Properties

Label 225.4.k.b.124.2
Level $225$
Weight $4$
Character 225.124
Analytic conductor $13.275$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(49,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.49");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.k (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: 8.0.303595776.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 9)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.2
Root \(-1.26217 - 1.18614i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.4.k.b.49.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.18843 - 0.686141i) q^{2} +(-1.18843 - 5.05842i) q^{3} +(-3.05842 - 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(-4.43132 - 2.55842i) q^{7} +19.3723i q^{8} +(-24.1753 + 12.0232i) q^{9} +O(q^{10})\) \(q+(-1.18843 - 0.686141i) q^{2} +(-1.18843 - 5.05842i) q^{3} +(-3.05842 - 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(-4.43132 - 2.55842i) q^{7} +19.3723i q^{8} +(-24.1753 + 12.0232i) q^{9} +(-27.9891 + 48.4786i) q^{11} +(-23.1615 + 21.7663i) q^{12} +(32.5489 - 18.7921i) q^{13} +(3.51087 + 6.08101i) q^{14} +(-11.1753 + 19.3561i) q^{16} -23.6495i q^{17} +(36.9802 + 2.29894i) q^{18} -39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(66.5263 - 38.4090i) q^{22} +(61.5513 - 35.5367i) q^{23} +(97.9932 - 23.0226i) q^{24} -51.5761 q^{26} +(89.5489 + 108.000i) q^{27} +31.2989i q^{28} +(-14.1861 + 24.5711i) q^{29} +(-6.44158 - 11.1571i) q^{31} +(160.777 - 92.8247i) q^{32} +(278.488 + 83.9674i) q^{33} +(-16.2269 + 28.1057i) q^{34} +(137.629 + 91.2927i) q^{36} +180.103i q^{37} +(46.4101 + 26.7949i) q^{38} +(-133.741 - 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(26.5879 - 24.9863i) q^{42} +(-53.0299 - 30.6168i) q^{43} +342.410 q^{44} -97.5326 q^{46} +(-53.5876 - 30.9388i) q^{47} +(111.192 + 33.5258i) q^{48} +(-158.409 - 274.372i) q^{49} +(-119.629 + 28.1057i) q^{51} +(-199.096 - 114.948i) q^{52} +492.310i q^{53} +(-32.3194 - 189.794i) q^{54} +(49.5625 - 85.8447i) q^{56} +(46.4101 + 197.539i) q^{57} +(33.7185 - 19.4674i) q^{58} +(394.815 + 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +17.6793i q^{62} +(137.889 + 8.57207i) q^{63} -75.9590 q^{64} +(-273.351 - 290.872i) q^{66} +(-263.644 + 152.215i) q^{67} +(-125.279 + 72.3301i) q^{68} +(-252.909 - 269.120i) q^{69} +270.391 q^{71} +(-232.916 - 468.330i) q^{72} -925.464i q^{73} +(123.576 - 214.040i) q^{74} +(119.436 + 206.870i) q^{76} +(248.057 - 143.216i) q^{77} +(61.2946 + 260.894i) q^{78} +(-644.517 + 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} -295.704i q^{82} +(-618.198 - 356.917i) q^{83} +(158.323 - 37.1966i) q^{84} +(42.0149 + 72.7720i) q^{86} +(141.150 + 42.5584i) q^{87} +(-939.141 - 542.213i) q^{88} +404.804 q^{89} -192.313 q^{91} +(-376.500 - 217.372i) q^{92} +(-48.7822 + 45.8437i) q^{93} +(42.4567 + 73.5372i) q^{94} +(-660.619 - 702.963i) q^{96} +(64.9756 + 37.5137i) q^{97} +434.763i q^{98} +(93.7785 - 1508.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 10 q^{4} + 18 q^{6} - 90 q^{9} - 132 q^{11} + 120 q^{14} + 14 q^{16} + 308 q^{19} + 42 q^{21} + 198 q^{24} - 1056 q^{26} - 102 q^{29} - 86 q^{31} + 594 q^{34} - 450 q^{36} - 1518 q^{39} - 264 q^{41} + 924 q^{44} - 1056 q^{46} - 1026 q^{49} + 594 q^{51} - 2430 q^{54} - 132 q^{56} + 1596 q^{59} - 878 q^{61} + 2908 q^{64} - 1980 q^{66} - 1782 q^{69} + 5472 q^{71} + 1632 q^{74} + 3058 q^{76} - 1606 q^{79} - 1134 q^{81} - 1284 q^{84} - 66 q^{86} + 1584 q^{89} - 3124 q^{91} + 4200 q^{94} + 2160 q^{96} - 594 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.18843 0.686141i −0.420174 0.242587i 0.274978 0.961451i \(-0.411329\pi\)
−0.695152 + 0.718863i \(0.744663\pi\)
\(3\) −1.18843 5.05842i −0.228714 0.973494i
\(4\) −3.05842 5.29734i −0.382303 0.662168i
\(5\) 0 0
\(6\) −2.05842 + 6.82701i −0.140058 + 0.464519i
\(7\) −4.43132 2.55842i −0.239269 0.138142i 0.375572 0.926793i \(-0.377446\pi\)
−0.614841 + 0.788651i \(0.710780\pi\)
\(8\) 19.3723i 0.856142i
\(9\) −24.1753 + 12.0232i −0.895380 + 0.445302i
\(10\) 0 0
\(11\) −27.9891 + 48.4786i −0.767185 + 1.32880i 0.171898 + 0.985115i \(0.445010\pi\)
−0.939083 + 0.343689i \(0.888323\pi\)
\(12\) −23.1615 + 21.7663i −0.557178 + 0.523616i
\(13\) 32.5489 18.7921i 0.694418 0.400923i −0.110847 0.993838i \(-0.535356\pi\)
0.805265 + 0.592915i \(0.202023\pi\)
\(14\) 3.51087 + 6.08101i 0.0670229 + 0.116087i
\(15\) 0 0
\(16\) −11.1753 + 19.3561i −0.174614 + 0.302440i
\(17\) 23.6495i 0.337402i −0.985667 0.168701i \(-0.946043\pi\)
0.985667 0.168701i \(-0.0539573\pi\)
\(18\) 36.9802 + 2.29894i 0.484240 + 0.0301036i
\(19\) −39.0516 −0.471529 −0.235764 0.971810i \(-0.575759\pi\)
−0.235764 + 0.971810i \(0.575759\pi\)
\(20\) 0 0
\(21\) −7.67527 + 25.4560i −0.0797562 + 0.264521i
\(22\) 66.5263 38.4090i 0.644702 0.372219i
\(23\) 61.5513 35.5367i 0.558015 0.322170i −0.194334 0.980936i \(-0.562254\pi\)
0.752348 + 0.658766i \(0.228921\pi\)
\(24\) 97.9932 23.0226i 0.833449 0.195811i
\(25\) 0 0
\(26\) −51.5761 −0.389035
\(27\) 89.5489 + 108.000i 0.638285 + 0.769800i
\(28\) 31.2989i 0.211248i
\(29\) −14.1861 + 24.5711i −0.0908379 + 0.157336i −0.907864 0.419265i \(-0.862288\pi\)
0.817026 + 0.576601i \(0.195621\pi\)
\(30\) 0 0
\(31\) −6.44158 11.1571i −0.0373207 0.0646413i 0.846762 0.531972i \(-0.178549\pi\)
−0.884082 + 0.467331i \(0.845216\pi\)
\(32\) 160.777 92.8247i 0.888177 0.512789i
\(33\) 278.488 + 83.9674i 1.46905 + 0.442935i
\(34\) −16.2269 + 28.1057i −0.0818495 + 0.141768i
\(35\) 0 0
\(36\) 137.629 + 91.2927i 0.637171 + 0.422652i
\(37\) 180.103i 0.800237i 0.916463 + 0.400119i \(0.131031\pi\)
−0.916463 + 0.400119i \(0.868969\pi\)
\(38\) 46.4101 + 26.7949i 0.198124 + 0.114387i
\(39\) −133.741 142.313i −0.549119 0.584315i
\(40\) 0 0
\(41\) 107.742 + 186.614i 0.410401 + 0.710835i 0.994934 0.100535i \(-0.0320554\pi\)
−0.584533 + 0.811370i \(0.698722\pi\)
\(42\) 26.5879 24.9863i 0.0976810 0.0917971i
\(43\) −53.0299 30.6168i −0.188069 0.108582i 0.403009 0.915196i \(-0.367964\pi\)
−0.591078 + 0.806614i \(0.701298\pi\)
\(44\) 342.410 1.17319
\(45\) 0 0
\(46\) −97.5326 −0.312617
\(47\) −53.5876 30.9388i −0.166310 0.0960189i 0.414535 0.910033i \(-0.363944\pi\)
−0.580845 + 0.814014i \(0.697278\pi\)
\(48\) 111.192 + 33.5258i 0.334359 + 0.100813i
\(49\) −158.409 274.372i −0.461834 0.799919i
\(50\) 0 0
\(51\) −119.629 + 28.1057i −0.328459 + 0.0771685i
\(52\) −199.096 114.948i −0.530956 0.306548i
\(53\) 492.310i 1.27592i 0.770068 + 0.637962i \(0.220222\pi\)
−0.770068 + 0.637962i \(0.779778\pi\)
\(54\) −32.3194 189.794i −0.0814466 0.478290i
\(55\) 0 0
\(56\) 49.5625 85.8447i 0.118269 0.204848i
\(57\) 46.4101 + 197.539i 0.107845 + 0.459031i
\(58\) 33.7185 19.4674i 0.0763354 0.0440723i
\(59\) 394.815 + 683.840i 0.871196 + 1.50896i 0.860761 + 0.509010i \(0.169988\pi\)
0.0104351 + 0.999946i \(0.496678\pi\)
\(60\) 0 0
\(61\) −260.545 + 451.277i −0.546874 + 0.947214i 0.451612 + 0.892214i \(0.350849\pi\)
−0.998486 + 0.0549998i \(0.982484\pi\)
\(62\) 17.6793i 0.0362141i
\(63\) 137.889 + 8.57207i 0.275751 + 0.0171425i
\(64\) −75.9590 −0.148358
\(65\) 0 0
\(66\) −273.351 290.872i −0.509805 0.542482i
\(67\) −263.644 + 152.215i −0.480734 + 0.277552i −0.720722 0.693224i \(-0.756190\pi\)
0.239988 + 0.970776i \(0.422856\pi\)
\(68\) −125.279 + 72.3301i −0.223417 + 0.128990i
\(69\) −252.909 269.120i −0.441256 0.469539i
\(70\) 0 0
\(71\) 270.391 0.451966 0.225983 0.974131i \(-0.427441\pi\)
0.225983 + 0.974131i \(0.427441\pi\)
\(72\) −232.916 468.330i −0.381242 0.766573i
\(73\) 925.464i 1.48380i −0.670510 0.741900i \(-0.733925\pi\)
0.670510 0.741900i \(-0.266075\pi\)
\(74\) 123.576 214.040i 0.194127 0.336239i
\(75\) 0 0
\(76\) 119.436 + 206.870i 0.180267 + 0.312231i
\(77\) 248.057 143.216i 0.367127 0.211961i
\(78\) 61.2946 + 260.894i 0.0889776 + 0.378723i
\(79\) −644.517 + 1116.34i −0.917897 + 1.58984i −0.115294 + 0.993331i \(0.536781\pi\)
−0.802603 + 0.596513i \(0.796552\pi\)
\(80\) 0 0
\(81\) 439.887 581.326i 0.603411 0.797430i
\(82\) 295.704i 0.398232i
\(83\) −618.198 356.917i −0.817543 0.472009i 0.0320252 0.999487i \(-0.489804\pi\)
−0.849569 + 0.527478i \(0.823138\pi\)
\(84\) 158.323 37.1966i 0.205649 0.0483153i
\(85\) 0 0
\(86\) 42.0149 + 72.7720i 0.0526812 + 0.0912466i
\(87\) 141.150 + 42.5584i 0.173941 + 0.0524453i
\(88\) −939.141 542.213i −1.13764 0.656820i
\(89\) 404.804 0.482125 0.241063 0.970510i \(-0.422504\pi\)
0.241063 + 0.970510i \(0.422504\pi\)
\(90\) 0 0
\(91\) −192.313 −0.221537
\(92\) −376.500 217.372i −0.426661 0.246333i
\(93\) −48.7822 + 45.8437i −0.0543922 + 0.0511158i
\(94\) 42.4567 + 73.5372i 0.0465859 + 0.0806892i
\(95\) 0 0
\(96\) −660.619 702.963i −0.702335 0.747353i
\(97\) 64.9756 + 37.5137i 0.0680131 + 0.0392674i 0.533621 0.845724i \(-0.320831\pi\)
−0.465608 + 0.884991i \(0.654164\pi\)
\(98\) 434.763i 0.448140i
\(99\) 93.7785 1508.50i 0.0952029 1.53141i
\(100\) 0 0
\(101\) 543.939 942.130i 0.535881 0.928172i −0.463240 0.886233i \(-0.653313\pi\)
0.999120 0.0419392i \(-0.0133536\pi\)
\(102\) 161.455 + 48.6806i 0.156730 + 0.0472558i
\(103\) −945.542 + 545.909i −0.904534 + 0.522233i −0.878669 0.477432i \(-0.841568\pi\)
−0.0258657 + 0.999665i \(0.508234\pi\)
\(104\) 364.046 + 630.546i 0.343247 + 0.594521i
\(105\) 0 0
\(106\) 337.794 585.076i 0.309523 0.536109i
\(107\) 1029.15i 0.929833i 0.885354 + 0.464917i \(0.153916\pi\)
−0.885354 + 0.464917i \(0.846084\pi\)
\(108\) 298.235 804.681i 0.265719 0.716948i
\(109\) −1776.52 −1.56110 −0.780548 0.625096i \(-0.785060\pi\)
−0.780548 + 0.625096i \(0.785060\pi\)
\(110\) 0 0
\(111\) 911.038 214.040i 0.779026 0.183025i
\(112\) 99.0423 57.1821i 0.0835591 0.0482429i
\(113\) −1399.44 + 807.969i −1.16503 + 0.672631i −0.952505 0.304524i \(-0.901502\pi\)
−0.212526 + 0.977155i \(0.568169\pi\)
\(114\) 80.3847 266.606i 0.0660413 0.219034i
\(115\) 0 0
\(116\) 173.549 0.138910
\(117\) −560.937 + 845.645i −0.443237 + 0.668204i
\(118\) 1083.59i 0.845364i
\(119\) −60.5053 + 104.798i −0.0466094 + 0.0807298i
\(120\) 0 0
\(121\) −901.282 1561.07i −0.677147 1.17285i
\(122\) 619.279 357.541i 0.459564 0.265330i
\(123\) 815.930 766.781i 0.598130 0.562100i
\(124\) −39.4021 + 68.2465i −0.0285356 + 0.0494251i
\(125\) 0 0
\(126\) −157.989 104.798i −0.111705 0.0740966i
\(127\) 1206.10i 0.842711i 0.906895 + 0.421356i \(0.138446\pi\)
−0.906895 + 0.421356i \(0.861554\pi\)
\(128\) −1195.95 690.479i −0.825841 0.476799i
\(129\) −91.8505 + 304.634i −0.0626898 + 0.207919i
\(130\) 0 0
\(131\) 513.928 + 890.149i 0.342764 + 0.593684i 0.984945 0.172869i \(-0.0553036\pi\)
−0.642181 + 0.766553i \(0.721970\pi\)
\(132\) −406.931 1732.06i −0.268324 1.14209i
\(133\) 173.050 + 99.9105i 0.112822 + 0.0651379i
\(134\) 417.763 0.269322
\(135\) 0 0
\(136\) 458.144 0.288864
\(137\) −1091.98 630.454i −0.680978 0.393163i 0.119245 0.992865i \(-0.461952\pi\)
−0.800223 + 0.599702i \(0.795286\pi\)
\(138\) 115.911 + 493.361i 0.0714998 + 0.304331i
\(139\) 230.916 + 399.958i 0.140907 + 0.244057i 0.927838 0.372983i \(-0.121665\pi\)
−0.786932 + 0.617040i \(0.788332\pi\)
\(140\) 0 0
\(141\) −92.8164 + 307.837i −0.0554365 + 0.183862i
\(142\) −321.341 185.527i −0.189904 0.109641i
\(143\) 2103.90i 1.23033i
\(144\) 37.4431 602.302i 0.0216685 0.348554i
\(145\) 0 0
\(146\) −634.999 + 1099.85i −0.359951 + 0.623454i
\(147\) −1199.63 + 1127.37i −0.673089 + 0.632545i
\(148\) 954.068 550.832i 0.529891 0.305933i
\(149\) 729.661 + 1263.81i 0.401182 + 0.694868i 0.993869 0.110565i \(-0.0352660\pi\)
−0.592687 + 0.805433i \(0.701933\pi\)
\(150\) 0 0
\(151\) −770.659 + 1334.82i −0.415333 + 0.719378i −0.995463 0.0951456i \(-0.969668\pi\)
0.580130 + 0.814524i \(0.303002\pi\)
\(152\) 756.518i 0.403696i
\(153\) 284.341 + 571.732i 0.150246 + 0.302103i
\(154\) −393.065 −0.205676
\(155\) 0 0
\(156\) −344.845 + 1143.72i −0.176985 + 0.586994i
\(157\) 2784.77 1607.79i 1.41560 0.817295i 0.419688 0.907668i \(-0.362139\pi\)
0.995908 + 0.0903734i \(0.0288060\pi\)
\(158\) 1531.93 884.459i 0.771352 0.445341i
\(159\) 2490.31 585.076i 1.24210 0.291821i
\(160\) 0 0
\(161\) −363.671 −0.178021
\(162\) −921.647 + 389.042i −0.446984 + 0.188679i
\(163\) 947.587i 0.455342i 0.973738 + 0.227671i \(0.0731111\pi\)
−0.973738 + 0.227671i \(0.926889\pi\)
\(164\) 659.040 1141.49i 0.313795 0.543509i
\(165\) 0 0
\(166\) 489.791 + 848.342i 0.229007 + 0.396651i
\(167\) −594.058 + 342.980i −0.275267 + 0.158926i −0.631279 0.775556i \(-0.717470\pi\)
0.356012 + 0.934481i \(0.384136\pi\)
\(168\) −493.140 148.687i −0.226468 0.0682826i
\(169\) −392.213 + 679.333i −0.178522 + 0.309209i
\(170\) 0 0
\(171\) 944.083 469.524i 0.422198 0.209973i
\(172\) 374.557i 0.166045i
\(173\) 1916.36 + 1106.41i 0.842188 + 0.486237i 0.858007 0.513637i \(-0.171702\pi\)
−0.0158193 + 0.999875i \(0.505036\pi\)
\(174\) −138.546 147.427i −0.0603630 0.0642321i
\(175\) 0 0
\(176\) −625.572 1083.52i −0.267922 0.464054i
\(177\) 2989.94 2809.84i 1.26970 1.19322i
\(178\) −481.082 277.753i −0.202576 0.116958i
\(179\) −3023.22 −1.26238 −0.631190 0.775629i \(-0.717433\pi\)
−0.631190 + 0.775629i \(0.717433\pi\)
\(180\) 0 0
\(181\) 391.445 0.160751 0.0803753 0.996765i \(-0.474388\pi\)
0.0803753 + 0.996765i \(0.474388\pi\)
\(182\) 228.550 + 131.953i 0.0930839 + 0.0537420i
\(183\) 2592.39 + 781.634i 1.04718 + 0.315738i
\(184\) 688.426 + 1192.39i 0.275823 + 0.477740i
\(185\) 0 0
\(186\) 89.4294 21.0106i 0.0352542 0.00828266i
\(187\) 1146.49 + 661.928i 0.448341 + 0.258850i
\(188\) 378.496i 0.146833i
\(189\) −120.510 707.686i −0.0463799 0.272363i
\(190\) 0 0
\(191\) −1742.79 + 3018.61i −0.660231 + 1.14355i 0.320324 + 0.947308i \(0.396208\pi\)
−0.980555 + 0.196246i \(0.937125\pi\)
\(192\) 90.2720 + 384.233i 0.0339314 + 0.144425i
\(193\) 1918.31 1107.53i 0.715455 0.413068i −0.0976228 0.995223i \(-0.531124\pi\)
0.813077 + 0.582156i \(0.197791\pi\)
\(194\) −51.4793 89.1647i −0.0190515 0.0329982i
\(195\) 0 0
\(196\) −968.963 + 1678.29i −0.353121 + 0.611623i
\(197\) 3975.11i 1.43764i 0.695196 + 0.718820i \(0.255318\pi\)
−0.695196 + 0.718820i \(0.744682\pi\)
\(198\) −1146.49 + 1728.40i −0.411504 + 0.620365i
\(199\) 1555.34 0.554046 0.277023 0.960863i \(-0.410652\pi\)
0.277023 + 0.960863i \(0.410652\pi\)
\(200\) 0 0
\(201\) 1083.29 + 1152.72i 0.380146 + 0.404512i
\(202\) −1292.87 + 746.437i −0.450326 + 0.259996i
\(203\) 125.727 72.5883i 0.0434693 0.0250970i
\(204\) 514.762 + 547.756i 0.176669 + 0.187993i
\(205\) 0 0
\(206\) 1498.28 0.506749
\(207\) −1060.76 + 1599.15i −0.356172 + 0.536950i
\(208\) 840.027i 0.280026i
\(209\) 1093.02 1893.17i 0.361750 0.626570i
\(210\) 0 0
\(211\) −873.865 1513.58i −0.285115 0.493834i 0.687522 0.726164i \(-0.258699\pi\)
−0.972637 + 0.232329i \(0.925365\pi\)
\(212\) 2607.93 1505.69i 0.844875 0.487789i
\(213\) −321.341 1367.75i −0.103371 0.439986i
\(214\) 706.145 1223.08i 0.225566 0.390691i
\(215\) 0 0
\(216\) −2092.21 + 1734.77i −0.659058 + 0.546462i
\(217\) 65.9211i 0.0206222i
\(218\) 2111.27 + 1218.94i 0.655931 + 0.378702i
\(219\) −4681.39 + 1099.85i −1.44447 + 0.339365i
\(220\) 0 0
\(221\) −444.423 769.764i −0.135272 0.234298i
\(222\) −1229.57 370.728i −0.371726 0.112080i
\(223\) 2201.39 + 1270.97i 0.661057 + 0.381662i 0.792680 0.609638i \(-0.208685\pi\)
−0.131622 + 0.991300i \(0.542019\pi\)
\(224\) −949.939 −0.283350
\(225\) 0 0
\(226\) 2217.52 0.652687
\(227\) −2592.24 1496.63i −0.757943 0.437598i 0.0706140 0.997504i \(-0.477504\pi\)
−0.828557 + 0.559905i \(0.810837\pi\)
\(228\) 904.492 850.009i 0.262726 0.246900i
\(229\) −2152.65 3728.50i −0.621185 1.07592i −0.989265 0.146130i \(-0.953318\pi\)
0.368081 0.929794i \(-0.380015\pi\)
\(230\) 0 0
\(231\) −1019.25 1084.58i −0.290309 0.308917i
\(232\) −475.999 274.818i −0.134702 0.0777702i
\(233\) 5581.34i 1.56930i −0.619942 0.784648i \(-0.712844\pi\)
0.619942 0.784648i \(-0.287156\pi\)
\(234\) 1246.87 620.108i 0.348334 0.173238i
\(235\) 0 0
\(236\) 2415.02 4182.94i 0.666121 1.15376i
\(237\) 6412.87 + 1933.55i 1.75764 + 0.529948i
\(238\) 143.813 83.0303i 0.0391680 0.0226137i
\(239\) 704.814 + 1220.77i 0.190756 + 0.330399i 0.945501 0.325619i \(-0.105573\pi\)
−0.754745 + 0.656018i \(0.772239\pi\)
\(240\) 0 0
\(241\) −313.286 + 542.627i −0.0837366 + 0.145036i −0.904852 0.425726i \(-0.860019\pi\)
0.821116 + 0.570762i \(0.193352\pi\)
\(242\) 2473.63i 0.657069i
\(243\) −3463.37 1534.27i −0.914302 0.405034i
\(244\) 3187.42 0.836286
\(245\) 0 0
\(246\) −1495.80 + 351.424i −0.387677 + 0.0910811i
\(247\) −1271.09 + 733.862i −0.327438 + 0.189047i
\(248\) 216.139 124.788i 0.0553422 0.0319518i
\(249\) −1070.75 + 3551.28i −0.272514 + 0.903828i
\(250\) 0 0
\(251\) 1705.53 0.428892 0.214446 0.976736i \(-0.431205\pi\)
0.214446 + 0.976736i \(0.431205\pi\)
\(252\) −376.312 756.660i −0.0940692 0.189147i
\(253\) 3978.56i 0.988656i
\(254\) 827.556 1433.37i 0.204431 0.354085i
\(255\) 0 0
\(256\) 1251.37 + 2167.43i 0.305510 + 0.529158i
\(257\) 3115.42 1798.69i 0.756166 0.436573i −0.0717513 0.997423i \(-0.522859\pi\)
0.827918 + 0.560850i \(0.189525\pi\)
\(258\) 318.180 299.014i 0.0767791 0.0721542i
\(259\) 460.780 798.094i 0.110546 0.191472i
\(260\) 0 0
\(261\) 47.5311 764.576i 0.0112724 0.181326i
\(262\) 1410.51i 0.332601i
\(263\) −3583.18 2068.75i −0.840108 0.485037i 0.0171926 0.999852i \(-0.494527\pi\)
−0.857301 + 0.514815i \(0.827860\pi\)
\(264\) −1626.64 + 5394.95i −0.379215 + 1.25771i
\(265\) 0 0
\(266\) −137.105 237.473i −0.0316032 0.0547384i
\(267\) −481.082 2047.67i −0.110269 0.469346i
\(268\) 1612.67 + 931.074i 0.367572 + 0.212218i
\(269\) −6090.99 −1.38057 −0.690287 0.723536i \(-0.742516\pi\)
−0.690287 + 0.723536i \(0.742516\pi\)
\(270\) 0 0
\(271\) −3196.62 −0.716534 −0.358267 0.933619i \(-0.616632\pi\)
−0.358267 + 0.933619i \(0.616632\pi\)
\(272\) 457.762 + 264.289i 0.102044 + 0.0589150i
\(273\) 228.550 + 972.798i 0.0506684 + 0.215665i
\(274\) 865.160 + 1498.50i 0.190753 + 0.330393i
\(275\) 0 0
\(276\) −652.117 + 2162.83i −0.142220 + 0.471692i
\(277\) −2701.45 1559.68i −0.585972 0.338311i 0.177531 0.984115i \(-0.443189\pi\)
−0.763503 + 0.645804i \(0.776522\pi\)
\(278\) 633.763i 0.136729i
\(279\) 289.871 + 192.279i 0.0622012 + 0.0412596i
\(280\) 0 0
\(281\) −2474.17 + 4285.38i −0.525254 + 0.909767i 0.474313 + 0.880356i \(0.342696\pi\)
−0.999567 + 0.0294105i \(0.990637\pi\)
\(282\) 321.525 302.158i 0.0678956 0.0638058i
\(283\) −3936.03 + 2272.47i −0.826758 + 0.477329i −0.852741 0.522333i \(-0.825062\pi\)
0.0259834 + 0.999662i \(0.491728\pi\)
\(284\) −826.971 1432.36i −0.172788 0.299277i
\(285\) 0 0
\(286\) 1443.57 2500.34i 0.298462 0.516951i
\(287\) 1102.60i 0.226774i
\(288\) −2770.78 + 4177.11i −0.566910 + 0.854648i
\(289\) 4353.70 0.886160
\(290\) 0 0
\(291\) 112.541 373.256i 0.0226710 0.0751913i
\(292\) −4902.50 + 2830.46i −0.982525 + 0.567261i
\(293\) 5941.03 3430.05i 1.18457 0.683911i 0.227501 0.973778i \(-0.426944\pi\)
0.957067 + 0.289867i \(0.0936111\pi\)
\(294\) 2199.22 516.686i 0.436262 0.102496i
\(295\) 0 0
\(296\) −3489.01 −0.685117
\(297\) −7742.08 + 1318.38i −1.51260 + 0.257576i
\(298\) 2002.60i 0.389287i
\(299\) 1335.62 2313.36i 0.258330 0.447441i
\(300\) 0 0
\(301\) 156.662 + 271.346i 0.0299994 + 0.0519605i
\(302\) 1831.75 1057.56i 0.349024 0.201509i
\(303\) −5412.12 1631.82i −1.02613 0.309391i
\(304\) 436.412 755.888i 0.0823353 0.142609i
\(305\) 0 0
\(306\) 54.3686 874.562i 0.0101570 0.163384i
\(307\) 6332.25i 1.17720i −0.808424 0.588600i \(-0.799679\pi\)
0.808424 0.588600i \(-0.200321\pi\)
\(308\) −1517.33 876.030i −0.280707 0.162066i
\(309\) 3885.15 + 4134.18i 0.715270 + 0.761117i
\(310\) 0 0
\(311\) −3538.84 6129.44i −0.645238 1.11758i −0.984247 0.176801i \(-0.943425\pi\)
0.339009 0.940783i \(-0.389908\pi\)
\(312\) 2756.93 2590.86i 0.500257 0.470123i
\(313\) −1196.24 690.649i −0.216024 0.124721i 0.388084 0.921624i \(-0.373137\pi\)
−0.604108 + 0.796903i \(0.706470\pi\)
\(314\) −4412.67 −0.793062
\(315\) 0 0
\(316\) 7884.83 1.40366
\(317\) −7079.70 4087.47i −1.25437 0.724211i −0.282396 0.959298i \(-0.591129\pi\)
−0.971974 + 0.235086i \(0.924463\pi\)
\(318\) −3361.00 1013.38i −0.592691 0.178703i
\(319\) −794.115 1375.45i −0.139379 0.241412i
\(320\) 0 0
\(321\) 5205.90 1223.08i 0.905187 0.212665i
\(322\) 432.198 + 249.530i 0.0747995 + 0.0431855i
\(323\) 923.549i 0.159095i
\(324\) −4424.85 552.290i −0.758718 0.0947000i
\(325\) 0 0
\(326\) 650.178 1126.14i 0.110460 0.191323i
\(327\) 2111.27 + 8986.37i 0.357044 + 1.51972i
\(328\) −3615.14 + 2087.20i −0.608576 + 0.351361i
\(329\) 158.309 + 274.199i 0.0265284 + 0.0459486i
\(330\) 0 0
\(331\) 4830.64 8366.92i 0.802163 1.38939i −0.116026 0.993246i \(-0.537016\pi\)
0.918189 0.396142i \(-0.129651\pi\)
\(332\) 4366.41i 0.721801i
\(333\) −2165.41 4354.04i −0.356348 0.716517i
\(334\) 941.329 0.154213
\(335\) 0 0
\(336\) −406.956 433.041i −0.0660752 0.0703104i
\(337\) 4292.04 2478.01i 0.693776 0.400552i −0.111249 0.993793i \(-0.535485\pi\)
0.805025 + 0.593241i \(0.202152\pi\)
\(338\) 932.236 538.227i 0.150021 0.0866144i
\(339\) 5750.19 + 6118.76i 0.921260 + 0.980311i
\(340\) 0 0
\(341\) 721.177 0.114528
\(342\) −1444.14 89.7771i −0.228333 0.0141947i
\(343\) 3376.19i 0.531478i
\(344\) 593.118 1027.31i 0.0929616 0.161014i
\(345\) 0 0
\(346\) −1518.31 2629.79i −0.235910 0.408608i
\(347\) 879.540 507.802i 0.136070 0.0785598i −0.430420 0.902629i \(-0.641635\pi\)
0.566490 + 0.824069i \(0.308301\pi\)
\(348\) −206.251 877.883i −0.0317707 0.135228i
\(349\) 6079.29 10529.6i 0.932426 1.61501i 0.153267 0.988185i \(-0.451021\pi\)
0.779160 0.626825i \(-0.215646\pi\)
\(350\) 0 0
\(351\) 4944.26 + 1832.47i 0.751867 + 0.278661i
\(352\) 10392.3i 1.57362i
\(353\) −3668.56 2118.04i −0.553138 0.319354i 0.197249 0.980353i \(-0.436799\pi\)
−0.750387 + 0.660999i \(0.770133\pi\)
\(354\) −5481.28 + 1287.78i −0.822957 + 0.193346i
\(355\) 0 0
\(356\) −1238.06 2144.39i −0.184318 0.319248i
\(357\) 602.020 + 181.516i 0.0892501 + 0.0269099i
\(358\) 3592.88 + 2074.35i 0.530418 + 0.306237i
\(359\) 517.939 0.0761443 0.0380721 0.999275i \(-0.487878\pi\)
0.0380721 + 0.999275i \(0.487878\pi\)
\(360\) 0 0
\(361\) −5333.97 −0.777660
\(362\) −465.205 268.586i −0.0675432 0.0389961i
\(363\) −6825.42 + 6414.29i −0.986892 + 0.927445i
\(364\) 588.173 + 1018.75i 0.0846941 + 0.146694i
\(365\) 0 0
\(366\) −2544.56 2707.66i −0.363405 0.386699i
\(367\) −3997.83 2308.15i −0.568624 0.328295i 0.187976 0.982174i \(-0.439807\pi\)
−0.756600 + 0.653879i \(0.773141\pi\)
\(368\) 1588.53i 0.225021i
\(369\) −4848.38 3216.05i −0.684002 0.453715i
\(370\) 0 0
\(371\) 1259.54 2181.58i 0.176258 0.305288i
\(372\) 392.046 + 118.206i 0.0546415 + 0.0164750i
\(373\) 4126.98 2382.71i 0.572887 0.330756i −0.185415 0.982660i \(-0.559363\pi\)
0.758301 + 0.651904i \(0.226030\pi\)
\(374\) −908.351 1573.31i −0.125588 0.217524i
\(375\) 0 0
\(376\) 599.355 1038.11i 0.0822058 0.142385i
\(377\) 1066.35i 0.145676i
\(378\) −342.355 + 923.722i −0.0465842 + 0.125691i
\(379\) 2000.33 0.271108 0.135554 0.990770i \(-0.456719\pi\)
0.135554 + 0.990770i \(0.456719\pi\)
\(380\) 0 0
\(381\) 6100.98 1433.37i 0.820374 0.192740i
\(382\) 4142.38 2391.60i 0.554823 0.320327i
\(383\) 857.619 495.147i 0.114419 0.0660596i −0.441699 0.897164i \(-0.645624\pi\)
0.556117 + 0.831104i \(0.312291\pi\)
\(384\) −2071.44 + 6870.18i −0.275280 + 0.913001i
\(385\) 0 0
\(386\) −3039.70 −0.400820
\(387\) 1650.12 + 102.583i 0.216746 + 0.0134743i
\(388\) 458.930i 0.0600481i
\(389\) 202.205 350.230i 0.0263553 0.0456487i −0.852547 0.522651i \(-0.824943\pi\)
0.878902 + 0.477002i \(0.158277\pi\)
\(390\) 0 0
\(391\) −840.423 1455.66i −0.108701 0.188275i
\(392\) 5315.22 3068.74i 0.684845 0.395395i
\(393\) 3891.98 3657.54i 0.499553 0.469462i
\(394\) 2727.49 4724.15i 0.348753 0.604059i
\(395\) 0 0
\(396\) −8277.86 + 4116.85i −1.05045 + 0.522424i
\(397\) 2919.61i 0.369096i −0.982824 0.184548i \(-0.940918\pi\)
0.982824 0.184548i \(-0.0590821\pi\)
\(398\) −1848.42 1067.18i −0.232796 0.134405i
\(399\) 299.731 994.097i 0.0376074 0.124730i
\(400\) 0 0
\(401\) 5093.10 + 8821.52i 0.634258 + 1.09857i 0.986672 + 0.162723i \(0.0520277\pi\)
−0.352414 + 0.935844i \(0.614639\pi\)
\(402\) −496.482 2113.22i −0.0615977 0.262184i
\(403\) −419.332 242.102i −0.0518323 0.0299254i
\(404\) −6654.38 −0.819474
\(405\) 0 0
\(406\) −199.223 −0.0243529
\(407\) −8731.15 5040.93i −1.06336 0.613930i
\(408\) −544.472 2317.49i −0.0660672 0.281208i
\(409\) 3457.12 + 5987.91i 0.417955 + 0.723920i 0.995734 0.0922740i \(-0.0294136\pi\)
−0.577778 + 0.816194i \(0.696080\pi\)
\(410\) 0 0
\(411\) −1891.36 + 6272.94i −0.226993 + 0.752850i
\(412\) 5783.73 + 3339.24i 0.691612 + 0.399302i
\(413\) 4040.41i 0.481394i
\(414\) 2357.88 1172.65i 0.279911 0.139209i
\(415\) 0 0
\(416\) 3488.75 6042.68i 0.411177 0.712180i
\(417\) 1748.73 1643.39i 0.205361 0.192991i
\(418\) −2597.96 + 1499.93i −0.303996 + 0.175512i
\(419\) 2560.16 + 4434.32i 0.298501 + 0.517019i 0.975793 0.218695i \(-0.0701801\pi\)
−0.677292 + 0.735714i \(0.736847\pi\)
\(420\) 0 0
\(421\) −933.246 + 1616.43i −0.108037 + 0.187126i −0.914975 0.403511i \(-0.867790\pi\)
0.806938 + 0.590636i \(0.201123\pi\)
\(422\) 2398.38i 0.276662i
\(423\) 1667.48 + 103.661i 0.191668 + 0.0119153i
\(424\) −9537.16 −1.09237
\(425\) 0 0
\(426\) −556.580 + 1845.97i −0.0633014 + 0.209947i
\(427\) 2309.11 1333.17i 0.261700 0.151092i
\(428\) 5451.79 3147.59i 0.615706 0.355478i
\(429\) 10642.4 2500.34i 1.19772 0.281393i
\(430\) 0 0
\(431\) −4090.64 −0.457168 −0.228584 0.973524i \(-0.573410\pi\)
−0.228584 + 0.973524i \(0.573410\pi\)
\(432\) −3091.19 + 526.391i −0.344271 + 0.0586250i
\(433\) 633.052i 0.0702599i 0.999383 + 0.0351299i \(0.0111845\pi\)
−0.999383 + 0.0351299i \(0.988815\pi\)
\(434\) 45.2311 78.3426i 0.00500268 0.00866490i
\(435\) 0 0
\(436\) 5433.34 + 9410.81i 0.596811 + 1.03371i
\(437\) −2403.68 + 1387.76i −0.263120 + 0.151912i
\(438\) 6318.16 + 1905.00i 0.689254 + 0.207818i
\(439\) −5653.26 + 9791.74i −0.614614 + 1.06454i 0.375838 + 0.926685i \(0.377355\pi\)
−0.990452 + 0.137857i \(0.955979\pi\)
\(440\) 0 0
\(441\) 7128.40 + 4728.45i 0.769723 + 0.510576i
\(442\) 1219.75i 0.131261i
\(443\) 7171.82 + 4140.65i 0.769172 + 0.444082i 0.832579 0.553906i \(-0.186863\pi\)
−0.0634071 + 0.997988i \(0.520197\pi\)
\(444\) −3920.18 4171.45i −0.419017 0.445875i
\(445\) 0 0
\(446\) −1744.13 3020.92i −0.185173 0.320728i
\(447\) 5525.73 5192.88i 0.584694 0.549474i
\(448\) 336.599 + 194.335i 0.0354973 + 0.0204944i
\(449\) −6888.40 −0.724017 −0.362008 0.932175i \(-0.617909\pi\)
−0.362008 + 0.932175i \(0.617909\pi\)
\(450\) 0 0
\(451\) −12062.4 −1.25941
\(452\) 8560.17 + 4942.22i 0.890789 + 0.514297i
\(453\) 7667.96 + 2311.98i 0.795302 + 0.239793i
\(454\) 2053.80 + 3557.28i 0.212312 + 0.367735i
\(455\) 0 0
\(456\) −3826.79 + 899.070i −0.392995 + 0.0923307i
\(457\) 3709.71 + 2141.80i 0.379722 + 0.219233i 0.677697 0.735341i \(-0.262978\pi\)
−0.297975 + 0.954574i \(0.596311\pi\)
\(458\) 5908.09i 0.602766i
\(459\) 2554.14 2117.78i 0.259732 0.215359i
\(460\) 0 0
\(461\) −6889.16 + 11932.4i −0.696009 + 1.20552i 0.273831 + 0.961778i \(0.411709\pi\)
−0.969840 + 0.243744i \(0.921624\pi\)
\(462\) 467.131 + 1988.29i 0.0470409 + 0.200224i
\(463\) 4966.25 2867.27i 0.498491 0.287804i −0.229599 0.973285i \(-0.573742\pi\)
0.728090 + 0.685481i \(0.240408\pi\)
\(464\) −317.068 549.178i −0.0317231 0.0549460i
\(465\) 0 0
\(466\) −3829.59 + 6633.04i −0.380691 + 0.659377i
\(467\) 8950.97i 0.886941i 0.896289 + 0.443470i \(0.146253\pi\)
−0.896289 + 0.443470i \(0.853747\pi\)
\(468\) 6195.25 + 385.138i 0.611914 + 0.0380406i
\(469\) 1557.72 0.153366
\(470\) 0 0
\(471\) −11442.4 12175.8i −1.11940 1.19115i
\(472\) −13247.5 + 7648.47i −1.29188 + 0.745867i
\(473\) 2968.52 1713.88i 0.288568 0.166605i
\(474\) −6294.56 6698.02i −0.609955 0.649051i
\(475\) 0 0
\(476\) 740.203 0.0712755
\(477\) −5919.12 11901.7i −0.568172 1.14244i
\(478\) 1934.41i 0.185100i
\(479\) 4840.51 8384.00i 0.461729 0.799739i −0.537318 0.843380i \(-0.680562\pi\)
0.999047 + 0.0436411i \(0.0138958\pi\)
\(480\) 0 0
\(481\) 3384.52 + 5862.16i 0.320833 + 0.555699i
\(482\) 744.637 429.917i 0.0703678 0.0406269i
\(483\) 432.198 + 1839.60i 0.0407157 + 0.173302i
\(484\) −5513.00 + 9548.80i −0.517750 + 0.896769i
\(485\) 0 0
\(486\) 3063.25 + 4199.73i 0.285909 + 0.391983i
\(487\) 8704.66i 0.809950i −0.914328 0.404975i \(-0.867280\pi\)
0.914328 0.404975i \(-0.132720\pi\)
\(488\) −8742.26 5047.35i −0.810950 0.468202i
\(489\) 4793.30 1126.14i 0.443273 0.104143i
\(490\) 0 0
\(491\) 7797.85 + 13506.3i 0.716725 + 1.24140i 0.962290 + 0.272024i \(0.0876930\pi\)
−0.245565 + 0.969380i \(0.578974\pi\)
\(492\) −6557.36 1977.12i −0.600871 0.181170i
\(493\) 581.094 + 335.495i 0.0530855 + 0.0306489i
\(494\) 2014.13 0.183441
\(495\) 0 0
\(496\) 287.945 0.0260668
\(497\) −1198.19 691.776i −0.108141 0.0624354i
\(498\) 3709.19 3485.76i 0.333761 0.313656i
\(499\) −4848.14 8397.22i −0.434935 0.753329i 0.562355 0.826896i \(-0.309895\pi\)
−0.997290 + 0.0735663i \(0.976562\pi\)
\(500\) 0 0
\(501\) 2440.93 + 2597.39i 0.217670 + 0.231622i
\(502\) −2026.90 1170.23i −0.180209 0.104044i
\(503\) 20949.7i 1.85706i 0.371253 + 0.928532i \(0.378928\pi\)
−0.371253 + 0.928532i \(0.621072\pi\)
\(504\) −166.061 + 2671.22i −0.0146764 + 0.236082i
\(505\) 0 0
\(506\) 2729.85 4728.24i 0.239835 0.415407i
\(507\) 3902.47 + 1176.64i 0.341844 + 0.103070i
\(508\) 6389.14 3688.77i 0.558016 0.322171i
\(509\) 5637.37 + 9764.22i 0.490908 + 0.850278i 0.999945 0.0104668i \(-0.00333174\pi\)
−0.509037 + 0.860745i \(0.669998\pi\)
\(510\) 0 0
\(511\) −2367.73 + 4101.03i −0.204975 + 0.355027i
\(512\) 7613.21i 0.657148i
\(513\) −3497.03 4217.57i −0.300970 0.362983i
\(514\) −4936.62 −0.423628
\(515\) 0 0
\(516\) 1894.67 445.135i 0.161644 0.0379767i
\(517\) 2999.74 1731.90i 0.255181 0.147329i
\(518\) −1095.21 + 632.320i −0.0928972 + 0.0536342i
\(519\) 3319.24 11008.7i 0.280729 0.931074i
\(520\) 0 0
\(521\) 8675.49 0.729520 0.364760 0.931102i \(-0.381151\pi\)
0.364760 + 0.931102i \(0.381151\pi\)
\(522\) −581.094 + 876.032i −0.0487237 + 0.0734538i
\(523\) 4226.14i 0.353339i −0.984270 0.176670i \(-0.943468\pi\)
0.984270 0.176670i \(-0.0565324\pi\)
\(524\) 3143.62 5444.90i 0.262079 0.453934i
\(525\) 0 0
\(526\) 2838.91 + 4917.14i 0.235328 + 0.407599i
\(527\) −263.860 + 152.340i −0.0218101 + 0.0125921i
\(528\) −4737.46 + 4452.10i −0.390477 + 0.366956i
\(529\) −3557.79 + 6162.27i −0.292413 + 0.506474i
\(530\) 0 0
\(531\) −17766.7 11785.1i −1.45199 0.963143i
\(532\) 1222.27i 0.0996095i
\(533\) 7013.75 + 4049.39i 0.569980 + 0.329078i
\(534\) −833.258 + 2763.60i −0.0675255 + 0.223957i
\(535\) 0 0
\(536\) −2948.75 5107.38i −0.237624 0.411577i
\(537\) 3592.88 + 15292.7i 0.288723 + 1.22892i
\(538\) 7238.72 + 4179.28i 0.580081 + 0.334910i
\(539\) 17734.9 1.41725
\(540\) 0 0
\(541\) 13357.8 1.06154 0.530771 0.847515i \(-0.321902\pi\)
0.530771 + 0.847515i \(0.321902\pi\)
\(542\) 3798.96 + 2193.33i 0.301069 + 0.173822i
\(543\) −465.205 1980.09i −0.0367658 0.156490i
\(544\) −2195.26 3802.29i −0.173016 0.299673i
\(545\) 0 0
\(546\) 395.860 1312.92i 0.0310280 0.102908i
\(547\) 18767.7 + 10835.6i 1.46700 + 0.846974i 0.999318 0.0369219i \(-0.0117553\pi\)
0.467684 + 0.883896i \(0.345089\pi\)
\(548\) 7712.78i 0.601229i
\(549\) 872.964 14042.3i 0.0678637 1.09164i
\(550\) 0 0
\(551\) 553.991 959.541i 0.0428327 0.0741884i
\(552\) 5213.46 4899.42i 0.401992 0.377778i
\(553\) 5712.12 3297.90i 0.439248 0.253600i
\(554\) 2140.32 + 3707.15i 0.164140 + 0.284299i
\(555\) 0 0
\(556\) 1412.48 2446.48i 0.107738 0.186608i
\(557\) 7477.63i 0.568828i −0.958702 0.284414i \(-0.908201\pi\)
0.958702 0.284414i \(-0.0917991\pi\)
\(558\) −212.561 427.402i −0.0161262 0.0324254i
\(559\) −2301.42 −0.174132
\(560\) 0 0
\(561\) 1985.78 6586.10i 0.149447 0.495660i
\(562\) 5880.75 3395.25i 0.441396 0.254840i
\(563\) −20182.4 + 11652.3i −1.51082 + 0.872269i −0.510895 + 0.859643i \(0.670686\pi\)
−0.999920 + 0.0126262i \(0.995981\pi\)
\(564\) 1914.59 449.816i 0.142941 0.0335827i
\(565\) 0 0
\(566\) 6236.92 0.463176
\(567\) −3436.56 + 1450.63i −0.254536 + 0.107444i
\(568\) 5238.10i 0.386947i
\(569\) −7324.54 + 12686.5i −0.539650 + 0.934701i 0.459273 + 0.888295i \(0.348110\pi\)
−0.998923 + 0.0464057i \(0.985223\pi\)
\(570\) 0 0
\(571\) −11582.0 20060.6i −0.848846 1.47025i −0.882239 0.470803i \(-0.843964\pi\)
0.0333922 0.999442i \(-0.489369\pi\)
\(572\) 11145.1 6434.61i 0.814683 0.470358i
\(573\) 17340.6 + 5228.38i 1.26425 + 0.381185i
\(574\) −756.536 + 1310.36i −0.0550125 + 0.0952845i
\(575\) 0 0
\(576\) 1836.33 913.268i 0.132836 0.0660640i
\(577\) 7865.97i 0.567529i −0.958894 0.283765i \(-0.908417\pi\)
0.958894 0.283765i \(-0.0915834\pi\)
\(578\) −5174.07 2987.25i −0.372341 0.214971i
\(579\) −7882.15 8387.38i −0.565753 0.602016i
\(580\) 0 0
\(581\) 1826.29 + 3163.23i 0.130408 + 0.225874i
\(582\) −389.853 + 366.370i −0.0277662 + 0.0260937i
\(583\) −23866.5 13779.3i −1.69545 0.978869i
\(584\) 17928.4 1.27034
\(585\) 0 0
\(586\) −9413.99 −0.663632
\(587\) −828.078 478.091i −0.0582256 0.0336166i 0.470605 0.882344i \(-0.344036\pi\)
−0.528830 + 0.848728i \(0.677369\pi\)
\(588\) 9641.06 + 2906.89i 0.676174 + 0.203874i
\(589\) 251.554 + 435.704i 0.0175978 + 0.0304803i
\(590\) 0 0
\(591\) 20107.8 4724.15i 1.39953 0.328808i
\(592\) −3486.10 2012.70i −0.242023 0.139732i
\(593\) 16966.0i 1.17489i −0.809265 0.587444i \(-0.800134\pi\)
0.809265 0.587444i \(-0.199866\pi\)
\(594\) 10105.5 + 3745.36i 0.698038 + 0.258710i
\(595\) 0 0
\(596\) 4463.22 7730.53i 0.306746 0.531300i
\(597\) −1848.42 7867.57i −0.126718 0.539361i
\(598\) −3174.58 + 1832.84i −0.217087 + 0.125335i
\(599\) −3095.70 5361.92i −0.211164 0.365746i 0.740915 0.671598i \(-0.234392\pi\)
−0.952079 + 0.305852i \(0.901059\pi\)
\(600\) 0 0
\(601\) 1359.27 2354.33i 0.0922559 0.159792i −0.816204 0.577764i \(-0.803926\pi\)
0.908460 + 0.417972i \(0.137259\pi\)
\(602\) 429.968i 0.0291099i
\(603\) 4543.55 6849.66i 0.306845 0.462587i
\(604\) 9428.00 0.635132
\(605\) 0 0
\(606\) 5312.28 + 5652.78i 0.356100 + 0.378925i
\(607\) −14570.9 + 8412.49i −0.974321 + 0.562524i −0.900551 0.434751i \(-0.856836\pi\)
−0.0737701 + 0.997275i \(0.523503\pi\)
\(608\) −6278.60 + 3624.95i −0.418801 + 0.241795i
\(609\) −516.599 549.712i −0.0343738 0.0365771i
\(610\) 0 0
\(611\) −2325.62 −0.153985
\(612\) 2159.02 3254.85i 0.142604 0.214983i
\(613\) 20175.1i 1.32930i −0.747153 0.664652i \(-0.768580\pi\)
0.747153 0.664652i \(-0.231420\pi\)
\(614\) −4344.81 + 7525.44i −0.285574 + 0.494629i
\(615\) 0 0
\(616\) 2774.42 + 4805.44i 0.181468 + 0.314313i
\(617\) −9795.29 + 5655.31i −0.639130 + 0.369002i −0.784280 0.620408i \(-0.786967\pi\)
0.145149 + 0.989410i \(0.453634\pi\)
\(618\) −1780.60 7578.94i −0.115900 0.493317i
\(619\) −8529.94 + 14774.3i −0.553873 + 0.959336i 0.444117 + 0.895969i \(0.353517\pi\)
−0.997990 + 0.0633676i \(0.979816\pi\)
\(620\) 0 0
\(621\) 9349.81 + 3465.27i 0.604179 + 0.223924i
\(622\) 9712.56i 0.626106i
\(623\) −1793.82 1035.66i −0.115357 0.0666017i
\(624\) 4249.21 998.314i 0.272604 0.0640457i
\(625\) 0 0
\(626\) 947.764 + 1641.58i 0.0605116 + 0.104809i
\(627\) −10875.4 3279.06i −0.692699 0.208857i
\(628\) −17034.0 9834.58i −1.08237 0.624908i
\(629\) 4259.34 0.270002
\(630\) 0 0
\(631\) −13186.3 −0.831916 −0.415958 0.909384i \(-0.636554\pi\)
−0.415958 + 0.909384i \(0.636554\pi\)
\(632\) −21626.0 12485.8i −1.36113 0.785850i
\(633\) −6617.79 + 6219.16i −0.415535 + 0.390505i
\(634\) 5609.15 + 9715.34i 0.351369 + 0.608589i
\(635\) 0 0
\(636\) −10715.8 11402.6i −0.668094 0.710917i
\(637\) −10312.1 5953.68i −0.641412 0.370319i
\(638\) 2179.50i 0.135246i
\(639\) −6536.79 + 3250.96i −0.404681 + 0.201261i
\(640\) 0 0
\(641\) −8180.99 + 14169.9i −0.504102 + 0.873131i 0.495886 + 0.868387i \(0.334843\pi\)
−0.999989 + 0.00474343i \(0.998490\pi\)
\(642\) −7026.05 2118.43i −0.431926 0.130230i
\(643\) −24287.6 + 14022.5i −1.48960 + 0.860019i −0.999929 0.0118907i \(-0.996215\pi\)
−0.489667 + 0.871910i \(0.662882\pi\)
\(644\) 1112.26 + 1926.49i 0.0680577 + 0.117879i
\(645\) 0 0
\(646\) 633.685 1097.57i 0.0385944 0.0668475i
\(647\) 21247.7i 1.29109i −0.763724 0.645543i \(-0.776631\pi\)
0.763724 0.645543i \(-0.223369\pi\)
\(648\) 11261.6 + 8521.61i 0.682713 + 0.516606i
\(649\) −44202.1 −2.67347
\(650\) 0 0
\(651\) 333.457 78.3426i 0.0200756 0.00471657i
\(652\) 5019.69 2898.12i 0.301513 0.174079i
\(653\) 1091.07 629.928i 0.0653856 0.0377504i −0.466951 0.884283i \(-0.654647\pi\)
0.532336 + 0.846533i \(0.321314\pi\)
\(654\) 3656.82 12128.3i 0.218644 0.725159i
\(655\) 0 0
\(656\) −4816.17 −0.286646
\(657\) 11127.0 + 22373.3i 0.660740 + 1.32857i
\(658\) 434.489i 0.0257419i
\(659\) −6023.35 + 10432.7i −0.356049 + 0.616695i −0.987297 0.158886i \(-0.949210\pi\)
0.631248 + 0.775581i \(0.282543\pi\)
\(660\) 0 0
\(661\) −6554.04 11351.9i −0.385662 0.667986i 0.606199 0.795313i \(-0.292693\pi\)
−0.991861 + 0.127327i \(0.959360\pi\)
\(662\) −11481.8 + 6629.00i −0.674096 + 0.389189i
\(663\) −3365.62 + 3162.89i −0.197149 + 0.185274i
\(664\) 6914.30 11975.9i 0.404107 0.699933i
\(665\) 0 0
\(666\) −414.046 + 6660.25i −0.0240900 + 0.387507i
\(667\) 2016.51i 0.117061i
\(668\) 3633.76 + 2097.95i 0.210471 + 0.121515i
\(669\) 3812.91 12646.0i 0.220352 0.730826i
\(670\) 0 0
\(671\) −14584.8 25261.7i −0.839108 1.45338i
\(672\) 1128.94 + 4805.19i 0.0648061 + 0.275840i
\(673\) −2376.07 1371.82i −0.136093 0.0785734i 0.430408 0.902635i \(-0.358370\pi\)
−0.566501 + 0.824061i \(0.691703\pi\)
\(674\) −6801.06 −0.388675
\(675\) 0 0
\(676\) 4798.21 0.272998
\(677\) 21654.1 + 12502.0i 1.22930 + 0.709735i 0.966883 0.255220i \(-0.0821478\pi\)
0.262415 + 0.964955i \(0.415481\pi\)
\(678\) −2635.37 11217.2i −0.149278 0.635387i
\(679\) −191.952 332.470i −0.0108489 0.0187909i
\(680\) 0 0
\(681\) −4489.89 + 14891.3i −0.252648 + 0.837937i
\(682\) −857.068 494.829i −0.0481215 0.0277829i
\(683\) 4846.23i 0.271502i −0.990743 0.135751i \(-0.956655\pi\)
0.990743 0.135751i \(-0.0433447\pi\)
\(684\) −5374.63 3565.13i −0.300445 0.199292i
\(685\) 0 0
\(686\) 2316.54 4012.36i 0.128930 0.223313i
\(687\) −16302.1 + 15320.1i −0.905331 + 0.850798i
\(688\) 1185.25 684.303i 0.0656790 0.0379198i
\(689\) 9251.54 + 16024.1i 0.511546 + 0.886024i
\(690\) 0 0
\(691\) −1742.29 + 3017.73i −0.0959187 + 0.166136i −0.909992 0.414627i \(-0.863912\pi\)
0.814073 + 0.580763i \(0.197246\pi\)
\(692\) 13535.5i 0.743560i
\(693\) −4274.94 + 6444.72i −0.234331 + 0.353268i
\(694\) −1393.70 −0.0762305
\(695\) 0 0
\(696\) −824.454 + 2734.40i −0.0449006 + 0.148919i
\(697\) 4413.33 2548.04i 0.239837 0.138470i
\(698\) −14449.6 + 8342.49i −0.783562 + 0.452390i
\(699\) −28232.8 + 6633.04i −1.52770 + 0.358919i
\(700\) 0 0
\(701\) 15701.4 0.845981 0.422991 0.906134i \(-0.360980\pi\)
0.422991 + 0.906134i \(0.360980\pi\)
\(702\) −4618.58 5570.22i −0.248315 0.299479i
\(703\) 7033.32i 0.377335i
\(704\) 2126.03 3682.39i 0.113818 0.197138i
\(705\) 0 0
\(706\) 2906.55 + 5034.29i 0.154943 + 0.268368i
\(707\) −4820.73 + 2783.25i −0.256439 + 0.148055i
\(708\) −24029.2 7245.07i −1.27552 0.384585i
\(709\) 7821.72 13547.6i 0.414317 0.717618i −0.581039 0.813875i \(-0.697354\pi\)
0.995356 + 0.0962572i \(0.0306871\pi\)
\(710\) 0 0
\(711\) 2159.48 34736.9i 0.113905 1.83226i
\(712\) 7841.98i 0.412768i
\(713\) −792.975 457.824i −0.0416510 0.0240472i
\(714\) −590.914 628.790i −0.0309725 0.0329578i
\(715\) 0 0
\(716\) 9246.27 + 16015.0i 0.482611 + 0.835907i
\(717\) 5337.57 5016.05i 0.278013 0.261266i
\(718\) −615.535 355.379i −0.0319938 0.0184716i
\(719\) 6964.13 0.361222 0.180611 0.983555i \(-0.442193\pi\)
0.180611 + 0.983555i \(0.442193\pi\)
\(720\) 0 0
\(721\) 5586.66 0.288569
\(722\) 6339.06 + 3659.86i 0.326752 + 0.188651i
\(723\) 3117.16 + 939.858i 0.160343 + 0.0483454i
\(724\) −1197.20 2073.62i −0.0614554 0.106444i
\(725\) 0 0
\(726\) 12512.6 2939.73i 0.639652 0.150281i
\(727\) −12303.8 7103.61i −0.627680 0.362391i 0.152173 0.988354i \(-0.451373\pi\)
−0.779853 + 0.625963i \(0.784706\pi\)
\(728\) 3725.53i 0.189667i
\(729\) −3645.00 + 19342.6i −0.185185 + 0.982704i
\(730\) 0 0
\(731\) −724.072 + 1254.13i −0.0366358 + 0.0634551i
\(732\) −3788.03 16123.3i −0.191270 0.814120i
\(733\) 22976.1 13265.3i 1.15777 0.668437i 0.206998 0.978341i \(-0.433630\pi\)
0.950768 + 0.309905i \(0.100297\pi\)
\(734\) 3167.43 + 5486.15i 0.159280 + 0.275882i
\(735\) 0 0
\(736\) 6597.36 11427.0i 0.330410 0.572288i
\(737\) 17041.4i 0.851735i
\(738\) 3555.30 + 7148.72i 0.177334 + 0.356569i
\(739\) 5683.47 0.282909 0.141455 0.989945i \(-0.454822\pi\)
0.141455 + 0.989945i \(0.454822\pi\)
\(740\) 0 0
\(741\) 5222.78 + 5557.55i 0.258925 + 0.275522i
\(742\) −2993.74 + 1728.44i −0.148118 + 0.0855161i
\(743\) −13482.8 + 7784.28i −0.665727 + 0.384358i −0.794456 0.607322i \(-0.792244\pi\)
0.128729 + 0.991680i \(0.458910\pi\)
\(744\) −888.097 945.022i −0.0437624 0.0465674i
\(745\) 0 0
\(746\) −6539.50 −0.320949
\(747\) 19236.4 + 1195.86i 0.942199 + 0.0585734i
\(748\) 8097.82i 0.395836i
\(749\) 2633.01 4560.51i 0.128449 0.222480i
\(750\) 0 0
\(751\) 4130.82 + 7154.79i 0.200713 + 0.347646i 0.948758 0.316002i \(-0.102341\pi\)
−0.748045 + 0.663648i \(0.769007\pi\)
\(752\) 1197.71 691.499i 0.0580798 0.0335324i
\(753\) −2026.90 8627.27i −0.0980933 0.417523i
\(754\) 731.666 1267.28i 0.0353391 0.0612092i
\(755\) 0 0
\(756\) −3380.29 + 2802.78i −0.162619 + 0.134836i
\(757\) 13381.5i 0.642481i 0.946998 + 0.321240i \(0.104100\pi\)
−0.946998 + 0.321240i \(0.895900\pi\)
\(758\) −2377.25 1372.51i −0.113913 0.0657674i
\(759\) 20125.2 4728.24i 0.962451 0.226119i
\(760\) 0 0
\(761\) −2724.92 4719.70i −0.129801 0.224821i 0.793799 0.608181i \(-0.208100\pi\)
−0.923599 + 0.383359i \(0.874767\pi\)
\(762\) −8234.08 2482.67i −0.391456 0.118028i
\(763\) 7872.31 + 4545.08i 0.373521 + 0.215652i
\(764\) 21320.8 1.00963
\(765\) 0 0
\(766\) −1358.96 −0.0641009
\(767\) 25701.6 + 14838.8i 1.20995 + 0.698564i
\(768\) 9476.63 8905.79i 0.445258 0.418438i
\(769\) −9681.98 16769.7i −0.454020 0.786385i 0.544612 0.838688i \(-0.316677\pi\)
−0.998631 + 0.0523033i \(0.983344\pi\)
\(770\) 0 0
\(771\) −12801.0 13621.5i −0.597946 0.636273i
\(772\) −11734.0 6774.62i −0.547041 0.315834i
\(773\) 1865.54i 0.0868033i −0.999058 0.0434017i \(-0.986180\pi\)
0.999058 0.0434017i \(-0.0138195\pi\)
\(774\) −1890.67 1254.13i −0.0878020 0.0582413i
\(775\) 0 0
\(776\) −726.725 + 1258.72i −0.0336184 + 0.0582288i
\(777\) −4584.70 1382.34i −0.211680 0.0638239i
\(778\) −480.614 + 277.483i −0.0221476 + 0.0127869i
\(779\) −4207.49 7287.58i −0.193516 0.335179i
\(780\) 0 0
\(781\) −7568.02 + 13108.2i −0.346741 + 0.600574i
\(782\) 2306.59i 0.105478i
\(783\) −3924.03 + 668.212i −0.179098 + 0.0304980i
\(784\) 7081.05 0.322570
\(785\) 0 0
\(786\) −7134.94 + 1676.29i −0.323785 + 0.0760703i
\(787\) 16634.0 9603.65i 0.753416 0.434985i −0.0735110 0.997294i \(-0.523420\pi\)
0.826927 + 0.562310i \(0.190087\pi\)
\(788\) 21057.5 12157.6i 0.951959 0.549614i
\(789\) −6206.25 + 20583.8i −0.280036 + 0.928775i
\(790\) 0 0
\(791\) 8268.50 0.371674
\(792\) 29223.1 + 1816.70i 1.31111 + 0.0815072i
\(793\) 19584.7i 0.877017i
\(794\) −2003.26 + 3469.76i −0.0895380 + 0.155084i
\(795\) 0 0
\(796\) −4756.89 8239.18i −0.211813 0.366872i
\(797\) −161.145 + 93.0372i −0.00716193 + 0.00413494i −0.503577 0.863951i \(-0.667983\pi\)
0.496415 + 0.868085i \(0.334650\pi\)
\(798\) −1038.30 + 975.757i −0.0460594 + 0.0432850i
\(799\) −731.686 + 1267.32i −0.0323970 + 0.0561132i
\(800\) 0 0
\(801\) −9786.25 + 4867.03i −0.431686 + 0.214692i
\(802\) 13978.3i 0.615452i
\(803\) 44865.2 + 25902.9i 1.97168 + 1.13835i
\(804\) 2793.22 9264.07i 0.122524 0.406366i
\(805\) 0 0
\(806\) 332.232 + 575.442i 0.0145191 + 0.0251477i
\(807\) 7238.72 + 30810.8i 0.315756 + 1.34398i
\(808\) 18251.2 + 10537.3i 0.794647 + 0.458790i
\(809\) −5903.09 −0.256541 −0.128270 0.991739i \(-0.540943\pi\)
−0.128270 + 0.991739i \(0.540943\pi\)
\(810\) 0 0
\(811\) 23111.0 1.00066 0.500331 0.865834i \(-0.333212\pi\)
0.500331 + 0.865834i \(0.333212\pi\)
\(812\) −769.050 444.011i −0.0332369 0.0191893i
\(813\) 3798.96 + 16169.8i 0.163881 + 0.697542i
\(814\) 6917.58 + 11981.6i 0.297863 + 0.515915i
\(815\) 0 0
\(816\) 792.867 2629.64i 0.0340146 0.112814i
\(817\) 2070.90 + 1195.64i 0.0886802 + 0.0511995i
\(818\) 9488.29i 0.405563i
\(819\) 4649.21 2312.21i 0.198360 0.0986508i
\(820\) 0 0
\(821\) 4822.14 8352.20i 0.204987 0.355047i −0.745142 0.666906i \(-0.767618\pi\)
0.950128 + 0.311859i \(0.100952\pi\)
\(822\) 6551.87 6157.21i 0.278008 0.261262i
\(823\) −29075.5 + 16786.7i −1.23148 + 0.710994i −0.967338 0.253490i \(-0.918422\pi\)
−0.264140 + 0.964484i \(0.585088\pi\)
\(824\) −10575.5 18317.3i −0.447106 0.774410i
\(825\) 0 0
\(826\) −2772.29 + 4801.75i −0.116780 + 0.202269i
\(827\) 25916.1i 1.08971i 0.838530 + 0.544855i \(0.183415\pi\)
−0.838530 + 0.544855i \(0.816585\pi\)
\(828\) 11715.5 + 728.313i 0.491717 + 0.0305684i
\(829\) 28650.6 1.20033 0.600166 0.799876i \(-0.295101\pi\)
0.600166 + 0.799876i \(0.295101\pi\)
\(830\) 0 0
\(831\) −4679.04 + 15518.6i −0.195324 + 0.647816i
\(832\) −2472.38 + 1427.43i −0.103022 + 0.0594799i
\(833\) −6488.76 + 3746.29i −0.269895 + 0.155824i
\(834\) −3205.84 + 753.183i −0.133105 + 0.0312717i
\(835\) 0 0
\(836\) −13371.7 −0.553192
\(837\) 628.135 1694.80i 0.0259397 0.0699891i
\(838\) 7026.51i 0.289650i
\(839\) 356.480 617.441i 0.0146687 0.0254070i −0.858598 0.512650i \(-0.828664\pi\)
0.873267 + 0.487243i \(0.161997\pi\)
\(840\) 0 0
\(841\) 11792.0 + 20424.4i 0.483497 + 0.837441i
\(842\) 2218.20 1280.68i 0.0907887 0.0524169i
\(843\) 24617.6 + 7422.50i 1.00578 + 0.303256i
\(844\) −5345.30 + 9258.32i −0.218001 + 0.377588i
\(845\) 0 0
\(846\) −1910.55 1267.32i −0.0776432 0.0515027i
\(847\) 9223.44i 0.374169i
\(848\) −9529.21 5501.69i −0.385890 0.222793i
\(849\) 16172.8 + 17209.4i 0.653767 + 0.695672i
\(850\) 0 0
\(851\) 6400.27 + 11085.6i 0.257812 + 0.446544i
\(852\) −6262.66 + 5885.43i −0.251826 + 0.236657i
\(853\) 26298.8 + 15183.6i 1.05563 + 0.609469i 0.924221 0.381859i \(-0.124716\pi\)
0.131411 + 0.991328i \(0.458049\pi\)
\(854\) −3658.96 −0.146612
\(855\) 0 0
\(856\) −19937.1 −0.796069
\(857\) 7864.12 + 4540.35i 0.313458 + 0.180975i 0.648473 0.761238i \(-0.275408\pi\)
−0.335015 + 0.942213i \(0.608741\pi\)
\(858\) −14363.3 4330.71i −0.571511 0.172317i
\(859\) 13080.1 + 22655.4i 0.519543 + 0.899874i 0.999742 + 0.0227150i \(0.00723102\pi\)
−0.480199 + 0.877159i \(0.659436\pi\)
\(860\) 0 0
\(861\) −5577.39 + 1310.36i −0.220763 + 0.0518663i
\(862\) 4861.45 + 2806.76i 0.192090 + 0.110903i
\(863\) 40102.0i 1.58180i −0.611949 0.790898i \(-0.709614\pi\)
0.611949 0.790898i \(-0.290386\pi\)
\(864\) 24422.5 + 9051.58i 0.961655 + 0.356413i
\(865\) 0 0
\(866\) 434.362 752.338i 0.0170442 0.0295213i
\(867\) −5174.07 22022.9i −0.202677 0.862671i
\(868\) 349.207 201.615i 0.0136554 0.00788392i
\(869\) −36079.0 62490.6i −1.40839 2.43941i
\(870\) 0 0
\(871\) −5720.87 + 9908.84i −0.222554 + 0.385474i
\(872\) 34415.2i 1.33652i
\(873\) −2021.83 125.691i −0.0783834 0.00487284i
\(874\) 3808.80 0.147408
\(875\) 0 0
\(876\) 20143.9 + 21435.1i 0.776942 + 0.826741i
\(877\) −21869.0 + 12626.1i −0.842036 + 0.486149i −0.857956 0.513724i \(-0.828266\pi\)
0.0159201 + 0.999873i \(0.494932\pi\)
\(878\) 13437.0 7757.86i 0.516489 0.298195i
\(879\) −24411.1 25975.8i −0.936709 0.996750i
\(880\) 0 0
\(881\) −2049.26 −0.0783670 −0.0391835 0.999232i \(-0.512476\pi\)
−0.0391835 + 0.999232i \(0.512476\pi\)
\(882\) −5227.23 10510.5i −0.199558 0.401256i
\(883\) 39413.4i 1.50211i 0.660237 + 0.751057i \(0.270456\pi\)
−0.660237 + 0.751057i \(0.729544\pi\)
\(884\) −2718.47 + 4708.53i −0.103430 + 0.179146i
\(885\) 0 0
\(886\) −5682.14 9841.75i −0.215457 0.373183i
\(887\) −32015.6 + 18484.2i −1.21193 + 0.699707i −0.963179 0.268861i \(-0.913353\pi\)
−0.248749 + 0.968568i \(0.580019\pi\)
\(888\) 4146.45 + 17648.9i 0.156695 + 0.666957i
\(889\) 3085.72 5344.63i 0.116414 0.201634i
\(890\) 0 0
\(891\) 15869.8 + 37595.9i 0.596700 + 1.41359i
\(892\) 15548.7i 0.583641i
\(893\) 2092.68 + 1208.21i 0.0784198 + 0.0452757i
\(894\) −10130.0 + 2379.95i −0.378969 + 0.0890352i
\(895\) 0 0
\(896\) 3533.07 + 6119.46i 0.131732 + 0.228166i
\(897\) −13289.2 4006.85i −0.494665 0.149147i
\(898\) 8186.38 + 4726.41i 0.304213 + 0.175637i
\(899\) 365.525 0.0135605
\(900\) 0 0
\(901\) 11642.9 0.430499
\(902\) 14335.3 + 8276.50i 0.529173 + 0.305518i
\(903\) 1186.40 1114.94i 0.0437220 0.0410883i
\(904\) −15652.2 27110.4i −0.575868 0.997432i
\(905\) 0 0
\(906\) −7526.49 8008.92i −0.275994 0.293685i
\(907\) 2347.47 + 1355.31i 0.0859386 + 0.0496167i 0.542353 0.840150i \(-0.317533\pi\)
−0.456415 + 0.889767i \(0.650867\pi\)
\(908\) 18309.3i 0.669180i
\(909\) −1822.48 + 29316.1i −0.0664994 + 1.06970i
\(910\) 0 0
\(911\) −11498.3 + 19915.6i −0.418172 + 0.724296i −0.995756 0.0920360i \(-0.970663\pi\)
0.577583 + 0.816332i \(0.303996\pi\)
\(912\) −4342.24 1309.24i −0.157660 0.0475363i
\(913\) 34605.7 19979.6i 1.25441 0.724237i
\(914\) −2939.15 5090.77i −0.106366 0.184231i
\(915\) 0 0
\(916\) −13167.4 + 22806.7i −0.474961 + 0.822657i
\(917\) 5259.38i 0.189400i
\(918\) −4488.52 + 764.337i −0.161376 + 0.0274803i
\(919\) 39103.8 1.40361 0.701804 0.712370i \(-0.252378\pi\)
0.701804 + 0.712370i \(0.252378\pi\)
\(920\) 0 0
\(921\) −32031.2 + 7525.44i −1.14600 + 0.269242i
\(922\) 16374.6 9453.86i 0.584889 0.337686i
\(923\) 8800.94 5081.23i 0.313853 0.181203i
\(924\) −2628.09 + 8716.39i −0.0935690 + 0.310333i
\(925\) 0 0
\(926\) −7869.39 −0.279270
\(927\) 16295.2 24565.9i 0.577350 0.870388i
\(928\) 5267.30i 0.186323i
\(929\) −17977.3 + 31137.6i −0.634894 + 1.09967i 0.351644 + 0.936134i \(0.385623\pi\)
−0.986538 + 0.163534i \(0.947711\pi\)
\(930\) 0 0
\(931\) 6186.12 + 10714.7i 0.217768 + 0.377185i
\(932\) −29566.3 + 17070.1i −1.03914 + 0.599946i
\(933\) −26799.6 + 25185.3i −0.940387 + 0.883742i
\(934\) 6141.62 10637.6i 0.215161 0.372669i
\(935\) 0 0
\(936\) −16382.1 10866.6i −0.572078 0.379473i
\(937\) 7263.94i 0.253258i 0.991950 + 0.126629i \(0.0404157\pi\)
−0.991950 + 0.126629i \(0.959584\pi\)
\(938\) −1851.24 1068.81i −0.0644404 0.0372047i
\(939\) −2071.95 + 6871.87i −0.0720079 + 0.238823i
\(940\) 0 0
\(941\) −3739.45 6476.92i −0.129546 0.224380i 0.793955 0.607977i \(-0.208019\pi\)
−0.923501 + 0.383597i \(0.874685\pi\)
\(942\) 5244.15 + 22321.1i 0.181384 + 0.772041i
\(943\) 13263.3 + 7657.57i 0.458020 + 0.264438i
\(944\) −17648.7 −0.608490
\(945\) 0 0
\(946\) −4703.84 −0.161665
\(947\) 11683.9 + 6745.68i 0.400923 + 0.231473i 0.686882 0.726769i \(-0.258979\pi\)
−0.285959 + 0.958242i \(0.592312\pi\)
\(948\) −9370.57 39884.8i −0.321036 1.36645i
\(949\) −17391.4 30122.8i −0.594889 1.03038i
\(950\) 0 0
\(951\) −12262.4 + 40669.8i −0.418124 + 1.38676i
\(952\) −2030.18 1172.13i −0.0691161 0.0399042i
\(953\) 13981.6i 0.475246i −0.971357 0.237623i \(-0.923632\pi\)
0.971357 0.237623i \(-0.0763682\pi\)
\(954\) −1131.79 + 18205.7i −0.0384099 + 0.617853i
\(955\) 0 0
\(956\) 4311.24 7467.29i 0.145853 0.252625i
\(957\) −6013.85 + 5651.59i −0.203135 + 0.190899i
\(958\) −11505.2 + 6642.54i −0.388013 + 0.224019i
\(959\) 3225.93 + 5587.48i 0.108624 + 0.188143i
\(960\) 0 0
\(961\) 14812.5 25656.0i 0.497214 0.861200i
\(962\) 9289.02i 0.311320i
\(963\) −12373.7 24880.1i −0.414057 0.832554i
\(964\) 3832.64 0.128051
\(965\) 0 0
\(966\) 748.589 2482.79i 0.0249332 0.0826940i
\(967\) 7864.78 4540.73i 0.261545 0.151003i −0.363494 0.931597i \(-0.618416\pi\)
0.625039 + 0.780593i \(0.285083\pi\)
\(968\) 30241.4 17459.9i 1.00413 0.579734i
\(969\) 4671.70 1097.57i 0.154878 0.0363872i
\(970\) 0 0
\(971\) −9709.13 −0.320887 −0.160443 0.987045i \(-0.551292\pi\)
−0.160443 + 0.987045i \(0.551292\pi\)
\(972\) 2464.90 + 23039.1i 0.0813393 + 0.760267i
\(973\) 2363.12i 0.0778604i
\(974\) −5972.62 + 10344.9i −0.196484 + 0.340320i
\(975\) 0 0
\(976\) −5823.31 10086.3i −0.190983 0.330793i
\(977\) −9400.63 + 5427.45i −0.307833 + 0.177727i −0.645956 0.763374i \(-0.723541\pi\)
0.338123 + 0.941102i \(0.390208\pi\)
\(978\) −6469.19 1950.53i −0.211515 0.0637742i
\(979\) −11330.1 + 19624.3i −0.369880 + 0.640650i
\(980\) 0 0
\(981\) 42947.7 21359.3i 1.39777 0.695159i
\(982\) 21401.7i 0.695474i
\(983\) 6503.94 + 3755.05i 0.211031 + 0.121839i 0.601790 0.798654i \(-0.294454\pi\)
−0.390759 + 0.920493i \(0.627788\pi\)
\(984\) 14854.3 + 15806.4i 0.481238 + 0.512084i
\(985\) 0 0
\(986\) −460.393 797.424i −0.0148701 0.0257557i
\(987\) 1198.88 1126.66i 0.0386633 0.0363343i
\(988\) 7775.04 + 4488.92i 0.250361 + 0.144546i
\(989\) −4352.08 −0.139927
\(990\) 0 0
\(991\) 46125.6 1.47854 0.739268 0.673412i \(-0.235172\pi\)
0.739268 + 0.673412i \(0.235172\pi\)
\(992\) −2071.32 1195.88i −0.0662947 0.0382753i
\(993\) −48064.3 14491.9i −1.53603 0.463129i
\(994\) 949.311 + 1644.25i 0.0302921 + 0.0524674i
\(995\) 0 0
\(996\) 22087.2 5189.18i 0.702669 0.165086i
\(997\) 39274.3 + 22675.0i 1.24757 + 0.720287i 0.970625 0.240598i \(-0.0773436\pi\)
0.276948 + 0.960885i \(0.410677\pi\)
\(998\) 13306.0i 0.422039i
\(999\) −19451.1 + 16128.0i −0.616023 + 0.510779i
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 225.4.k.b.124.2 8
5.2 odd 4 9.4.c.a.7.2 yes 4
5.3 odd 4 225.4.e.b.151.1 4
5.4 even 2 inner 225.4.k.b.124.3 8
9.4 even 3 inner 225.4.k.b.49.3 8
15.2 even 4 27.4.c.a.19.1 4
20.7 even 4 144.4.i.c.97.2 4
45.2 even 12 81.4.a.a.1.2 2
45.4 even 6 inner 225.4.k.b.49.2 8
45.7 odd 12 81.4.a.d.1.1 2
45.13 odd 12 225.4.e.b.76.1 4
45.22 odd 12 9.4.c.a.4.2 4
45.32 even 12 27.4.c.a.10.1 4
45.38 even 12 2025.4.a.n.1.1 2
45.43 odd 12 2025.4.a.g.1.2 2
60.47 odd 4 432.4.i.c.289.2 4
180.7 even 12 1296.4.a.u.1.2 2
180.47 odd 12 1296.4.a.i.1.1 2
180.67 even 12 144.4.i.c.49.2 4
180.167 odd 12 432.4.i.c.145.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9.4.c.a.4.2 4 45.22 odd 12
9.4.c.a.7.2 yes 4 5.2 odd 4
27.4.c.a.10.1 4 45.32 even 12
27.4.c.a.19.1 4 15.2 even 4
81.4.a.a.1.2 2 45.2 even 12
81.4.a.d.1.1 2 45.7 odd 12
144.4.i.c.49.2 4 180.67 even 12
144.4.i.c.97.2 4 20.7 even 4
225.4.e.b.76.1 4 45.13 odd 12
225.4.e.b.151.1 4 5.3 odd 4
225.4.k.b.49.2 8 45.4 even 6 inner
225.4.k.b.49.3 8 9.4 even 3 inner
225.4.k.b.124.2 8 1.1 even 1 trivial
225.4.k.b.124.3 8 5.4 even 2 inner
432.4.i.c.145.2 4 180.167 odd 12
432.4.i.c.289.2 4 60.47 odd 4
1296.4.a.i.1.1 2 180.47 odd 12
1296.4.a.u.1.2 2 180.7 even 12
2025.4.a.g.1.2 2 45.43 odd 12
2025.4.a.n.1.1 2 45.38 even 12