 29.8007 + 29.8007i 0.986800 + 0.986800i
\(913\) 0 0
\(914\) 48.7687i 1.61312i
\(915\) −0.259616 0.394663i −0.00858264 0.0130471i
\(916\) 9.51631 0.314428
\(917\) −25.0693 + 25.0693i −0.827861 + 0.827861i
\(918\) 0.510944 + 0.510944i 0.0168637 + 0.0168637i
\(919\) −26.7907 −0.883742 −0.441871 0.897079i \(-0.645685\pi\)
−0.441871 + 0.897079i \(0.645685\pi\)
\(920\) 9.84267 47.6860i 0.324503 1.57216i
\(921\) 29.2715i 0.964528i
\(922\) −17.2634 + 17.2634i −0.568541 + 0.568541i
\(923\) −39.6149 + 39.6149i −1.30394 + 1.30394i
\(924\) 0 0
\(925\) 29.9841 11.9171i 0.985872 0.391832i
\(926\) 24.5760i 0.807617i
\(927\) −2.20393 + 2.20393i −0.0723865 + 0.0723865i
\(928\) 6.22529 + 6.22529i 0.204355 + 0.204355i
\(929\) 25.4532i 0.835094i 0.908655 + 0.417547i \(0.137110\pi\)
−0.908655 + 0.417547i \(0.862890\pi\)
\(930\) 47.8559 + 9.87774i 1.56926 + 0.323904i
\(931\) 2.63693i 0.0864218i
\(932\) 4.04514 + 4.04514i 0.132503 + 0.132503i
\(933\) 30.3005 + 30.3005i 0.991993 + 0.991993i
\(934\) −46.0237 −1.50594
\(935\) 0 0
\(936\) −32.7484 −1.07041
\(937\) 27.9630 + 27.9630i 0.913513 + 0.913513i 0.996547 0.0830341i \(-0.0264610\pi\)
−0.0830341 + 0.996547i \(0.526461\pi\)
\(938\) −22.9502 22.9502i −0.749351 0.749351i
\(939\) 21.8142i 0.711880i
\(940\) 2.61888 1.72275i 0.0854185 0.0561898i
\(941\) 41.0094i 1.33687i −0.743772 0.668433i \(-0.766965\pi\)
0.743772 0.668433i \(-0.233035\pi\)
\(942\) −11.0966 11.0966i −0.361547 0.361547i
\(943\) 12.3052 12.3052i 0.400712 0.400712i
\(944\) 3.58121i 0.116559i
\(945\) −2.19660 + 10.6421i −0.0714553 + 0.346188i
\(946\) 0 0
\(947\) 42.9022 42.9022i 1.39413 1.39413i 0.578336 0.815799i \(-0.303702\pi\)
0.815799 0.578336i \(-0.196298\pi\)
\(948\) 1.50436 1.50436i 0.0488593 0.0488593i
\(949\) 19.7756i 0.641942i
\(950\) 14.2219 + 35.7831i 0.461419 + 1.16096i
\(951\) 29.9982 0.972759
\(952\) 1.65484 + 1.65484i 0.0536336 + 0.0536336i
\(953\) 3.22534 3.22534i 0.104479 0.104479i −0.652935 0.757414i \(-0.726463\pi\)
0.757414 + 0.652935i \(0.226463\pi\)
\(954\) 24.0966 0.780158
\(955\) −3.40522 + 16.4977i −0.110190 + 0.533853i
\(956\) 6.00049i 0.194070i
\(957\) 0 0
\(958\) −7.62489 7.62489i −0.246349 0.246349i
\(959\) 5.02687 0.162326
\(960\) −24.8435 37.7666i −0.801822 1.21891i
\(961\) 26.6693 0.860299
\(962\) 28.7882 28.7882i 0.928167 0.928167i
\(963\) 17.1245 17.1245i 0.551828 0.551828i
\(964\) 1.24222 0.0400091
\(965\) −31.0534 47.2067i −0.999643 1.51964i
\(966\) 52.9101 1.70235
\(967\) 27.0023 + 27.0023i 0.868336 + 0.868336i 0.992288 0.123952i \(-0.0395569\pi\)
−0.123952 + 0.992288i \(0.539557\pi\)
\(968\) 0 0
\(969\) 4.16018i 0.133644i
\(970\) −4.30891 + 20.8759i −0.138351 + 0.670286i
\(971\) −39.6545 −1.27257 −0.636287 0.771452i \(-0.719531\pi\)
−0.636287 + 0.771452i \(0.719531\pi\)
\(972\) −5.29688 + 5.29688i −0.169898 + 0.169898i
\(973\) 15.6987 + 15.6987i 0.503277 + 0.503277i
\(974\) −5.52537 −0.177044
\(975\) −51.9978 22.4205i −1.66526 0.718029i
\(976\) 0.283378i 0.00907070i
\(977\) −4.49528 + 4.49528i −0.143817 + 0.143817i −0.775349 0.631533i \(-0.782426\pi\)
0.631533 + 0.775349i \(0.282426\pi\)
\(978\) −4.55869 + 4.55869i −0.145771 + 0.145771i
\(979\) 0 0
\(980\) 0.0777799 0.376830i 0.00248459 0.0120374i
\(981\) 35.2141i 1.12430i
\(982\) −15.5884 + 15.5884i −0.497447 + 0.497447i
\(983\) 0.848538 + 0.848538i 0.0270642 + 0.0270642i 0.720509 0.693445i \(-0.243908\pi\)
−0.693445 + 0.720509i \(0.743908\pi\)
\(984\) 16.7286i 0.533289i
\(985\) 27.3646 18.0009i 0.871908 0.573556i
\(986\) 1.51810i 0.0483461i
\(987\) 14.5453 + 14.5453i 0.462983 + 0.462983i
\(988\) −8.50638 8.50638i −0.270624 0.270624i
\(989\) 14.5675 0.463220
\(990\) 0 0
\(991\) 9.57879 0.304280 0.152140 0.988359i \(-0.451383\pi\)
0.152140 + 0.988359i \(0.451383\pi\)
\(992\) −11.8654 11.8654i −0.376728 0.376728i
\(993\) 20.4111 + 20.4111i 0.647727 + 0.647727i
\(994\) 36.4784i 1.15703i
\(995\) 18.8978 + 3.90061i 0.599100 + 0.123658i
\(996\) 7.48837i 0.237278i
\(997\) −11.9246 11.9246i −0.377657 0.377657i 0.492599 0.870256i \(-0.336047\pi\)
−0.870256 + 0.492599i \(0.836047\pi\)
\(998\) −7.07631 + 7.07631i −0.223997 + 0.223997i
\(999\) 12.2379i 0.387189i
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.483.7 yes 20
5.2 odd 4 inner 605.2.e.a.362.4 20
11.2 odd 10 605.2.m.f.403.7 80
11.3 even 5 605.2.m.f.233.7 80
11.4 even 5 605.2.m.f.578.4 80
11.5 even 5 605.2.m.f.118.4 80
11.6 odd 10 605.2.m.f.118.7 80
11.7 odd 10 605.2.m.f.578.7 80
11.8 odd 10 605.2.m.f.233.4 80
11.9 even 5 605.2.m.f.403.4 80
11.10 odd 2 inner 605.2.e.a.483.4 yes 20
55.2 even 20 605.2.m.f.282.4 80
55.7 even 20 605.2.m.f.457.7 80
55.17 even 20 605.2.m.f.602.4 80
55.27 odd 20 605.2.m.f.602.7 80
55.32 even 4 inner 605.2.e.a.362.7 yes 20
55.37 odd 20 605.2.m.f.457.4 80
55.42 odd 20 605.2.m.f.282.7 80
55.47 odd 20 605.2.m.f.112.7 80
55.52 even 20 605.2.m.f.112.4 80
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
605.2.e.a.362.4 20 5.2 odd 4 inner
605.2.e.a.362.7 yes 20 55.32 even 4 inner
605.2.e.a.483.4 yes 20 11.10 odd 2 inner
605.2.e.a.483.7 yes 20 1.1 even 1 trivial
605.2.m.f.112.4 80 55.52 even 20
605.2.m.f.112.7 80 55.47 odd 20
605.2.m.f.118.4 80 11.5 even 5
605.2.m.f.118.7 80 11.6 odd 10
605.2.m.f.233.4 80 11.8 odd 10
605.2.m.f.233.7 80 11.3 even 5
605.2.m.f.282.4 80 55.2 even 20
605.2.m.f.282.7 80 55.42 odd 20
605.2.m.f.403.4 80 11.9 even 5
605.2.m.f.403.7 80 11.2 odd 10
605.2.m.f.457.4 80 55.37 odd 20
605.2.m.f.457.7 80 55.7 even 20
605.2.m.f.578.4 80 11.4 even 5
605.2.m.f.578.7 80 11.7 odd 10
605.2.m.f.602.4 80 55.17 even 20
605.2.m.f.602.7 80 55.27 odd 20