Properties

Label 37.3.d.a.6.3
Level $37$
Weight $3$
Character 37.6
Analytic conductor $1.008$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [37,3,Mod(6,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.6");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 37.d (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: \(1.00817697813\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 18 x^{10} + 8 x^{9} + 42 x^{8} - 268 x^{7} + 884 x^{6} + 704 x^{5} + 761 x^{4} - 2054 x^{3} + 3042 x^{2} + 312 x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 6.3
Root \(-0.0496173 + 0.0496173i\) of defining polynomial
Character \(\chi\) \(=\) 37.6
Dual form 37.3.d.a.31.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.04962 + 1.04962i) q^{2} -0.377912i q^{3} +1.79661i q^{4} +(5.26886 + 5.26886i) q^{5} +(0.396663 + 0.396663i) q^{6} -5.54265 q^{7} +(-6.08422 - 6.08422i) q^{8} +8.85718 q^{9} +O(q^{10})\) \(q+(-1.04962 + 1.04962i) q^{2} -0.377912i q^{3} +1.79661i q^{4} +(5.26886 + 5.26886i) q^{5} +(0.396663 + 0.396663i) q^{6} -5.54265 q^{7} +(-6.08422 - 6.08422i) q^{8} +8.85718 q^{9} -11.0606 q^{10} -18.1924i q^{11} +0.678959 q^{12} +(7.75987 + 7.75987i) q^{13} +(5.81766 - 5.81766i) q^{14} +(1.99117 - 1.99117i) q^{15} +5.58578 q^{16} +(-18.1161 - 18.1161i) q^{17} +(-9.29665 + 9.29665i) q^{18} +(2.37917 + 2.37917i) q^{19} +(-9.46607 + 9.46607i) q^{20} +2.09463i q^{21} +(19.0950 + 19.0950i) q^{22} +(16.3967 + 16.3967i) q^{23} +(-2.29930 + 2.29930i) q^{24} +30.5218i q^{25} -16.2898 q^{26} -6.74844i q^{27} -9.95796i q^{28} +(20.1686 - 20.1686i) q^{29} +4.17992i q^{30} +(-10.4372 + 10.4372i) q^{31} +(18.4739 - 18.4739i) q^{32} -6.87512 q^{33} +38.0300 q^{34} +(-29.2034 - 29.2034i) q^{35} +15.9129i q^{36} +(-32.1547 + 18.3051i) q^{37} -4.99444 q^{38} +(2.93255 - 2.93255i) q^{39} -64.1138i q^{40} +2.51067i q^{41} +(-2.19856 - 2.19856i) q^{42} +(-19.0228 - 19.0228i) q^{43} +32.6846 q^{44} +(46.6673 + 46.6673i) q^{45} -34.4206 q^{46} -33.0588 q^{47} -2.11093i q^{48} -18.2791 q^{49} +(-32.0362 - 32.0362i) q^{50} +(-6.84630 + 6.84630i) q^{51} +(-13.9414 + 13.9414i) q^{52} -39.9577 q^{53} +(7.08328 + 7.08328i) q^{54} +(95.8532 - 95.8532i) q^{55} +(33.7227 + 33.7227i) q^{56} +(0.899117 - 0.899117i) q^{57} +42.3387i q^{58} +(46.2148 + 46.2148i) q^{59} +(3.57734 + 3.57734i) q^{60} +(3.22864 - 3.22864i) q^{61} -21.9101i q^{62} -49.0922 q^{63} +61.1243i q^{64} +81.7713i q^{65} +(7.21625 - 7.21625i) q^{66} -44.2028i q^{67} +(32.5476 - 32.5476i) q^{68} +(6.19652 - 6.19652i) q^{69} +61.3049 q^{70} -92.4046 q^{71} +(-53.8890 - 53.8890i) q^{72} +87.3712i q^{73} +(14.5368 - 52.9635i) q^{74} +11.5346 q^{75} +(-4.27443 + 4.27443i) q^{76} +100.834i q^{77} +6.15610i q^{78} +(39.7257 + 39.7257i) q^{79} +(29.4307 + 29.4307i) q^{80} +77.1643 q^{81} +(-2.63525 - 2.63525i) q^{82} -112.357 q^{83} -3.76323 q^{84} -190.903i q^{85} +39.9334 q^{86} +(-7.62196 - 7.62196i) q^{87} +(-110.686 + 110.686i) q^{88} +(113.101 - 113.101i) q^{89} -97.9655 q^{90} +(-43.0102 - 43.0102i) q^{91} +(-29.4585 + 29.4585i) q^{92} +(3.94434 + 3.94434i) q^{93} +(34.6991 - 34.6991i) q^{94} +25.0710i q^{95} +(-6.98153 - 6.98153i) q^{96} +(-6.42063 - 6.42063i) q^{97} +(19.1860 - 19.1860i) q^{98} -161.133i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 6 q^{2} - 6 q^{5} + 6 q^{6} - 4 q^{7} + 36 q^{8} - 60 q^{9} - 16 q^{10} + 64 q^{12} + 14 q^{13} - 70 q^{14} - 2 q^{15} - 96 q^{16} + 2 q^{17} + 132 q^{18} + 14 q^{19} - 24 q^{20} + 22 q^{22} + 56 q^{23} - 84 q^{24} - 48 q^{26} + 60 q^{29} + 72 q^{31} + 208 q^{32} + 56 q^{33} + 112 q^{34} - 154 q^{35} - 66 q^{37} - 336 q^{38} - 46 q^{39} + 90 q^{42} + 70 q^{43} + 80 q^{44} + 232 q^{45} - 424 q^{46} - 384 q^{47} + 144 q^{49} - 34 q^{50} - 126 q^{51} + 328 q^{52} - 56 q^{53} - 194 q^{54} + 70 q^{55} + 16 q^{56} - 94 q^{57} + 184 q^{59} + 276 q^{60} + 132 q^{61} - 400 q^{63} + 614 q^{66} + 116 q^{68} + 368 q^{69} + 556 q^{70} + 68 q^{71} - 692 q^{72} - 382 q^{74} + 116 q^{75} + 12 q^{76} - 2 q^{79} + 4 q^{80} - 76 q^{81} + 374 q^{82} + 108 q^{83} - 1436 q^{84} + 140 q^{86} - 420 q^{87} - 788 q^{88} + 278 q^{89} - 664 q^{90} - 450 q^{91} + 652 q^{92} + 584 q^{93} + 118 q^{94} + 1584 q^{96} - 244 q^{97} + 416 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.04962 + 1.04962i −0.524809 + 0.524809i −0.919020 0.394211i \(-0.871018\pi\)
0.394211 + 0.919020i \(0.371018\pi\)
\(3\) 0.377912i 0.125971i −0.998014 0.0629853i \(-0.979938\pi\)
0.998014 0.0629853i \(-0.0200621\pi\)
\(4\) 1.79661i 0.449152i
\(5\) 5.26886 + 5.26886i 1.05377 + 1.05377i 0.998470 + 0.0553026i \(0.0176123\pi\)
0.0553026 + 0.998470i \(0.482388\pi\)
\(6\) 0.396663 + 0.396663i 0.0661105 + 0.0661105i
\(7\) −5.54265 −0.791807 −0.395903 0.918292i \(-0.629568\pi\)
−0.395903 + 0.918292i \(0.629568\pi\)
\(8\) −6.08422 6.08422i −0.760527 0.760527i
\(9\) 8.85718 0.984131
\(10\) −11.0606 −1.10606
\(11\) 18.1924i 1.65385i −0.562310 0.826927i \(-0.690087\pi\)
0.562310 0.826927i \(-0.309913\pi\)
\(12\) 0.678959 0.0565799
\(13\) 7.75987 + 7.75987i 0.596913 + 0.596913i 0.939490 0.342577i \(-0.111300\pi\)
−0.342577 + 0.939490i \(0.611300\pi\)
\(14\) 5.81766 5.81766i 0.415547 0.415547i
\(15\) 1.99117 1.99117i 0.132744 0.132744i
\(16\) 5.58578 0.349111
\(17\) −18.1161 18.1161i −1.06565 1.06565i −0.997688 0.0679669i \(-0.978349\pi\)
−0.0679669 0.997688i \(-0.521651\pi\)
\(18\) −9.29665 + 9.29665i −0.516481 + 0.516481i
\(19\) 2.37917 + 2.37917i 0.125219 + 0.125219i 0.766939 0.641720i \(-0.221779\pi\)
−0.641720 + 0.766939i \(0.721779\pi\)
\(20\) −9.46607 + 9.46607i −0.473304 + 0.473304i
\(21\) 2.09463i 0.0997444i
\(22\) 19.0950 + 19.0950i 0.867957 + 0.867957i
\(23\) 16.3967 + 16.3967i 0.712901 + 0.712901i 0.967141 0.254240i \(-0.0818254\pi\)
−0.254240 + 0.967141i \(0.581825\pi\)
\(24\) −2.29930 + 2.29930i −0.0958041 + 0.0958041i
\(25\) 30.5218i 1.22087i
\(26\) −16.2898 −0.626530
\(27\) 6.74844i 0.249942i
\(28\) 9.95796i 0.355641i
\(29\) 20.1686 20.1686i 0.695469 0.695469i −0.267960 0.963430i \(-0.586350\pi\)
0.963430 + 0.267960i \(0.0863497\pi\)
\(30\) 4.17992i 0.139331i
\(31\) −10.4372 + 10.4372i −0.336684 + 0.336684i −0.855118 0.518434i \(-0.826515\pi\)
0.518434 + 0.855118i \(0.326515\pi\)
\(32\) 18.4739 18.4739i 0.577311 0.577311i
\(33\) −6.87512 −0.208337
\(34\) 38.0300 1.11853
\(35\) −29.2034 29.2034i −0.834384 0.834384i
\(36\) 15.9129i 0.442024i
\(37\) −32.1547 + 18.3051i −0.869045 + 0.494732i
\(38\) −4.99444 −0.131433
\(39\) 2.93255 2.93255i 0.0751935 0.0751935i
\(40\) 64.1138i 1.60285i
\(41\) 2.51067i 0.0612359i 0.999531 + 0.0306180i \(0.00974753\pi\)
−0.999531 + 0.0306180i \(0.990252\pi\)
\(42\) −2.19856 2.19856i −0.0523467 0.0523467i
\(43\) −19.0228 19.0228i −0.442391 0.442391i 0.450424 0.892815i \(-0.351273\pi\)
−0.892815 + 0.450424i \(0.851273\pi\)
\(44\) 32.6846 0.742831
\(45\) 46.6673 + 46.6673i 1.03705 + 1.03705i
\(46\) −34.4206 −0.748273
\(47\) −33.0588 −0.703378 −0.351689 0.936117i \(-0.614393\pi\)
−0.351689 + 0.936117i \(0.614393\pi\)
\(48\) 2.11093i 0.0439777i
\(49\) −18.2791 −0.373042
\(50\) −32.0362 32.0362i −0.640724 0.640724i
\(51\) −6.84630 + 6.84630i −0.134241 + 0.134241i
\(52\) −13.9414 + 13.9414i −0.268104 + 0.268104i
\(53\) −39.9577 −0.753918 −0.376959 0.926230i \(-0.623030\pi\)
−0.376959 + 0.926230i \(0.623030\pi\)
\(54\) 7.08328 + 7.08328i 0.131172 + 0.131172i
\(55\) 95.8532 95.8532i 1.74278 1.74278i
\(56\) 33.7227 + 33.7227i 0.602191 + 0.602191i
\(57\) 0.899117 0.899117i 0.0157740 0.0157740i
\(58\) 42.3387i 0.729977i
\(59\) 46.2148 + 46.2148i 0.783303 + 0.783303i 0.980387 0.197084i \(-0.0631472\pi\)
−0.197084 + 0.980387i \(0.563147\pi\)
\(60\) 3.57734 + 3.57734i 0.0596224 + 0.0596224i
\(61\) 3.22864 3.22864i 0.0529286 0.0529286i −0.680147 0.733076i \(-0.738084\pi\)
0.733076 + 0.680147i \(0.238084\pi\)
\(62\) 21.9101i 0.353389i
\(63\) −49.0922 −0.779242
\(64\) 61.1243i 0.955066i
\(65\) 81.7713i 1.25802i
\(66\) 7.21625 7.21625i 0.109337 0.109337i
\(67\) 44.2028i 0.659743i −0.944026 0.329872i \(-0.892995\pi\)
0.944026 0.329872i \(-0.107005\pi\)
\(68\) 32.5476 32.5476i 0.478641 0.478641i
\(69\) 6.19652 6.19652i 0.0898046 0.0898046i
\(70\) 61.3049 0.875784
\(71\) −92.4046 −1.30147 −0.650736 0.759304i \(-0.725540\pi\)
−0.650736 + 0.759304i \(0.725540\pi\)
\(72\) −53.8890 53.8890i −0.748459 0.748459i
\(73\) 87.3712i 1.19687i 0.801173 + 0.598433i \(0.204210\pi\)
−0.801173 + 0.598433i \(0.795790\pi\)
\(74\) 14.5368 52.9635i 0.196443 0.715722i
\(75\) 11.5346 0.153794
\(76\) −4.27443 + 4.27443i −0.0562425 + 0.0562425i
\(77\) 100.834i 1.30953i
\(78\) 6.15610i 0.0789244i
\(79\) 39.7257 + 39.7257i 0.502857 + 0.502857i 0.912325 0.409467i \(-0.134285\pi\)
−0.409467 + 0.912325i \(0.634285\pi\)
\(80\) 29.4307 + 29.4307i 0.367883 + 0.367883i
\(81\) 77.1643 0.952646
\(82\) −2.63525 2.63525i −0.0321372 0.0321372i
\(83\) −112.357 −1.35370 −0.676849 0.736122i \(-0.736655\pi\)
−0.676849 + 0.736122i \(0.736655\pi\)
\(84\) −3.76323 −0.0448004
\(85\) 190.903i 2.24591i
\(86\) 39.9334 0.464342
\(87\) −7.62196 7.62196i −0.0876087 0.0876087i
\(88\) −110.686 + 110.686i −1.25780 + 1.25780i
\(89\) 113.101 113.101i 1.27080 1.27080i 0.325124 0.945671i \(-0.394594\pi\)
0.945671 0.325124i \(-0.105406\pi\)
\(90\) −97.9655 −1.08851
\(91\) −43.0102 43.0102i −0.472639 0.472639i
\(92\) −29.4585 + 29.4585i −0.320201 + 0.320201i
\(93\) 3.94434 + 3.94434i 0.0424123 + 0.0424123i
\(94\) 34.6991 34.6991i 0.369139 0.369139i
\(95\) 25.0710i 0.263906i
\(96\) −6.98153 6.98153i −0.0727242 0.0727242i
\(97\) −6.42063 6.42063i −0.0661921 0.0661921i 0.673236 0.739428i \(-0.264904\pi\)
−0.739428 + 0.673236i \(0.764904\pi\)
\(98\) 19.1860 19.1860i 0.195776 0.195776i
\(99\) 161.133i 1.62761i
\(100\) −54.8357 −0.548357
\(101\) 72.9137i 0.721918i 0.932582 + 0.360959i \(0.117551\pi\)
−0.932582 + 0.360959i \(0.882449\pi\)
\(102\) 14.3720i 0.140902i
\(103\) 59.4600 59.4600i 0.577282 0.577282i −0.356872 0.934153i \(-0.616157\pi\)
0.934153 + 0.356872i \(0.116157\pi\)
\(104\) 94.4255i 0.907937i
\(105\) −11.0363 + 11.0363i −0.105108 + 0.105108i
\(106\) 41.9402 41.9402i 0.395663 0.395663i
\(107\) 64.2881 0.600824 0.300412 0.953810i \(-0.402876\pi\)
0.300412 + 0.953810i \(0.402876\pi\)
\(108\) 12.1243 0.112262
\(109\) −25.6002 25.6002i −0.234864 0.234864i 0.579855 0.814720i \(-0.303109\pi\)
−0.814720 + 0.579855i \(0.803109\pi\)
\(110\) 201.218i 1.82926i
\(111\) 6.91772 + 12.1516i 0.0623218 + 0.109474i
\(112\) −30.9600 −0.276428
\(113\) 55.8577 55.8577i 0.494316 0.494316i −0.415347 0.909663i \(-0.636340\pi\)
0.909663 + 0.415347i \(0.136340\pi\)
\(114\) 1.88746i 0.0165566i
\(115\) 172.784i 1.50247i
\(116\) 36.2351 + 36.2351i 0.312371 + 0.312371i
\(117\) 68.7306 + 68.7306i 0.587441 + 0.587441i
\(118\) −97.0158 −0.822168
\(119\) 100.411 + 100.411i 0.843792 + 0.843792i
\(120\) −24.2294 −0.201911
\(121\) −209.963 −1.73523
\(122\) 6.77768i 0.0555547i
\(123\) 0.948814 0.00771393
\(124\) −18.7515 18.7515i −0.151222 0.151222i
\(125\) −29.0936 + 29.0936i −0.232749 + 0.232749i
\(126\) 51.5281 51.5281i 0.408953 0.408953i
\(127\) 132.802 1.04568 0.522841 0.852430i \(-0.324872\pi\)
0.522841 + 0.852430i \(0.324872\pi\)
\(128\) 9.73872 + 9.73872i 0.0760838 + 0.0760838i
\(129\) −7.18896 + 7.18896i −0.0557283 + 0.0557283i
\(130\) −85.8286 85.8286i −0.660220 0.660220i
\(131\) −90.8033 + 90.8033i −0.693155 + 0.693155i −0.962925 0.269770i \(-0.913052\pi\)
0.269770 + 0.962925i \(0.413052\pi\)
\(132\) 12.3519i 0.0935749i
\(133\) −13.1869 13.1869i −0.0991496 0.0991496i
\(134\) 46.3960 + 46.3960i 0.346239 + 0.346239i
\(135\) 35.5566 35.5566i 0.263382 0.263382i
\(136\) 220.445i 1.62092i
\(137\) 15.1210 0.110372 0.0551860 0.998476i \(-0.482425\pi\)
0.0551860 + 0.998476i \(0.482425\pi\)
\(138\) 13.0079i 0.0942605i
\(139\) 218.618i 1.57279i 0.617724 + 0.786395i \(0.288055\pi\)
−0.617724 + 0.786395i \(0.711945\pi\)
\(140\) 52.4671 52.4671i 0.374765 0.374765i
\(141\) 12.4933i 0.0886050i
\(142\) 96.9894 96.9894i 0.683024 0.683024i
\(143\) 141.170 141.170i 0.987206 0.987206i
\(144\) 49.4742 0.343571
\(145\) 212.531 1.46573
\(146\) −91.7063 91.7063i −0.628126 0.628126i
\(147\) 6.90788i 0.0469924i
\(148\) −32.8871 57.7693i −0.222210 0.390333i
\(149\) −224.519 −1.50684 −0.753421 0.657539i \(-0.771598\pi\)
−0.753421 + 0.657539i \(0.771598\pi\)
\(150\) −12.1069 + 12.1069i −0.0807124 + 0.0807124i
\(151\) 220.465i 1.46004i −0.683428 0.730018i \(-0.739512\pi\)
0.683428 0.730018i \(-0.260488\pi\)
\(152\) 28.9508i 0.190466i
\(153\) −160.458 160.458i −1.04874 1.04874i
\(154\) −105.837 105.837i −0.687254 0.687254i
\(155\) −109.984 −0.709576
\(156\) 5.26863 + 5.26863i 0.0337733 + 0.0337733i
\(157\) 82.7157 0.526851 0.263426 0.964680i \(-0.415148\pi\)
0.263426 + 0.964680i \(0.415148\pi\)
\(158\) −83.3936 −0.527808
\(159\) 15.1005i 0.0949716i
\(160\) 194.673 1.21671
\(161\) −90.8812 90.8812i −0.564480 0.564480i
\(162\) −80.9930 + 80.9930i −0.499957 + 0.499957i
\(163\) −139.231 + 139.231i −0.854180 + 0.854180i −0.990645 0.136465i \(-0.956426\pi\)
0.136465 + 0.990645i \(0.456426\pi\)
\(164\) −4.51069 −0.0275042
\(165\) −36.2241 36.2241i −0.219540 0.219540i
\(166\) 117.932 117.932i 0.710433 0.710433i
\(167\) 75.9417 + 75.9417i 0.454741 + 0.454741i 0.896924 0.442184i \(-0.145796\pi\)
−0.442184 + 0.896924i \(0.645796\pi\)
\(168\) 12.7442 12.7442i 0.0758583 0.0758583i
\(169\) 48.5690i 0.287390i
\(170\) 200.375 + 200.375i 1.17868 + 1.17868i
\(171\) 21.0727 + 21.0727i 0.123232 + 0.123232i
\(172\) 34.1766 34.1766i 0.198701 0.198701i
\(173\) 79.1788i 0.457681i −0.973464 0.228841i \(-0.926507\pi\)
0.973464 0.228841i \(-0.0734935\pi\)
\(174\) 16.0003 0.0919557
\(175\) 169.171i 0.966694i
\(176\) 101.619i 0.577378i
\(177\) 17.4651 17.4651i 0.0986731 0.0986731i
\(178\) 237.425i 1.33385i
\(179\) −122.752 + 122.752i −0.685767 + 0.685767i −0.961293 0.275527i \(-0.911148\pi\)
0.275527 + 0.961293i \(0.411148\pi\)
\(180\) −83.8427 + 83.8427i −0.465793 + 0.465793i
\(181\) 136.182 0.752387 0.376193 0.926541i \(-0.377233\pi\)
0.376193 + 0.926541i \(0.377233\pi\)
\(182\) 90.2885 0.496091
\(183\) −1.22014 1.22014i −0.00666745 0.00666745i
\(184\) 199.523i 1.08436i
\(185\) −265.866 72.9715i −1.43711 0.394441i
\(186\) −8.28010 −0.0445167
\(187\) −329.576 + 329.576i −1.76244 + 1.76244i
\(188\) 59.3936i 0.315924i
\(189\) 37.4042i 0.197906i
\(190\) −26.3150 26.3150i −0.138500 0.138500i
\(191\) 124.156 + 124.156i 0.650033 + 0.650033i 0.953001 0.302968i \(-0.0979774\pi\)
−0.302968 + 0.953001i \(0.597977\pi\)
\(192\) 23.0996 0.120310
\(193\) 66.0477 + 66.0477i 0.342216 + 0.342216i 0.857200 0.514984i \(-0.172202\pi\)
−0.514984 + 0.857200i \(0.672202\pi\)
\(194\) 13.4784 0.0694763
\(195\) 30.9024 0.158474
\(196\) 32.8403i 0.167553i
\(197\) 59.3236 0.301135 0.150568 0.988600i \(-0.451890\pi\)
0.150568 + 0.988600i \(0.451890\pi\)
\(198\) 169.128 + 169.128i 0.854183 + 0.854183i
\(199\) 24.4969 24.4969i 0.123100 0.123100i −0.642873 0.765973i \(-0.722258\pi\)
0.765973 + 0.642873i \(0.222258\pi\)
\(200\) 185.701 185.701i 0.928506 0.928506i
\(201\) −16.7048 −0.0831083
\(202\) −76.5315 76.5315i −0.378869 0.378869i
\(203\) −111.787 + 111.787i −0.550677 + 0.550677i
\(204\) −12.3001 12.3001i −0.0602947 0.0602947i
\(205\) −13.2284 + 13.2284i −0.0645287 + 0.0645287i
\(206\) 124.821i 0.605925i
\(207\) 145.229 + 145.229i 0.701588 + 0.701588i
\(208\) 43.3449 + 43.3449i 0.208389 + 0.208389i
\(209\) 43.2828 43.2828i 0.207095 0.207095i
\(210\) 23.1678i 0.110323i
\(211\) 33.2939 0.157791 0.0788955 0.996883i \(-0.474861\pi\)
0.0788955 + 0.996883i \(0.474861\pi\)
\(212\) 71.7882i 0.338624i
\(213\) 34.9208i 0.163947i
\(214\) −67.4779 + 67.4779i −0.315317 + 0.315317i
\(215\) 200.457i 0.932360i
\(216\) −41.0590 + 41.0590i −0.190088 + 0.190088i
\(217\) 57.8497 57.8497i 0.266588 0.266588i
\(218\) 53.7409 0.246518
\(219\) 33.0186 0.150770
\(220\) 172.210 + 172.210i 0.782775 + 0.782775i
\(221\) 281.157i 1.27221i
\(222\) −20.0155 5.49362i −0.0901600 0.0247460i
\(223\) 356.943 1.60064 0.800320 0.599574i \(-0.204663\pi\)
0.800320 + 0.599574i \(0.204663\pi\)
\(224\) −102.395 + 102.395i −0.457119 + 0.457119i
\(225\) 270.337i 1.20150i
\(226\) 117.258i 0.518843i
\(227\) −126.548 126.548i −0.557479 0.557479i 0.371110 0.928589i \(-0.378977\pi\)
−0.928589 + 0.371110i \(0.878977\pi\)
\(228\) 1.61536 + 1.61536i 0.00708491 + 0.00708491i
\(229\) −235.918 −1.03021 −0.515104 0.857128i \(-0.672247\pi\)
−0.515104 + 0.857128i \(0.672247\pi\)
\(230\) −181.357 181.357i −0.788510 0.788510i
\(231\) 38.1064 0.164963
\(232\) −245.421 −1.05785
\(233\) 33.5791i 0.144116i −0.997400 0.0720582i \(-0.977043\pi\)
0.997400 0.0720582i \(-0.0229567\pi\)
\(234\) −144.282 −0.616588
\(235\) −174.182 174.182i −0.741200 0.741200i
\(236\) −83.0299 + 83.0299i −0.351822 + 0.351822i
\(237\) 15.0128 15.0128i 0.0633453 0.0633453i
\(238\) −210.787 −0.885659
\(239\) −5.37141 5.37141i −0.0224745 0.0224745i 0.695780 0.718255i \(-0.255059\pi\)
−0.718255 + 0.695780i \(0.755059\pi\)
\(240\) 11.1222 11.1222i 0.0463425 0.0463425i
\(241\) 264.741 + 264.741i 1.09851 + 1.09851i 0.994585 + 0.103924i \(0.0331400\pi\)
0.103924 + 0.994585i \(0.466860\pi\)
\(242\) 220.381 220.381i 0.910664 0.910664i
\(243\) 89.8973i 0.369948i
\(244\) 5.80060 + 5.80060i 0.0237730 + 0.0237730i
\(245\) −96.3099 96.3099i −0.393102 0.393102i
\(246\) −0.995891 + 0.995891i −0.00404834 + 0.00404834i
\(247\) 36.9241i 0.149490i
\(248\) 127.004 0.512115
\(249\) 42.4610i 0.170526i
\(250\) 61.0742i 0.244297i
\(251\) −60.1852 + 60.1852i −0.239782 + 0.239782i −0.816760 0.576978i \(-0.804232\pi\)
0.576978 + 0.816760i \(0.304232\pi\)
\(252\) 88.1994i 0.349998i
\(253\) 298.296 298.296i 1.17903 1.17903i
\(254\) −139.391 + 139.391i −0.548783 + 0.548783i
\(255\) −72.1444 −0.282919
\(256\) −264.941 −1.03493
\(257\) 103.677 + 103.677i 0.403412 + 0.403412i 0.879434 0.476021i \(-0.157922\pi\)
−0.476021 + 0.879434i \(0.657922\pi\)
\(258\) 15.0913i 0.0584934i
\(259\) 178.222 101.459i 0.688116 0.391732i
\(260\) −146.911 −0.565042
\(261\) 178.637 178.637i 0.684433 0.684433i
\(262\) 190.617i 0.727547i
\(263\) 232.453i 0.883851i 0.897052 + 0.441926i \(0.145704\pi\)
−0.897052 + 0.441926i \(0.854296\pi\)
\(264\) 41.8297 + 41.8297i 0.158446 + 0.158446i
\(265\) −210.531 210.531i −0.794458 0.794458i
\(266\) 27.6824 0.104069
\(267\) −42.7421 42.7421i −0.160083 0.160083i
\(268\) 79.4150 0.296325
\(269\) 183.875 0.683550 0.341775 0.939782i \(-0.388972\pi\)
0.341775 + 0.939782i \(0.388972\pi\)
\(270\) 74.6417i 0.276451i
\(271\) 10.9050 0.0402398 0.0201199 0.999798i \(-0.493595\pi\)
0.0201199 + 0.999798i \(0.493595\pi\)
\(272\) −101.193 101.193i −0.372032 0.372032i
\(273\) −16.2541 + 16.2541i −0.0595387 + 0.0595387i
\(274\) −15.8712 + 15.8712i −0.0579242 + 0.0579242i
\(275\) 555.264 2.01914
\(276\) 11.1327 + 11.1327i 0.0403359 + 0.0403359i
\(277\) −210.314 + 210.314i −0.759256 + 0.759256i −0.976187 0.216931i \(-0.930395\pi\)
0.216931 + 0.976187i \(0.430395\pi\)
\(278\) −229.465 229.465i −0.825414 0.825414i
\(279\) −92.4442 + 92.4442i −0.331341 + 0.331341i
\(280\) 355.360i 1.26914i
\(281\) −353.860 353.860i −1.25929 1.25929i −0.951433 0.307856i \(-0.900389\pi\)
−0.307856 0.951433i \(-0.599611\pi\)
\(282\) −13.1132 13.1132i −0.0465007 0.0465007i
\(283\) 305.613 305.613i 1.07991 1.07991i 0.0833885 0.996517i \(-0.473426\pi\)
0.996517 0.0833885i \(-0.0265742\pi\)
\(284\) 166.015i 0.584559i
\(285\) 9.47464 0.0332444
\(286\) 296.350i 1.03619i
\(287\) 13.9158i 0.0484870i
\(288\) 163.627 163.627i 0.568150 0.568150i
\(289\) 367.388i 1.27124i
\(290\) −223.076 + 223.076i −0.769229 + 0.769229i
\(291\) −2.42643 + 2.42643i −0.00833826 + 0.00833826i
\(292\) −156.972 −0.537574
\(293\) −81.8505 −0.279353 −0.139677 0.990197i \(-0.544606\pi\)
−0.139677 + 0.990197i \(0.544606\pi\)
\(294\) −7.25063 7.25063i −0.0246620 0.0246620i
\(295\) 486.999i 1.65084i
\(296\) 307.008 + 84.2639i 1.03719 + 0.284675i
\(297\) −122.770 −0.413368
\(298\) 235.659 235.659i 0.790804 0.790804i
\(299\) 254.473i 0.851079i
\(300\) 20.7231i 0.0690769i
\(301\) 105.437 + 105.437i 0.350288 + 0.350288i
\(302\) 231.404 + 231.404i 0.766239 + 0.766239i
\(303\) 27.5550 0.0909405
\(304\) 13.2895 + 13.2895i 0.0437155 + 0.0437155i
\(305\) 34.0225 0.111549
\(306\) 336.839 1.10078
\(307\) 441.470i 1.43801i 0.695003 + 0.719007i \(0.255403\pi\)
−0.695003 + 0.719007i \(0.744597\pi\)
\(308\) −181.159 −0.588179
\(309\) −22.4706 22.4706i −0.0727205 0.0727205i
\(310\) 115.441 115.441i 0.372392 0.372392i
\(311\) −26.4826 + 26.4826i −0.0851531 + 0.0851531i −0.748400 0.663247i \(-0.769178\pi\)
0.663247 + 0.748400i \(0.269178\pi\)
\(312\) −35.6845 −0.114373
\(313\) 301.149 + 301.149i 0.962137 + 0.962137i 0.999309 0.0371719i \(-0.0118349\pi\)
−0.0371719 + 0.999309i \(0.511835\pi\)
\(314\) −86.8198 + 86.8198i −0.276496 + 0.276496i
\(315\) −258.660 258.660i −0.821143 0.821143i
\(316\) −71.3715 + 71.3715i −0.225859 + 0.225859i
\(317\) 374.514i 1.18143i −0.806880 0.590716i \(-0.798845\pi\)
0.806880 0.590716i \(-0.201155\pi\)
\(318\) −15.8497 15.8497i −0.0498419 0.0498419i
\(319\) −366.915 366.915i −1.15020 1.15020i
\(320\) −322.055 + 322.055i −1.00642 + 1.00642i
\(321\) 24.2953i 0.0756861i
\(322\) 190.781 0.592488
\(323\) 86.2027i 0.266881i
\(324\) 138.634i 0.427883i
\(325\) −236.845 + 236.845i −0.728754 + 0.728754i
\(326\) 292.279i 0.896562i
\(327\) −9.67463 + 9.67463i −0.0295860 + 0.0295860i
\(328\) 15.2755 15.2755i 0.0465716 0.0465716i
\(329\) 183.233 0.556939
\(330\) 76.0428 0.230433
\(331\) −284.416 284.416i −0.859261 0.859261i 0.131990 0.991251i \(-0.457863\pi\)
−0.991251 + 0.131990i \(0.957863\pi\)
\(332\) 201.861i 0.608016i
\(333\) −284.800 + 162.132i −0.855255 + 0.486882i
\(334\) −159.419 −0.477304
\(335\) 232.898 232.898i 0.695219 0.695219i
\(336\) 11.7001i 0.0348219i
\(337\) 408.598i 1.21246i −0.795290 0.606229i \(-0.792681\pi\)
0.795290 0.606229i \(-0.207319\pi\)
\(338\) 50.9788 + 50.9788i 0.150825 + 0.150825i
\(339\) −21.1093 21.1093i −0.0622693 0.0622693i
\(340\) 342.977 1.00876
\(341\) 189.878 + 189.878i 0.556826 + 0.556826i
\(342\) −44.2366 −0.129347
\(343\) 372.904 1.08718
\(344\) 231.478i 0.672902i
\(345\) 65.2972 0.189267
\(346\) 83.1075 + 83.1075i 0.240195 + 0.240195i
\(347\) 169.743 169.743i 0.489173 0.489173i −0.418872 0.908045i \(-0.637574\pi\)
0.908045 + 0.418872i \(0.137574\pi\)
\(348\) 13.6937 13.6937i 0.0393496 0.0393496i
\(349\) −70.7682 −0.202774 −0.101387 0.994847i \(-0.532328\pi\)
−0.101387 + 0.994847i \(0.532328\pi\)
\(350\) 177.565 + 177.565i 0.507330 + 0.507330i
\(351\) 52.3670 52.3670i 0.149194 0.149194i
\(352\) −336.085 336.085i −0.954788 0.954788i
\(353\) 35.6639 35.6639i 0.101031 0.101031i −0.654785 0.755816i \(-0.727241\pi\)
0.755816 + 0.654785i \(0.227241\pi\)
\(354\) 36.6634i 0.103569i
\(355\) −486.867 486.867i −1.37146 1.37146i
\(356\) 203.198 + 203.198i 0.570780 + 0.570780i
\(357\) 37.9466 37.9466i 0.106293 0.106293i
\(358\) 257.686i 0.719793i
\(359\) −623.797 −1.73760 −0.868798 0.495168i \(-0.835107\pi\)
−0.868798 + 0.495168i \(0.835107\pi\)
\(360\) 567.868i 1.57741i
\(361\) 349.679i 0.968640i
\(362\) −142.939 + 142.939i −0.394859 + 0.394859i
\(363\) 79.3475i 0.218588i
\(364\) 77.2724 77.2724i 0.212287 0.212287i
\(365\) −460.347 + 460.347i −1.26122 + 1.26122i
\(366\) 2.56137 0.00699827
\(367\) −189.927 −0.517512 −0.258756 0.965943i \(-0.583313\pi\)
−0.258756 + 0.965943i \(0.583313\pi\)
\(368\) 91.5884 + 91.5884i 0.248882 + 0.248882i
\(369\) 22.2375i 0.0602642i
\(370\) 355.649 202.465i 0.961214 0.547202i
\(371\) 221.471 0.596957
\(372\) −7.08643 + 7.08643i −0.0190496 + 0.0190496i
\(373\) 149.878i 0.401817i 0.979610 + 0.200909i \(0.0643894\pi\)
−0.979610 + 0.200909i \(0.935611\pi\)
\(374\) 691.857i 1.84988i
\(375\) 10.9948 + 10.9948i 0.0293195 + 0.0293195i
\(376\) 201.137 + 201.137i 0.534938 + 0.534938i
\(377\) 313.011 0.830269
\(378\) −39.2601 39.2601i −0.103863 0.103863i
\(379\) −226.618 −0.597937 −0.298968 0.954263i \(-0.596643\pi\)
−0.298968 + 0.954263i \(0.596643\pi\)
\(380\) −45.0428 −0.118534
\(381\) 50.1873i 0.131725i
\(382\) −260.633 −0.682286
\(383\) 427.831 + 427.831i 1.11705 + 1.11705i 0.992172 + 0.124879i \(0.0398543\pi\)
0.124879 + 0.992172i \(0.460146\pi\)
\(384\) 3.68038 3.68038i 0.00958432 0.00958432i
\(385\) −531.280 + 531.280i −1.37995 + 1.37995i
\(386\) −138.650 −0.359196
\(387\) −168.489 168.489i −0.435371 0.435371i
\(388\) 11.5353 11.5353i 0.0297303 0.0297303i
\(389\) 539.254 + 539.254i 1.38626 + 1.38626i 0.833033 + 0.553223i \(0.186602\pi\)
0.553223 + 0.833033i \(0.313398\pi\)
\(390\) −32.4357 + 32.4357i −0.0831683 + 0.0831683i
\(391\) 594.090i 1.51941i
\(392\) 111.214 + 111.214i 0.283709 + 0.283709i
\(393\) 34.3157 + 34.3157i 0.0873172 + 0.0873172i
\(394\) −62.2671 + 62.2671i −0.158038 + 0.158038i
\(395\) 418.619i 1.05979i
\(396\) 289.493 0.731043
\(397\) 249.597i 0.628707i 0.949306 + 0.314354i \(0.101788\pi\)
−0.949306 + 0.314354i \(0.898212\pi\)
\(398\) 51.4248i 0.129208i
\(399\) −4.98349 + 4.98349i −0.0124899 + 0.0124899i
\(400\) 170.488i 0.426220i
\(401\) −252.449 + 252.449i −0.629550 + 0.629550i −0.947955 0.318405i \(-0.896853\pi\)
0.318405 + 0.947955i \(0.396853\pi\)
\(402\) 17.5336 17.5336i 0.0436159 0.0436159i
\(403\) −161.983 −0.401942
\(404\) −130.997 −0.324251
\(405\) 406.568 + 406.568i 1.00387 + 1.00387i
\(406\) 234.668i 0.578000i
\(407\) 333.013 + 584.970i 0.818215 + 1.43727i
\(408\) 83.3088 0.204188
\(409\) 27.2406 27.2406i 0.0666030 0.0666030i −0.673021 0.739624i \(-0.735004\pi\)
0.739624 + 0.673021i \(0.235004\pi\)
\(410\) 27.7695i 0.0677305i
\(411\) 5.71439i 0.0139036i
\(412\) 106.826 + 106.826i 0.259287 + 0.259287i
\(413\) −256.153 256.153i −0.620224 0.620224i
\(414\) −304.869 −0.736399
\(415\) −591.993 591.993i −1.42649 1.42649i
\(416\) 286.711 0.689209
\(417\) 82.6183 0.198125
\(418\) 90.8607i 0.217370i
\(419\) 221.675 0.529058 0.264529 0.964378i \(-0.414783\pi\)
0.264529 + 0.964378i \(0.414783\pi\)
\(420\) −19.8279 19.8279i −0.0472094 0.0472094i
\(421\) 138.621 138.621i 0.329266 0.329266i −0.523041 0.852307i \(-0.675203\pi\)
0.852307 + 0.523041i \(0.175203\pi\)
\(422\) −34.9458 + 34.9458i −0.0828101 + 0.0828101i
\(423\) −292.808 −0.692217
\(424\) 243.111 + 243.111i 0.573375 + 0.573375i
\(425\) 552.937 552.937i 1.30103 1.30103i
\(426\) −36.6535 36.6535i −0.0860410 0.0860410i
\(427\) −17.8952 + 17.8952i −0.0419092 + 0.0419092i
\(428\) 115.500i 0.269861i
\(429\) −53.3500 53.3500i −0.124359 0.124359i
\(430\) 210.403 + 210.403i 0.489310 + 0.489310i
\(431\) −525.402 + 525.402i −1.21903 + 1.21903i −0.251058 + 0.967972i \(0.580779\pi\)
−0.967972 + 0.251058i \(0.919221\pi\)
\(432\) 37.6953i 0.0872576i
\(433\) 229.718 0.530527 0.265263 0.964176i \(-0.414541\pi\)
0.265263 + 0.964176i \(0.414541\pi\)
\(434\) 121.440i 0.279816i
\(435\) 80.3181i 0.184639i
\(436\) 45.9935 45.9935i 0.105490 0.105490i
\(437\) 78.0212i 0.178538i
\(438\) −34.6569 + 34.6569i −0.0791254 + 0.0791254i
\(439\) 420.037 420.037i 0.956803 0.956803i −0.0423019 0.999105i \(-0.513469\pi\)
0.999105 + 0.0423019i \(0.0134691\pi\)
\(440\) −1166.38 −2.65087
\(441\) −161.901 −0.367123
\(442\) 295.108 + 295.108i 0.667665 + 0.667665i
\(443\) 637.682i 1.43946i −0.694252 0.719732i \(-0.744265\pi\)
0.694252 0.719732i \(-0.255735\pi\)
\(444\) −21.8317 + 12.4284i −0.0491705 + 0.0279919i
\(445\) 1191.82 2.67826
\(446\) −374.653 + 374.653i −0.840029 + 0.840029i
\(447\) 84.8486i 0.189818i
\(448\) 338.790i 0.756228i
\(449\) 208.249 + 208.249i 0.463807 + 0.463807i 0.899901 0.436094i \(-0.143639\pi\)
−0.436094 + 0.899901i \(0.643639\pi\)
\(450\) −283.750 283.750i −0.630557 0.630557i
\(451\) 45.6752 0.101275
\(452\) 100.354 + 100.354i 0.222023 + 0.222023i
\(453\) −83.3165 −0.183922
\(454\) 265.653 0.585139
\(455\) 453.229i 0.996109i
\(456\) −10.9408 −0.0239931
\(457\) 167.982 + 167.982i 0.367576 + 0.367576i 0.866592 0.499017i \(-0.166305\pi\)
−0.499017 + 0.866592i \(0.666305\pi\)
\(458\) 247.623 247.623i 0.540662 0.540662i
\(459\) −122.256 + 122.256i −0.266352 + 0.266352i
\(460\) −310.425 −0.674837
\(461\) −579.698 579.698i −1.25748 1.25748i −0.952293 0.305186i \(-0.901281\pi\)
−0.305186 0.952293i \(-0.598719\pi\)
\(462\) −39.9971 + 39.9971i −0.0865738 + 0.0865738i
\(463\) 235.818 + 235.818i 0.509325 + 0.509325i 0.914319 0.404994i \(-0.132726\pi\)
−0.404994 + 0.914319i \(0.632726\pi\)
\(464\) 112.657 112.657i 0.242796 0.242796i
\(465\) 41.5644i 0.0893858i
\(466\) 35.2452 + 35.2452i 0.0756335 + 0.0756335i
\(467\) −172.057 172.057i −0.368430 0.368430i 0.498474 0.866905i \(-0.333894\pi\)
−0.866905 + 0.498474i \(0.833894\pi\)
\(468\) −123.482 + 123.482i −0.263850 + 0.263850i
\(469\) 245.000i 0.522389i
\(470\) 365.649 0.777977
\(471\) 31.2592i 0.0663678i
\(472\) 562.363i 1.19145i
\(473\) −346.071 + 346.071i −0.731651 + 0.731651i
\(474\) 31.5155i 0.0664883i
\(475\) −72.6165 + 72.6165i −0.152877 + 0.152877i
\(476\) −180.400 + 180.400i −0.378991 + 0.378991i
\(477\) −353.912 −0.741954
\(478\) 11.2759 0.0235897
\(479\) 56.2384 + 56.2384i 0.117408 + 0.117408i 0.763370 0.645962i \(-0.223543\pi\)
−0.645962 + 0.763370i \(0.723543\pi\)
\(480\) 73.5694i 0.153270i
\(481\) −391.561 107.471i −0.814056 0.223432i
\(482\) −555.753 −1.15301
\(483\) −34.3451 + 34.3451i −0.0711079 + 0.0711079i
\(484\) 377.221i 0.779382i
\(485\) 67.6588i 0.139503i
\(486\) 94.3578 + 94.3578i 0.194152 + 0.194152i
\(487\) −152.415 152.415i −0.312967 0.312967i 0.533091 0.846058i \(-0.321030\pi\)
−0.846058 + 0.533091i \(0.821030\pi\)
\(488\) −39.2875 −0.0805072
\(489\) 52.6172 + 52.6172i 0.107602 + 0.107602i
\(490\) 202.177 0.412606
\(491\) 487.992 0.993874 0.496937 0.867786i \(-0.334458\pi\)
0.496937 + 0.867786i \(0.334458\pi\)
\(492\) 1.70465i 0.00346473i
\(493\) −730.754 −1.48226
\(494\) −38.7561 38.7561i −0.0784537 0.0784537i
\(495\) 848.989 848.989i 1.71513 1.71513i
\(496\) −58.2998 + 58.2998i −0.117540 + 0.117540i
\(497\) 512.166 1.03051
\(498\) −44.5678 44.5678i −0.0894937 0.0894937i
\(499\) −588.787 + 588.787i −1.17993 + 1.17993i −0.200174 + 0.979760i \(0.564151\pi\)
−0.979760 + 0.200174i \(0.935849\pi\)
\(500\) −52.2697 52.2697i −0.104539 0.104539i
\(501\) 28.6993 28.6993i 0.0572840 0.0572840i
\(502\) 126.343i 0.251679i
\(503\) −90.4426 90.4426i −0.179806 0.179806i 0.611465 0.791271i \(-0.290580\pi\)
−0.791271 + 0.611465i \(0.790580\pi\)
\(504\) 298.688 + 298.688i 0.592635 + 0.592635i
\(505\) −384.172 + 384.172i −0.760737 + 0.760737i
\(506\) 626.192i 1.23753i
\(507\) −18.3548 −0.0362027
\(508\) 238.592i 0.469670i
\(509\) 925.458i 1.81819i −0.416590 0.909094i \(-0.636775\pi\)
0.416590 0.909094i \(-0.363225\pi\)
\(510\) 75.7240 75.7240i 0.148478 0.148478i
\(511\) 484.268i 0.947686i
\(512\) 239.132 239.132i 0.467054 0.467054i
\(513\) 16.0557 16.0557i 0.0312976 0.0312976i
\(514\) −217.642 −0.423428
\(515\) 626.573 1.21665
\(516\) −12.9157 12.9157i −0.0250305 0.0250305i
\(517\) 601.418i 1.16328i
\(518\) −80.5721 + 293.558i −0.155545 + 0.566714i
\(519\) −29.9226 −0.0576544
\(520\) 497.515 497.515i 0.956759 0.956759i
\(521\) 87.8448i 0.168608i −0.996440 0.0843040i \(-0.973133\pi\)
0.996440 0.0843040i \(-0.0268667\pi\)
\(522\) 375.001i 0.718393i
\(523\) 17.6675 + 17.6675i 0.0337811 + 0.0337811i 0.723796 0.690014i \(-0.242396\pi\)
−0.690014 + 0.723796i \(0.742396\pi\)
\(524\) −163.138 163.138i −0.311332 0.311332i
\(525\) −63.9319 −0.121775
\(526\) −243.987 243.987i −0.463853 0.463853i
\(527\) 378.163 0.717577
\(528\) −38.4029 −0.0727327
\(529\) 8.70501i 0.0164556i
\(530\) 441.955 0.833877
\(531\) 409.333 + 409.333i 0.770873 + 0.770873i
\(532\) 23.6917 23.6917i 0.0445332 0.0445332i
\(533\) −19.4825 + 19.4825i −0.0365525 + 0.0365525i
\(534\) 89.7258 0.168026
\(535\) 338.725 + 338.725i 0.633131 + 0.633131i
\(536\) −268.939 + 268.939i −0.501753 + 0.501753i
\(537\) 46.3895 + 46.3895i 0.0863865 + 0.0863865i
\(538\) −192.998 + 192.998i −0.358733 + 0.358733i
\(539\) 332.540i 0.616957i
\(540\) 63.8813 + 63.8813i 0.118299 + 0.118299i
\(541\) 89.2845 + 89.2845i 0.165036 + 0.165036i 0.784793 0.619757i \(-0.212769\pi\)
−0.619757 + 0.784793i \(0.712769\pi\)
\(542\) −11.4461 + 11.4461i −0.0211182 + 0.0211182i
\(543\) 51.4648i 0.0947786i
\(544\) −669.353 −1.23043
\(545\) 269.768i 0.494987i
\(546\) 34.1211i 0.0624929i
\(547\) −75.5441 + 75.5441i −0.138106 + 0.138106i −0.772780 0.634674i \(-0.781134\pi\)
0.634674 + 0.772780i \(0.281134\pi\)
\(548\) 27.1664i 0.0495738i
\(549\) 28.5967 28.5967i 0.0520887 0.0520887i
\(550\) −582.815 + 582.815i −1.05966 + 1.05966i
\(551\) 95.9691 0.174173
\(552\) −75.4019 −0.136598
\(553\) −220.186 220.186i −0.398166 0.398166i
\(554\) 441.498i 0.796928i
\(555\) −27.5768 + 100.474i −0.0496880 + 0.181034i
\(556\) −392.770 −0.706422
\(557\) −154.792 + 154.792i −0.277902 + 0.277902i −0.832271 0.554369i \(-0.812960\pi\)
0.554369 + 0.832271i \(0.312960\pi\)
\(558\) 194.062i 0.347781i
\(559\) 295.229i 0.528138i
\(560\) −163.124 163.124i −0.291292 0.291292i
\(561\) 124.551 + 124.551i 0.222015 + 0.222015i
\(562\) 742.835 1.32177
\(563\) −65.2182 65.2182i −0.115840 0.115840i 0.646810 0.762651i \(-0.276103\pi\)
−0.762651 + 0.646810i \(0.776103\pi\)
\(564\) −22.4456 −0.0397971
\(565\) 588.613 1.04179
\(566\) 641.554i 1.13349i
\(567\) −427.695 −0.754311
\(568\) 562.210 + 562.210i 0.989806 + 0.989806i
\(569\) 511.812 511.812i 0.899494 0.899494i −0.0958970 0.995391i \(-0.530572\pi\)
0.995391 + 0.0958970i \(0.0305719\pi\)
\(570\) −9.94475 + 9.94475i −0.0174469 + 0.0174469i
\(571\) 124.918 0.218771 0.109386 0.993999i \(-0.465112\pi\)
0.109386 + 0.993999i \(0.465112\pi\)
\(572\) 253.628 + 253.628i 0.443405 + 0.443405i
\(573\) 46.9202 46.9202i 0.0818851 0.0818851i
\(574\) 14.6062 + 14.6062i 0.0254464 + 0.0254464i
\(575\) −500.457 + 500.457i −0.870361 + 0.870361i
\(576\) 541.389i 0.939911i
\(577\) −86.4511 86.4511i −0.149829 0.149829i 0.628213 0.778041i \(-0.283787\pi\)
−0.778041 + 0.628213i \(0.783787\pi\)
\(578\) −385.617 385.617i −0.667157 0.667157i
\(579\) 24.9602 24.9602i 0.0431092 0.0431092i
\(580\) 381.835i 0.658336i
\(581\) 622.755 1.07187
\(582\) 5.09365i 0.00875198i
\(583\) 726.925i 1.24687i
\(584\) 531.586 531.586i 0.910249 0.910249i
\(585\) 724.263i 1.23806i
\(586\) 85.9117 85.9117i 0.146607 0.146607i
\(587\) 500.633 500.633i 0.852867 0.852867i −0.137619 0.990485i \(-0.543945\pi\)
0.990485 + 0.137619i \(0.0439449\pi\)
\(588\) −12.4107 −0.0211067
\(589\) −49.6637 −0.0843187
\(590\) −511.163 511.163i −0.866378 0.866378i
\(591\) 22.4191i 0.0379342i
\(592\) −179.609 + 102.248i −0.303393 + 0.172716i
\(593\) −719.626 −1.21354 −0.606768 0.794879i \(-0.707534\pi\)
−0.606768 + 0.794879i \(0.707534\pi\)
\(594\) 128.862 128.862i 0.216939 0.216939i
\(595\) 1058.11i 1.77833i
\(596\) 403.373i 0.676801i
\(597\) −9.25768 9.25768i −0.0155070 0.0155070i
\(598\) −267.099 267.099i −0.446654 0.446654i
\(599\) −259.577 −0.433351 −0.216676 0.976244i \(-0.569521\pi\)
−0.216676 + 0.976244i \(0.569521\pi\)
\(600\) −70.1787 70.1787i −0.116965 0.116965i
\(601\) −292.942 −0.487424 −0.243712 0.969848i \(-0.578365\pi\)
−0.243712 + 0.969848i \(0.578365\pi\)
\(602\) −221.337 −0.367669
\(603\) 391.512i 0.649274i
\(604\) 396.090 0.655777
\(605\) −1106.27 1106.27i −1.82854 1.82854i
\(606\) −28.9222 + 28.9222i −0.0477263 + 0.0477263i
\(607\) −315.803 + 315.803i −0.520268 + 0.520268i −0.917652 0.397384i \(-0.869918\pi\)
0.397384 + 0.917652i \(0.369918\pi\)
\(608\) 87.9053 0.144581
\(609\) 42.2458 + 42.2458i 0.0693692 + 0.0693692i
\(610\) −35.7106 + 35.7106i −0.0585420 + 0.0585420i
\(611\) −256.532 256.532i −0.419855 0.419855i
\(612\) 288.280 288.280i 0.471045 0.471045i
\(613\) 405.498i 0.661498i −0.943719 0.330749i \(-0.892699\pi\)
0.943719 0.330749i \(-0.107301\pi\)
\(614\) −463.375 463.375i −0.754682 0.754682i
\(615\) 4.99917 + 4.99917i 0.00812873 + 0.00812873i
\(616\) 613.496 613.496i 0.995935 0.995935i
\(617\) 327.089i 0.530128i −0.964231 0.265064i \(-0.914607\pi\)
0.964231 0.265064i \(-0.0853931\pi\)
\(618\) 47.1712 0.0763287
\(619\) 525.496i 0.848943i −0.905441 0.424472i \(-0.860460\pi\)
0.905441 0.424472i \(-0.139540\pi\)
\(620\) 197.599i 0.318707i
\(621\) 110.652 110.652i 0.178184 0.178184i
\(622\) 55.5932i 0.0893782i
\(623\) −626.878 + 626.878i −1.00622 + 1.00622i
\(624\) 16.3805 16.3805i 0.0262509 0.0262509i
\(625\) 456.465 0.730344
\(626\) −632.182 −1.00988
\(627\) −16.3571 16.3571i −0.0260878 0.0260878i
\(628\) 148.608i 0.236636i
\(629\) 914.136 + 250.901i 1.45332 + 0.398888i
\(630\) 542.988 0.861886
\(631\) 517.188 517.188i 0.819632 0.819632i −0.166422 0.986055i \(-0.553221\pi\)
0.986055 + 0.166422i \(0.0532215\pi\)
\(632\) 483.400i 0.764874i
\(633\) 12.5822i 0.0198770i
\(634\) 393.096 + 393.096i 0.620026 + 0.620026i
\(635\) 699.713 + 699.713i 1.10191 + 1.10191i
\(636\) −27.1296 −0.0426566
\(637\) −141.843 141.843i −0.222674 0.222674i
\(638\) 770.241 1.20727
\(639\) −818.444 −1.28082
\(640\) 102.624i 0.160350i
\(641\) −1064.31 −1.66039 −0.830196 0.557472i \(-0.811772\pi\)
−0.830196 + 0.557472i \(0.811772\pi\)
\(642\) 25.5007 + 25.5007i 0.0397207 + 0.0397207i
\(643\) −607.938 + 607.938i −0.945470 + 0.945470i −0.998588 0.0531178i \(-0.983084\pi\)
0.0531178 + 0.998588i \(0.483084\pi\)
\(644\) 163.278 163.278i 0.253537 0.253537i
\(645\) −75.7552 −0.117450
\(646\) 90.4798 + 90.4798i 0.140062 + 0.140062i
\(647\) 506.664 506.664i 0.783097 0.783097i −0.197255 0.980352i \(-0.563203\pi\)
0.980352 + 0.197255i \(0.0632028\pi\)
\(648\) −469.485 469.485i −0.724513 0.724513i
\(649\) 840.758 840.758i 1.29547 1.29547i
\(650\) 497.193i 0.764913i
\(651\) −21.8621 21.8621i −0.0335823 0.0335823i
\(652\) −250.144 250.144i −0.383657 0.383657i
\(653\) 124.218 124.218i 0.190226 0.190226i −0.605568 0.795794i \(-0.707054\pi\)
0.795794 + 0.605568i \(0.207054\pi\)
\(654\) 20.3093i 0.0310540i
\(655\) −956.860 −1.46085
\(656\) 14.0241i 0.0213781i
\(657\) 773.863i 1.17787i
\(658\) −192.325 + 192.325i −0.292287 + 0.292287i
\(659\) 454.252i 0.689305i 0.938730 + 0.344653i \(0.112003\pi\)
−0.938730 + 0.344653i \(0.887997\pi\)
\(660\) 65.0804 65.0804i 0.0986067 0.0986067i
\(661\) −389.416 + 389.416i −0.589132 + 0.589132i −0.937396 0.348265i \(-0.886771\pi\)
0.348265 + 0.937396i \(0.386771\pi\)
\(662\) 597.055 0.901896
\(663\) −106.253 −0.160261
\(664\) 683.604 + 683.604i 1.02952 + 1.02952i
\(665\) 138.960i 0.208962i
\(666\) 128.755 469.107i 0.193325 0.704365i
\(667\) 661.398 0.991602
\(668\) −136.437 + 136.437i −0.204247 + 0.204247i
\(669\) 134.893i 0.201634i
\(670\) 488.908i 0.729714i
\(671\) −58.7367 58.7367i −0.0875361 0.0875361i
\(672\) 38.6961 + 38.6961i 0.0575835 + 0.0575835i
\(673\) −25.6563 −0.0381222 −0.0190611 0.999818i \(-0.506068\pi\)
−0.0190611 + 0.999818i \(0.506068\pi\)
\(674\) 428.872 + 428.872i 0.636309 + 0.636309i
\(675\) 205.975 0.305148
\(676\) 87.2593 0.129082
\(677\) 37.6324i 0.0555870i 0.999614 + 0.0277935i \(0.00884809\pi\)
−0.999614 + 0.0277935i \(0.991152\pi\)
\(678\) 44.3134 0.0653590
\(679\) 35.5873 + 35.5873i 0.0524113 + 0.0524113i
\(680\) −1161.49 + 1161.49i −1.70808 + 1.70808i
\(681\) −47.8239 + 47.8239i −0.0702260 + 0.0702260i
\(682\) −398.598 −0.584454
\(683\) −136.128 136.128i −0.199308 0.199308i 0.600395 0.799703i \(-0.295010\pi\)
−0.799703 + 0.600395i \(0.795010\pi\)
\(684\) −37.8594 + 37.8594i −0.0553500 + 0.0553500i
\(685\) 79.6702 + 79.6702i 0.116307 + 0.116307i
\(686\) −391.407 + 391.407i −0.570564 + 0.570564i
\(687\) 89.1561i 0.129776i
\(688\) −106.257 106.257i −0.154444 0.154444i
\(689\) −310.066 310.066i −0.450023 0.450023i
\(690\) −68.5371 + 68.5371i −0.0993291 + 0.0993291i
\(691\) 1141.32i 1.65170i −0.563890 0.825850i \(-0.690696\pi\)
0.563890 0.825850i \(-0.309304\pi\)
\(692\) 142.253 0.205568
\(693\) 893.105i 1.28875i
\(694\) 356.331i 0.513445i
\(695\) −1151.87 + 1151.87i −1.65736 + 1.65736i
\(696\) 92.7474i 0.133258i
\(697\) 45.4837 45.4837i 0.0652564 0.0652564i
\(698\) 74.2795 74.2795i 0.106418 0.106418i
\(699\) −12.6899 −0.0181544
\(700\) 303.935 0.434192
\(701\) 30.7153 + 30.7153i 0.0438163 + 0.0438163i 0.728675 0.684859i \(-0.240136\pi\)
−0.684859 + 0.728675i \(0.740136\pi\)
\(702\) 109.931i 0.156596i
\(703\) −120.052 32.9505i −0.170771 0.0468713i
\(704\) 1112.00 1.57954
\(705\) −65.8255 + 65.8255i −0.0933695 + 0.0933695i
\(706\) 74.8669i 0.106044i
\(707\) 404.135i 0.571619i
\(708\) 31.3780 + 31.3780i 0.0443192 + 0.0443192i
\(709\) 180.362 + 180.362i 0.254390 + 0.254390i 0.822768 0.568378i \(-0.192429\pi\)
−0.568378 + 0.822768i \(0.692429\pi\)
\(710\) 1022.05 1.43950
\(711\) 351.858 + 351.858i 0.494878 + 0.494878i
\(712\) −1376.26 −1.93295
\(713\) −342.272 −0.480044
\(714\) 79.6589i 0.111567i
\(715\) 1487.62 2.08058
\(716\) −220.538 220.538i −0.308013 0.308013i
\(717\) −2.02992 + 2.02992i −0.00283113 + 0.00283113i
\(718\) 654.748 654.748i 0.911905 0.911905i
\(719\) −171.807 −0.238952 −0.119476 0.992837i \(-0.538122\pi\)
−0.119476 + 0.992837i \(0.538122\pi\)
\(720\) 260.673 + 260.673i 0.362046 + 0.362046i
\(721\) −329.566 + 329.566i −0.457095 + 0.457095i
\(722\) 367.029 + 367.029i 0.508351 + 0.508351i
\(723\) 100.049 100.049i 0.138380 0.138380i
\(724\) 244.665i 0.337936i
\(725\) 615.582 + 615.582i 0.849079 + 0.849079i
\(726\) −83.2845 83.2845i −0.114717 0.114717i
\(727\) 304.684 304.684i 0.419098 0.419098i −0.465795 0.884893i \(-0.654232\pi\)
0.884893 + 0.465795i \(0.154232\pi\)
\(728\) 523.367i 0.718910i
\(729\) 660.506 0.906043
\(730\) 966.376i 1.32380i
\(731\) 689.240i 0.942873i
\(732\) 2.19212 2.19212i 0.00299469 0.00299469i
\(733\) 641.352i 0.874968i −0.899226 0.437484i \(-0.855870\pi\)
0.899226 0.437484i \(-0.144130\pi\)
\(734\) 199.351 199.351i 0.271595 0.271595i
\(735\) −36.3967 + 36.3967i −0.0495193 + 0.0495193i
\(736\) 605.824 0.823131
\(737\) −804.154 −1.09112
\(738\) −23.3409 23.3409i −0.0316272 0.0316272i
\(739\) 6.01293i 0.00813658i −0.999992 0.00406829i \(-0.998705\pi\)
0.999992 0.00406829i \(-0.00129498\pi\)
\(740\) 131.101 477.656i 0.177164 0.645481i
\(741\) 13.9541 0.0188314
\(742\) −232.460 + 232.460i −0.313288 + 0.313288i
\(743\) 529.715i 0.712941i 0.934307 + 0.356471i \(0.116020\pi\)
−0.934307 + 0.356471i \(0.883980\pi\)
\(744\) 47.9965i 0.0645114i
\(745\) −1182.96 1182.96i −1.58787 1.58787i
\(746\) −157.314 157.314i −0.210877 0.210877i
\(747\) −995.166 −1.33222
\(748\) −592.118 592.118i −0.791601 0.791601i
\(749\) −356.326 −0.475736
\(750\) −23.0807 −0.0307742
\(751\) 696.245i 0.927091i 0.886073 + 0.463545i \(0.153423\pi\)
−0.886073 + 0.463545i \(0.846577\pi\)
\(752\) −184.659 −0.245557
\(753\) 22.7447 + 22.7447i 0.0302054 + 0.0302054i
\(754\) −328.542 + 328.542i −0.435732 + 0.435732i
\(755\) 1161.60 1161.60i 1.53854 1.53854i
\(756\) −67.2007 −0.0888898
\(757\) −503.637 503.637i −0.665306 0.665306i 0.291320 0.956626i \(-0.405906\pi\)
−0.956626 + 0.291320i \(0.905906\pi\)
\(758\) 237.862 237.862i 0.313802 0.313802i
\(759\) −112.729 112.729i −0.148524 0.148524i
\(760\) 152.538 152.538i 0.200707 0.200707i
\(761\) 246.317i 0.323676i −0.986817 0.161838i \(-0.948258\pi\)
0.986817 0.161838i \(-0.0517422\pi\)
\(762\) 52.6774 + 52.6774i 0.0691305 + 0.0691305i
\(763\) 141.893 + 141.893i 0.185967 + 0.185967i
\(764\) −223.060 + 223.060i −0.291964 + 0.291964i
\(765\) 1690.86i 2.21027i
\(766\) −898.117 −1.17248
\(767\) 717.242i 0.935127i
\(768\) 100.124i 0.130370i
\(769\) 810.146 810.146i 1.05351 1.05351i 0.0550210 0.998485i \(-0.482477\pi\)
0.998485 0.0550210i \(-0.0175226\pi\)
\(770\) 1115.28i 1.44842i
\(771\) 39.1808 39.1808i 0.0508181 0.0508181i
\(772\) −118.662 + 118.662i −0.153707 + 0.153707i
\(773\) 294.190 0.380582 0.190291 0.981728i \(-0.439057\pi\)
0.190291 + 0.981728i \(0.439057\pi\)
\(774\) 353.697 0.456973
\(775\) −318.562 318.562i −0.411048 0.411048i
\(776\) 78.1290i 0.100682i
\(777\) −38.3424 67.3522i −0.0493468 0.0866824i
\(778\) −1132.02 −1.45504
\(779\) −5.97332 + 5.97332i −0.00766793 + 0.00766793i
\(780\) 55.5194i 0.0711787i
\(781\) 1681.06i 2.15245i
\(782\) 623.567 + 623.567i 0.797401 + 0.797401i
\(783\) −136.107 136.107i −0.173827 0.173827i
\(784\) −102.103 −0.130233
\(785\) 435.817 + 435.817i 0.555181 + 0.555181i
\(786\) −72.0366 −0.0916496
\(787\) 887.447 1.12763 0.563816 0.825900i \(-0.309333\pi\)
0.563816 + 0.825900i \(0.309333\pi\)
\(788\) 106.581i 0.135255i
\(789\) 87.8467 0.111339
\(790\) −439.389 439.389i −0.556189 0.556189i
\(791\) −309.600 + 309.600i −0.391403 + 0.391403i
\(792\) −980.370 + 980.370i −1.23784 + 1.23784i
\(793\) 50.1077 0.0631875
\(794\) −261.981 261.981i −0.329951 0.329951i
\(795\) −79.5623 + 79.5623i −0.100078 + 0.100078i
\(796\) 44.0113 + 44.0113i 0.0552906 + 0.0552906i
\(797\) −522.357 + 522.357i −0.655404 + 0.655404i −0.954289 0.298885i \(-0.903385\pi\)
0.298885 + 0.954289i \(0.403385\pi\)
\(798\) 10.4615i 0.0131097i
\(799\) 598.897 + 598.897i 0.749558 + 0.749558i
\(800\) 563.858 + 563.858i 0.704823 + 0.704823i
\(801\) 1001.75 1001.75i 1.25063 1.25063i
\(802\) 529.951i 0.660786i
\(803\) 1589.49 1.97944
\(804\) 30.0119i 0.0373282i
\(805\) 957.681i 1.18967i
\(806\) 170.020 170.020i 0.210943 0.210943i
\(807\) 69.4885i 0.0861072i
\(808\) 443.623 443.623i 0.549038 0.549038i
\(809\) 180.910 180.910i 0.223622 0.223622i −0.586400 0.810022i \(-0.699455\pi\)
0.810022 + 0.586400i \(0.199455\pi\)
\(810\) −853.482 −1.05368
\(811\) 914.793 1.12798 0.563991 0.825781i \(-0.309265\pi\)
0.563991 + 0.825781i \(0.309265\pi\)
\(812\) −200.838 200.838i −0.247338 0.247338i
\(813\) 4.12112i 0.00506903i
\(814\) −963.532 264.458i −1.18370 0.324888i
\(815\) −1467.18 −1.80022
\(816\) −38.2419 + 38.2419i −0.0468651 + 0.0468651i
\(817\) 90.5171i 0.110792i
\(818\) 57.1845i 0.0699077i
\(819\) −380.949 380.949i −0.465139 0.465139i
\(820\) −23.7662 23.7662i −0.0289832 0.0289832i
\(821\) −1307.60 −1.59270 −0.796348 0.604839i \(-0.793237\pi\)
−0.796348 + 0.604839i \(0.793237\pi\)
\(822\) 5.99792 + 5.99792i 0.00729675 + 0.00729675i
\(823\) 71.3330 0.0866743 0.0433372 0.999061i \(-0.486201\pi\)
0.0433372 + 0.999061i \(0.486201\pi\)
\(824\) −723.535 −0.878077
\(825\) 209.841i 0.254353i
\(826\) 537.724 0.650998
\(827\) −423.902 423.902i −0.512578 0.512578i 0.402737 0.915316i \(-0.368059\pi\)
−0.915316 + 0.402737i \(0.868059\pi\)
\(828\) −260.919 + 260.919i −0.315120 + 0.315120i
\(829\) 139.431 139.431i 0.168191 0.168191i −0.617993 0.786184i \(-0.712054\pi\)
0.786184 + 0.617993i \(0.212054\pi\)
\(830\) 1242.73 1.49727
\(831\) 79.4802 + 79.4802i 0.0956440 + 0.0956440i
\(832\) −474.316 + 474.316i −0.570091 + 0.570091i
\(833\) 331.146 + 331.146i 0.397534 + 0.397534i
\(834\) −86.7176 + 86.7176i −0.103978 + 0.103978i
\(835\) 800.252i 0.958386i
\(836\) 77.7621 + 77.7621i 0.0930169 + 0.0930169i
\(837\) 70.4348 + 70.4348i 0.0841515 + 0.0841515i
\(838\) −232.674 + 232.674i −0.277654 + 0.277654i
\(839\) 946.465i 1.12809i 0.825745 + 0.564043i \(0.190755\pi\)
−0.825745 + 0.564043i \(0.809245\pi\)
\(840\) 134.295 0.159875
\(841\) 27.4541i 0.0326446i
\(842\) 290.998i 0.345604i
\(843\) −133.728 + 133.728i −0.158633 + 0.158633i
\(844\) 59.8160i 0.0708721i
\(845\) 255.903 255.903i 0.302844 0.302844i
\(846\) 307.336 307.336i 0.363281 0.363281i
\(847\) 1163.75 1.37397
\(848\) −223.194 −0.263201
\(849\) −115.495 115.495i −0.136036 0.136036i
\(850\) 1160.74i 1.36558i
\(851\) −827.375 227.088i −0.972238 0.266848i
\(852\) −62.7389 −0.0736372
\(853\) −718.017 + 718.017i −0.841755 + 0.841755i −0.989087 0.147332i \(-0.952931\pi\)
0.147332 + 0.989087i \(0.452931\pi\)
\(854\) 37.5663i 0.0439886i
\(855\) 222.059i 0.259718i
\(856\) −391.143 391.143i −0.456943 0.456943i
\(857\) 241.022 + 241.022i 0.281239 + 0.281239i 0.833603 0.552364i \(-0.186274\pi\)
−0.552364 + 0.833603i \(0.686274\pi\)
\(858\) 111.994 0.130529
\(859\) 944.215 + 944.215i 1.09920 + 1.09920i 0.994504 + 0.104698i \(0.0333877\pi\)
0.104698 + 0.994504i \(0.466612\pi\)
\(860\) 360.143 0.418771
\(861\) −5.25894 −0.00610794
\(862\) 1102.94i 1.27952i
\(863\) 1108.91 1.28495 0.642473 0.766309i \(-0.277909\pi\)
0.642473 + 0.766309i \(0.277909\pi\)
\(864\) −124.670 124.670i −0.144294 0.144294i
\(865\) 417.182 417.182i 0.482292 0.482292i
\(866\) −241.116 + 241.116i −0.278425 + 0.278425i
\(867\) 138.840 0.160139
\(868\) 103.933 + 103.933i 0.119739 + 0.119739i
\(869\) 722.706 722.706i 0.831652 0.831652i
\(870\) 84.3033 + 84.3033i 0.0969003 + 0.0969003i
\(871\) 343.008 343.008i 0.393809 0.393809i
\(872\) 311.515i 0.357242i
\(873\) −56.8687 56.8687i −0.0651417 0.0651417i
\(874\) −81.8924 81.8924i −0.0936984 0.0936984i
\(875\) 161.255 161.255i 0.184292 0.184292i
\(876\) 59.3215i 0.0677186i
\(877\) −696.297 −0.793954 −0.396977 0.917829i \(-0.629941\pi\)
−0.396977 + 0.917829i \(0.629941\pi\)
\(878\) 881.755i 1.00428i
\(879\) 30.9323i 0.0351903i
\(880\) 535.414 535.414i 0.608425 0.608425i
\(881\) 310.219i 0.352121i 0.984379 + 0.176061i \(0.0563355\pi\)
−0.984379 + 0.176061i \(0.943664\pi\)
\(882\) 169.934 169.934i 0.192669 0.192669i
\(883\) 534.700 534.700i 0.605549 0.605549i −0.336231 0.941780i \(-0.609152\pi\)
0.941780 + 0.336231i \(0.109152\pi\)
\(884\) 505.129 0.571413
\(885\) 184.043 0.207958
\(886\) 669.322 + 669.322i 0.755443 + 0.755443i
\(887\) 474.335i 0.534764i −0.963591 0.267382i \(-0.913841\pi\)
0.963591 0.267382i \(-0.0861585\pi\)
\(888\) 31.8443 116.022i 0.0358607 0.130656i
\(889\) −736.072 −0.827977
\(890\) −1250.96 + 1250.96i −1.40557 + 1.40557i
\(891\) 1403.80i 1.57554i
\(892\) 641.285i 0.718930i
\(893\) −78.6524 78.6524i −0.0880766 0.0880766i
\(894\) −89.0585 89.0585i −0.0996181 0.0996181i
\(895\) −1293.53 −1.44528
\(896\) −53.9783 53.9783i −0.0602436 0.0602436i
\(897\) 96.1683 0.107211
\(898\) −437.164 −0.486820
\(899\) 421.008i 0.468307i
\(900\) −485.690 −0.539655
\(901\) 723.878 + 723.878i 0.803416 + 0.803416i
\(902\) −47.9414 + 47.9414i −0.0531501 + 0.0531501i
\(903\) 39.8458 39.8458i 0.0441261 0.0441261i
\(904\) −679.701 −0.751882
\(905\) 717.524 + 717.524i 0.792844 + 0.792844i
\(906\) 87.4504 87.4504i 0.0965236 0.0965236i
\(907\) −729.638 729.638i −0.804452 0.804452i 0.179336 0.983788i \(-0.442605\pi\)
−0.983788 + 0.179336i \(0.942605\pi\)
\(908\) 227.356 227.356i 0.250393 0.250393i
\(909\) 645.810i 0.710462i
\(910\) 475.717 + 475.717i 0.522766 + 0.522766i
\(911\) 199.232 + 199.232i 0.218696 + 0.218696i 0.807949 0.589253i \(-0.200578\pi\)
−0.589253 + 0.807949i \(0.700578\pi\)
\(912\) 5.02226 5.02226i 0.00550687 0.00550687i
\(913\) 2044.04i 2.23882i
\(914\) −352.634 −0.385814
\(915\) 12.8575i 0.0140519i
\(916\) 423.851i 0.462720i
\(917\) 503.291 503.291i 0.548845 0.548845i
\(918\) 256.643i 0.279568i
\(919\) −77.9734 + 77.9734i −0.0848459 + 0.0848459i −0.748256 0.663410i \(-0.769109\pi\)
0.663410 + 0.748256i \(0.269109\pi\)
\(920\) 1051.26 1051.26i 1.14267 1.14267i
\(921\) 166.837 0.181148
\(922\) 1216.92 1.31987
\(923\) −717.047 717.047i −0.776866 0.776866i
\(924\) 68.4622i 0.0740932i
\(925\) −558.704 981.419i −0.604005 1.06099i
\(926\) −495.037 −0.534597
\(927\) 526.648 526.648i 0.568121 0.568121i
\(928\) 745.188i 0.803004i
\(929\) 1756.58i 1.89083i 0.325870 + 0.945415i \(0.394343\pi\)
−0.325870 + 0.945415i \(0.605657\pi\)
\(930\) −43.6267 43.6267i −0.0469104 0.0469104i
\(931\) −43.4890 43.4890i −0.0467122 0.0467122i
\(932\) 60.3285 0.0647301
\(933\) 10.0081 + 10.0081i 0.0107268 + 0.0107268i
\(934\) 361.188 0.386711
\(935\) −3472.98 −3.71441
\(936\) 836.343i 0.893529i
\(937\) −1070.63 −1.14261 −0.571306 0.820737i \(-0.693563\pi\)
−0.571306 + 0.820737i \(0.693563\pi\)
\(938\) −257.157 257.157i −0.274154 0.274154i
\(939\) 113.808 113.808i 0.121201 0.121201i
\(940\) 312.937 312.937i 0.332911 0.332911i
\(941\) 1074.54 1.14191 0.570957 0.820980i \(-0.306572\pi\)
0.570957 + 0.820980i \(0.306572\pi\)
\(942\) 32.8102 + 32.8102i 0.0348304 + 0.0348304i
\(943\) −41.1668 + 41.1668i −0.0436552 + 0.0436552i
\(944\) 258.146 + 258.146i 0.273459 + 0.273459i
\(945\) −197.078 + 197.078i −0.208548 + 0.208548i
\(946\) 726.484i 0.767953i
\(947\) −129.643 129.643i −0.136899 0.136899i 0.635336 0.772236i \(-0.280861\pi\)
−0.772236 + 0.635336i \(0.780861\pi\)
\(948\) 26.9722 + 26.9722i 0.0284516 + 0.0284516i
\(949\) −677.989 + 677.989i −0.714425 + 0.714425i
\(950\) 152.439i 0.160462i
\(951\) −141.533 −0.148826
\(952\) 1221.85i 1.28345i
\(953\) 502.255i 0.527025i −0.964656 0.263512i \(-0.915119\pi\)
0.964656 0.263512i \(-0.0848810\pi\)
\(954\) 371.472 371.472i 0.389384 0.389384i
\(955\) 1308.32i 1.36997i
\(956\) 9.65032 9.65032i 0.0100945 0.0100945i
\(957\) −138.662 + 138.662i −0.144892 + 0.144892i
\(958\) −118.058 −0.123233
\(959\) −83.8101 −0.0873932
\(960\) 121.709 + 121.709i 0.126780 + 0.126780i
\(961\) 743.130i 0.773288i
\(962\) 523.793 298.186i 0.544483 0.309965i
\(963\) 569.412 0.591289
\(964\) −475.635 + 475.635i −0.493398 + 0.493398i
\(965\) 695.992i 0.721236i
\(966\) 72.0984i 0.0746361i
\(967\) −85.0575 85.0575i −0.0879602 0.0879602i 0.661758 0.749718i \(-0.269811\pi\)
−0.749718 + 0.661758i \(0.769811\pi\)
\(968\) 1277.46 + 1277.46i 1.31969 + 1.31969i
\(969\) −32.5770 −0.0336192
\(970\) 71.0159 + 71.0159i 0.0732122 + 0.0732122i
\(971\) −496.661 −0.511494 −0.255747 0.966744i \(-0.582321\pi\)
−0.255747 + 0.966744i \(0.582321\pi\)
\(972\) 161.510 0.166163
\(973\) 1211.72i 1.24535i
\(974\) 319.955 0.328496
\(975\) 89.5066 + 89.5066i 0.0918016 + 0.0918016i
\(976\) 18.0345 18.0345i 0.0184779 0.0184779i
\(977\) 1186.94 1186.94i 1.21488 1.21488i 0.245479 0.969402i \(-0.421055\pi\)
0.969402 0.245479i \(-0.0789451\pi\)
\(978\) −110.456 −0.112941
\(979\) −2057.57 2057.57i −2.10171 2.10171i
\(980\) 173.031 173.031i 0.176562 0.176562i
\(981\) −226.746 226.746i −0.231137 0.231137i
\(982\) −512.205 + 512.205i −0.521594 + 0.521594i
\(983\) 1471.76i 1.49721i −0.663017 0.748605i \(-0.730724\pi\)
0.663017 0.748605i \(-0.269276\pi\)
\(984\) −5.77279 5.77279i −0.00586666 0.00586666i
\(985\) 312.568 + 312.568i 0.317328 + 0.317328i
\(986\) 767.012 767.012i 0.777903 0.777903i
\(987\) 69.2460i 0.0701580i
\(988\) −66.3381 −0.0671438
\(989\) 623.824i 0.630763i
\(990\) 1782.23i 1.80023i
\(991\) 672.226 672.226i 0.678331 0.678331i −0.281291 0.959622i \(-0.590763\pi\)
0.959622 + 0.281291i \(0.0907628\pi\)
\(992\) 385.633i 0.388743i
\(993\) −107.484 + 107.484i −0.108242 + 0.108242i
\(994\) −537.578 + 537.578i −0.540823 + 0.540823i
\(995\) 258.142 0.259439
\(996\) −76.2858 −0.0765922
\(997\) −584.483 584.483i −0.586242 0.586242i 0.350370 0.936611i \(-0.386056\pi\)
−0.936611 + 0.350370i \(0.886056\pi\)
\(998\) 1236.00i 1.23848i
\(999\) 123.531 + 216.994i 0.123655 + 0.217211i
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 37.3.d.a.6.3 12
3.2 odd 2 333.3.i.a.154.4 12
4.3 odd 2 592.3.k.e.561.4 12
37.31 odd 4 inner 37.3.d.a.31.3 yes 12
111.68 even 4 333.3.i.a.253.4 12
148.31 even 4 592.3.k.e.401.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.3.d.a.6.3 12 1.1 even 1 trivial
37.3.d.a.31.3 yes 12 37.31 odd 4 inner
333.3.i.a.154.4 12 3.2 odd 2
333.3.i.a.253.4 12 111.68 even 4
592.3.k.e.401.3 12 148.31 even 4
592.3.k.e.561.4 12 4.3 odd 2