Properties

Label 375.2.g.b.301.1
Level $375$
Weight $2$
Character 375.301
Analytic conductor $2.994$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [375,2,Mod(76,375)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(375, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("375.76");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 375 = 3 \cdot 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 375.g (of order \(5\), degree \(4\), 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: \(2.99439007580\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.26265625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 2x^{6} + x^{4} + 8x^{2} - 24x + 16 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 301.1
Root \(-0.0272949 + 1.41395i\) of defining polynomial
Character \(\chi\) \(=\) 375.301
Dual form 375.2.g.b.76.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38048 + 1.00297i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.281722 - 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} +3.94243 q^{7} +(-0.573870 - 1.76619i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\) \(q+(-1.38048 + 1.00297i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(0.281722 - 0.867051i) q^{4} +(-0.527295 - 1.62285i) q^{6} +3.94243 q^{7} +(-0.573870 - 1.76619i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(4.78023 - 3.47304i) q^{11} +(0.737558 + 0.535867i) q^{12} +(2.66220 + 1.93420i) q^{13} +(-5.44243 + 3.95416i) q^{14} +(4.03877 + 2.93434i) q^{16} +(-0.836312 - 2.57390i) q^{17} +1.70636 q^{18} +(-0.728704 - 2.24272i) q^{19} +(-1.21828 + 3.74947i) q^{21} +(-3.11562 + 9.58890i) q^{22} +(-0.472705 + 0.343440i) q^{23} +1.85708 q^{24} -5.61505 q^{26} +(0.809017 - 0.587785i) q^{27} +(1.11067 - 3.41829i) q^{28} +(-1.20877 + 3.72022i) q^{29} +(0.837233 + 2.57674i) q^{31} -4.80433 q^{32} +(1.82589 + 5.61950i) q^{33} +(3.73607 + 2.71441i) q^{34} +(-0.737558 + 0.535867i) q^{36} +(-0.0168692 - 0.0122562i) q^{37} +(3.25535 + 2.36515i) q^{38} +(-2.66220 + 1.93420i) q^{39} +(-1.19098 - 0.865300i) q^{41} +(-2.07882 - 6.39796i) q^{42} -1.27279 q^{43} +(-1.66461 - 5.12314i) q^{44} +(0.308096 - 0.948222i) q^{46} +(-1.67907 + 5.16764i) q^{47} +(-4.03877 + 2.93434i) q^{48} +8.54276 q^{49} +2.70636 q^{51} +(2.42705 - 1.76336i) q^{52} +(-0.870050 + 2.67774i) q^{53} +(-0.527295 + 1.62285i) q^{54} +(-2.26244 - 6.96308i) q^{56} +2.35813 q^{57} +(-2.06260 - 6.34804i) q^{58} +(3.79456 + 2.75691i) q^{59} +(-4.51538 + 3.28061i) q^{61} +(-3.74018 - 2.71740i) q^{62} +(-3.18949 - 2.31730i) q^{63} +(-1.44528 + 1.05006i) q^{64} +(-8.15681 - 5.92627i) q^{66} +(-1.86361 - 5.73559i) q^{67} -2.46731 q^{68} +(-0.180557 - 0.555698i) q^{69} +(-2.50346 + 7.70487i) q^{71} +(-0.573870 + 1.76619i) q^{72} +(10.7734 - 7.82730i) q^{73} +0.0355801 q^{74} -2.14984 q^{76} +(18.8457 - 13.6922i) q^{77} +(1.73515 - 5.34023i) q^{78} +(5.14971 - 15.8492i) q^{79} +(0.309017 + 0.951057i) q^{81} +2.51200 q^{82} +(-0.241540 - 0.743385i) q^{83} +(2.90777 + 2.11262i) q^{84} +(1.75705 - 1.27657i) q^{86} +(-3.16461 - 2.29922i) q^{87} +(-8.87728 - 6.44972i) q^{88} +(2.80994 - 2.04154i) q^{89} +(10.4955 + 7.62545i) q^{91} +(0.164609 + 0.506614i) q^{92} -2.70934 q^{93} +(-2.86510 - 8.81786i) q^{94} +(1.48462 - 4.56919i) q^{96} +(0.758460 - 2.33430i) q^{97} +(-11.7931 + 8.56817i) q^{98} -5.90869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + 2 q^{3} + q^{4} - q^{6} - 4 q^{7} - 2 q^{9} + 16 q^{11} + 9 q^{12} + 8 q^{13} - 8 q^{14} - 17 q^{16} + q^{17} - 4 q^{18} - 5 q^{19} - 11 q^{21} - 13 q^{22} - 7 q^{23} + 30 q^{24} + 6 q^{26} + 2 q^{27} + 17 q^{28} + 5 q^{29} - 19 q^{31} - 24 q^{32} + 9 q^{33} + 12 q^{34} - 9 q^{36} + q^{37} + 10 q^{38} - 8 q^{39} - 14 q^{41} + 8 q^{42} - 32 q^{43} - 3 q^{44} + 16 q^{46} + q^{47} + 17 q^{48} + 16 q^{49} + 4 q^{51} + 6 q^{52} + 3 q^{53} - q^{54} - 15 q^{56} - 10 q^{57} - 5 q^{58} + 30 q^{59} - 14 q^{61} + 17 q^{62} - 9 q^{63} - 44 q^{64} - 7 q^{66} - 4 q^{67} + 22 q^{68} - 8 q^{69} + 21 q^{71} - 2 q^{73} - 38 q^{74} + 80 q^{76} + 37 q^{77} + 14 q^{78} - 30 q^{79} - 2 q^{81} + 12 q^{82} - 2 q^{83} + 8 q^{84} - 34 q^{86} - 15 q^{87} - 70 q^{88} + 21 q^{91} - 9 q^{92} - 46 q^{93} - 33 q^{94} + 34 q^{96} + 6 q^{97} - 73 q^{98} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/375\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(251\)
\(\chi(n)\) \(e\left(\frac{4}{5}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38048 + 1.00297i −0.976144 + 0.709210i −0.956844 0.290604i \(-0.906144\pi\)
−0.0193004 + 0.999814i \(0.506144\pi\)
\(3\) −0.309017 + 0.951057i −0.178411 + 0.549093i
\(4\) 0.281722 0.867051i 0.140861 0.433526i
\(5\) 0 0
\(6\) −0.527295 1.62285i −0.215267 0.662524i
\(7\) 3.94243 1.49010 0.745049 0.667009i \(-0.232426\pi\)
0.745049 + 0.667009i \(0.232426\pi\)
\(8\) −0.573870 1.76619i −0.202894 0.624442i
\(9\) −0.809017 0.587785i −0.269672 0.195928i
\(10\) 0 0
\(11\) 4.78023 3.47304i 1.44129 1.04716i 0.453524 0.891244i \(-0.350167\pi\)
0.987770 0.155918i \(-0.0498334\pi\)
\(12\) 0.737558 + 0.535867i 0.212915 + 0.154692i
\(13\) 2.66220 + 1.93420i 0.738361 + 0.536451i 0.892197 0.451646i \(-0.149163\pi\)
−0.153836 + 0.988096i \(0.549163\pi\)
\(14\) −5.44243 + 3.95416i −1.45455 + 1.05679i
\(15\) 0 0
\(16\) 4.03877 + 2.93434i 1.00969 + 0.733585i
\(17\) −0.836312 2.57390i −0.202835 0.624263i −0.999795 0.0202310i \(-0.993560\pi\)
0.796960 0.604032i \(-0.206440\pi\)
\(18\) 1.70636 0.402193
\(19\) −0.728704 2.24272i −0.167176 0.514515i 0.832014 0.554755i \(-0.187188\pi\)
−0.999190 + 0.0402396i \(0.987188\pi\)
\(20\) 0 0
\(21\) −1.21828 + 3.74947i −0.265850 + 0.818202i
\(22\) −3.11562 + 9.58890i −0.664253 + 2.04436i
\(23\) −0.472705 + 0.343440i −0.0985658 + 0.0716123i −0.635977 0.771708i \(-0.719403\pi\)
0.537411 + 0.843321i \(0.319403\pi\)
\(24\) 1.85708 0.379075
\(25\) 0 0
\(26\) −5.61505 −1.10120
\(27\) 0.809017 0.587785i 0.155695 0.113119i
\(28\) 1.11067 3.41829i 0.209897 0.645996i
\(29\) −1.20877 + 3.72022i −0.224464 + 0.690828i 0.773882 + 0.633330i \(0.218312\pi\)
−0.998346 + 0.0574980i \(0.981688\pi\)
\(30\) 0 0
\(31\) 0.837233 + 2.57674i 0.150371 + 0.462796i 0.997663 0.0683330i \(-0.0217680\pi\)
−0.847291 + 0.531129i \(0.821768\pi\)
\(32\) −4.80433 −0.849294
\(33\) 1.82589 + 5.61950i 0.317846 + 0.978229i
\(34\) 3.73607 + 2.71441i 0.640730 + 0.465518i
\(35\) 0 0
\(36\) −0.737558 + 0.535867i −0.122926 + 0.0893112i
\(37\) −0.0168692 0.0122562i −0.00277328 0.00201490i 0.586398 0.810023i \(-0.300546\pi\)
−0.589171 + 0.808008i \(0.700546\pi\)
\(38\) 3.25535 + 2.36515i 0.528087 + 0.383678i
\(39\) −2.66220 + 1.93420i −0.426293 + 0.309720i
\(40\) 0 0
\(41\) −1.19098 0.865300i −0.186000 0.135137i 0.490889 0.871222i \(-0.336672\pi\)
−0.676889 + 0.736085i \(0.736672\pi\)
\(42\) −2.07882 6.39796i −0.320769 0.987227i
\(43\) −1.27279 −0.194098 −0.0970491 0.995280i \(-0.530940\pi\)
−0.0970491 + 0.995280i \(0.530940\pi\)
\(44\) −1.66461 5.12314i −0.250949 0.772342i
\(45\) 0 0
\(46\) 0.308096 0.948222i 0.0454263 0.139808i
\(47\) −1.67907 + 5.16764i −0.244917 + 0.753777i 0.750733 + 0.660606i \(0.229701\pi\)
−0.995650 + 0.0931716i \(0.970299\pi\)
\(48\) −4.03877 + 2.93434i −0.582947 + 0.423536i
\(49\) 8.54276 1.22039
\(50\) 0 0
\(51\) 2.70636 0.378967
\(52\) 2.42705 1.76336i 0.336571 0.244533i
\(53\) −0.870050 + 2.67774i −0.119511 + 0.367816i −0.992861 0.119277i \(-0.961942\pi\)
0.873350 + 0.487092i \(0.161942\pi\)
\(54\) −0.527295 + 1.62285i −0.0717557 + 0.220841i
\(55\) 0 0
\(56\) −2.26244 6.96308i −0.302332 0.930481i
\(57\) 2.35813 0.312343
\(58\) −2.06260 6.34804i −0.270833 0.833539i
\(59\) 3.79456 + 2.75691i 0.494009 + 0.358919i 0.806724 0.590928i \(-0.201238\pi\)
−0.312715 + 0.949847i \(0.601238\pi\)
\(60\) 0 0
\(61\) −4.51538 + 3.28061i −0.578135 + 0.420040i −0.838051 0.545591i \(-0.816305\pi\)
0.259916 + 0.965631i \(0.416305\pi\)
\(62\) −3.74018 2.71740i −0.475004 0.345110i
\(63\) −3.18949 2.31730i −0.401838 0.291953i
\(64\) −1.44528 + 1.05006i −0.180660 + 0.131257i
\(65\) 0 0
\(66\) −8.15681 5.92627i −1.00403 0.729473i
\(67\) −1.86361 5.73559i −0.227676 0.700714i −0.998009 0.0630725i \(-0.979910\pi\)
0.770333 0.637642i \(-0.220090\pi\)
\(68\) −2.46731 −0.299206
\(69\) −0.180557 0.555698i −0.0217365 0.0668982i
\(70\) 0 0
\(71\) −2.50346 + 7.70487i −0.297106 + 0.914400i 0.685399 + 0.728167i \(0.259628\pi\)
−0.982506 + 0.186232i \(0.940372\pi\)
\(72\) −0.573870 + 1.76619i −0.0676312 + 0.208147i
\(73\) 10.7734 7.82730i 1.26093 0.916116i 0.262123 0.965035i \(-0.415578\pi\)
0.998803 + 0.0489187i \(0.0155775\pi\)
\(74\) 0.0355801 0.00413611
\(75\) 0 0
\(76\) −2.14984 −0.246604
\(77\) 18.8457 13.6922i 2.14767 1.56037i
\(78\) 1.73515 5.34023i 0.196467 0.604662i
\(79\) 5.14971 15.8492i 0.579388 1.78317i −0.0413379 0.999145i \(-0.513162\pi\)
0.620726 0.784028i \(-0.286838\pi\)
\(80\) 0 0
\(81\) 0.309017 + 0.951057i 0.0343352 + 0.105673i
\(82\) 2.51200 0.277404
\(83\) −0.241540 0.743385i −0.0265125 0.0815971i 0.936925 0.349531i \(-0.113659\pi\)
−0.963437 + 0.267934i \(0.913659\pi\)
\(84\) 2.90777 + 2.11262i 0.317264 + 0.230506i
\(85\) 0 0
\(86\) 1.75705 1.27657i 0.189468 0.137656i
\(87\) −3.16461 2.29922i −0.339282 0.246503i
\(88\) −8.87728 6.44972i −0.946322 0.687543i
\(89\) 2.80994 2.04154i 0.297853 0.216403i −0.428814 0.903393i \(-0.641068\pi\)
0.726667 + 0.686990i \(0.241068\pi\)
\(90\) 0 0
\(91\) 10.4955 + 7.62545i 1.10023 + 0.799364i
\(92\) 0.164609 + 0.506614i 0.0171617 + 0.0528182i
\(93\) −2.70934 −0.280946
\(94\) −2.86510 8.81786i −0.295512 0.909493i
\(95\) 0 0
\(96\) 1.48462 4.56919i 0.151523 0.466341i
\(97\) 0.758460 2.33430i 0.0770099 0.237012i −0.905139 0.425115i \(-0.860234\pi\)
0.982149 + 0.188103i \(0.0602337\pi\)
\(98\) −11.7931 + 8.56817i −1.19128 + 0.865515i
\(99\) −5.90869 −0.593846
\(100\) 0 0
\(101\) −6.87495 −0.684083 −0.342042 0.939685i \(-0.611118\pi\)
−0.342042 + 0.939685i \(0.611118\pi\)
\(102\) −3.73607 + 2.71441i −0.369926 + 0.268767i
\(103\) −3.63192 + 11.1779i −0.357864 + 1.10139i 0.596466 + 0.802638i \(0.296571\pi\)
−0.954330 + 0.298754i \(0.903429\pi\)
\(104\) 1.88841 5.81193i 0.185174 0.569906i
\(105\) 0 0
\(106\) −1.48462 4.56919i −0.144199 0.443799i
\(107\) −5.66780 −0.547927 −0.273964 0.961740i \(-0.588335\pi\)
−0.273964 + 0.961740i \(0.588335\pi\)
\(108\) −0.281722 0.867051i −0.0271087 0.0834321i
\(109\) 1.10130 + 0.800139i 0.105485 + 0.0766394i 0.639277 0.768976i \(-0.279234\pi\)
−0.533792 + 0.845616i \(0.679234\pi\)
\(110\) 0 0
\(111\) 0.0168692 0.0122562i 0.00160115 0.00116330i
\(112\) 15.9226 + 11.5684i 1.50454 + 1.09311i
\(113\) −8.64489 6.28088i −0.813243 0.590856i 0.101526 0.994833i \(-0.467627\pi\)
−0.914769 + 0.403977i \(0.867627\pi\)
\(114\) −3.25535 + 2.36515i −0.304891 + 0.221516i
\(115\) 0 0
\(116\) 2.88508 + 2.09614i 0.267873 + 0.194621i
\(117\) −1.01687 3.12960i −0.0940096 0.289332i
\(118\) −8.00341 −0.736773
\(119\) −3.29710 10.1474i −0.302245 0.930214i
\(120\) 0 0
\(121\) 7.38941 22.7423i 0.671765 2.06748i
\(122\) 2.94300 9.05762i 0.266447 0.820038i
\(123\) 1.19098 0.865300i 0.107387 0.0780215i
\(124\) 2.47003 0.221815
\(125\) 0 0
\(126\) 6.72721 0.599308
\(127\) −10.9563 + 7.96023i −0.972216 + 0.706356i −0.955956 0.293511i \(-0.905176\pi\)
−0.0162606 + 0.999868i \(0.505176\pi\)
\(128\) 3.91123 12.0375i 0.345708 1.06398i
\(129\) 0.393313 1.21049i 0.0346292 0.106578i
\(130\) 0 0
\(131\) 1.41912 + 4.36759i 0.123989 + 0.381599i 0.993716 0.111935i \(-0.0357049\pi\)
−0.869727 + 0.493534i \(0.835705\pi\)
\(132\) 5.38679 0.468860
\(133\) −2.87286 8.84176i −0.249109 0.766678i
\(134\) 8.32532 + 6.04870i 0.719198 + 0.522528i
\(135\) 0 0
\(136\) −4.06607 + 2.95417i −0.348662 + 0.253318i
\(137\) 12.3472 + 8.97078i 1.05489 + 0.766426i 0.973137 0.230227i \(-0.0739468\pi\)
0.0817573 + 0.996652i \(0.473947\pi\)
\(138\) 0.806606 + 0.586034i 0.0686629 + 0.0498865i
\(139\) −14.7550 + 10.7201i −1.25150 + 0.909269i −0.998308 0.0581460i \(-0.981481\pi\)
−0.253194 + 0.967416i \(0.581481\pi\)
\(140\) 0 0
\(141\) −4.39586 3.19378i −0.370198 0.268964i
\(142\) −4.27182 13.1473i −0.358483 1.10330i
\(143\) 19.4435 1.62595
\(144\) −1.54267 4.74786i −0.128556 0.395655i
\(145\) 0 0
\(146\) −7.02177 + 21.6108i −0.581126 + 1.78852i
\(147\) −2.63986 + 8.12464i −0.217732 + 0.670109i
\(148\) −0.0153792 + 0.0111736i −0.00126416 + 0.000918465i
\(149\) 14.7323 1.20692 0.603458 0.797394i \(-0.293789\pi\)
0.603458 + 0.797394i \(0.293789\pi\)
\(150\) 0 0
\(151\) −17.4354 −1.41887 −0.709437 0.704769i \(-0.751051\pi\)
−0.709437 + 0.704769i \(0.751051\pi\)
\(152\) −3.54289 + 2.57406i −0.287366 + 0.208784i
\(153\) −0.836312 + 2.57390i −0.0676118 + 0.208088i
\(154\) −12.2831 + 37.8036i −0.989803 + 3.04630i
\(155\) 0 0
\(156\) 0.927051 + 2.85317i 0.0742235 + 0.228436i
\(157\) −17.9105 −1.42942 −0.714708 0.699423i \(-0.753440\pi\)
−0.714708 + 0.699423i \(0.753440\pi\)
\(158\) 8.78728 + 27.0445i 0.699078 + 2.15154i
\(159\) −2.27782 1.65493i −0.180643 0.131245i
\(160\) 0 0
\(161\) −1.86361 + 1.35399i −0.146873 + 0.106709i
\(162\) −1.38048 1.00297i −0.108460 0.0788011i
\(163\) 17.6041 + 12.7901i 1.37886 + 1.00180i 0.996986 + 0.0775819i \(0.0247199\pi\)
0.381870 + 0.924216i \(0.375280\pi\)
\(164\) −1.08579 + 0.788869i −0.0847856 + 0.0616004i
\(165\) 0 0
\(166\) 1.07904 + 0.783966i 0.0837495 + 0.0608475i
\(167\) 6.98470 + 21.4967i 0.540492 + 1.66346i 0.731473 + 0.681871i \(0.238833\pi\)
−0.190980 + 0.981594i \(0.561167\pi\)
\(168\) 7.32142 0.564860
\(169\) −0.671052 2.06529i −0.0516194 0.158868i
\(170\) 0 0
\(171\) −0.728704 + 2.24272i −0.0557254 + 0.171505i
\(172\) −0.358572 + 1.10357i −0.0273409 + 0.0841465i
\(173\) 10.4458 7.58929i 0.794177 0.577003i −0.115023 0.993363i \(-0.536694\pi\)
0.909200 + 0.416360i \(0.136694\pi\)
\(174\) 6.67473 0.506010
\(175\) 0 0
\(176\) 29.4974 2.22345
\(177\) −3.79456 + 2.75691i −0.285216 + 0.207222i
\(178\) −1.83144 + 5.63659i −0.137272 + 0.422480i
\(179\) −1.98716 + 6.11586i −0.148528 + 0.457121i −0.997448 0.0714002i \(-0.977253\pi\)
0.848920 + 0.528521i \(0.177253\pi\)
\(180\) 0 0
\(181\) 4.54473 + 13.9873i 0.337807 + 1.03966i 0.965323 + 0.261060i \(0.0840720\pi\)
−0.627515 + 0.778604i \(0.715928\pi\)
\(182\) −22.1370 −1.64090
\(183\) −1.72472 5.30815i −0.127495 0.392389i
\(184\) 0.877852 + 0.637797i 0.0647161 + 0.0470190i
\(185\) 0 0
\(186\) 3.74018 2.71740i 0.274243 0.199250i
\(187\) −12.9370 9.39931i −0.946050 0.687346i
\(188\) 4.00758 + 2.91168i 0.292283 + 0.212356i
\(189\) 3.18949 2.31730i 0.232001 0.168559i
\(190\) 0 0
\(191\) −5.43095 3.94582i −0.392970 0.285509i 0.373702 0.927549i \(-0.378088\pi\)
−0.766671 + 0.642040i \(0.778088\pi\)
\(192\) −0.552047 1.69903i −0.0398406 0.122617i
\(193\) −4.82817 −0.347539 −0.173769 0.984786i \(-0.555595\pi\)
−0.173769 + 0.984786i \(0.555595\pi\)
\(194\) 1.29421 + 3.98316i 0.0929186 + 0.285974i
\(195\) 0 0
\(196\) 2.40668 7.40701i 0.171906 0.529072i
\(197\) 4.44492 13.6801i 0.316688 0.974664i −0.658367 0.752697i \(-0.728752\pi\)
0.975054 0.221967i \(-0.0712477\pi\)
\(198\) 8.15681 5.92627i 0.579679 0.421161i
\(199\) −8.72608 −0.618575 −0.309288 0.950969i \(-0.600091\pi\)
−0.309288 + 0.950969i \(0.600091\pi\)
\(200\) 0 0
\(201\) 6.03076 0.425377
\(202\) 9.49071 6.89540i 0.667764 0.485159i
\(203\) −4.76550 + 14.6667i −0.334473 + 1.02940i
\(204\) 0.762442 2.34656i 0.0533816 0.164292i
\(205\) 0 0
\(206\) −6.19738 19.0736i −0.431792 1.32892i
\(207\) 0.584296 0.0406114
\(208\) 5.07641 + 15.6236i 0.351986 + 1.08330i
\(209\) −11.2724 8.18990i −0.779730 0.566507i
\(210\) 0 0
\(211\) −2.40777 + 1.74935i −0.165758 + 0.120430i −0.667572 0.744546i \(-0.732666\pi\)
0.501814 + 0.864976i \(0.332666\pi\)
\(212\) 2.07663 + 1.50876i 0.142623 + 0.103622i
\(213\) −6.55415 4.76187i −0.449083 0.326278i
\(214\) 7.82426 5.68466i 0.534856 0.388595i
\(215\) 0 0
\(216\) −1.50241 1.09157i −0.102226 0.0742716i
\(217\) 3.30073 + 10.1586i 0.224068 + 0.689611i
\(218\) −2.32283 −0.157322
\(219\) 4.11505 + 12.6648i 0.278070 + 0.855810i
\(220\) 0 0
\(221\) 2.75202 8.46984i 0.185121 0.569743i
\(222\) −0.0109949 + 0.0338387i −0.000737927 + 0.00227111i
\(223\) −0.246494 + 0.179088i −0.0165064 + 0.0119926i −0.596008 0.802979i \(-0.703247\pi\)
0.579501 + 0.814971i \(0.303247\pi\)
\(224\) −18.9408 −1.26553
\(225\) 0 0
\(226\) 18.2336 1.21288
\(227\) −7.74408 + 5.62641i −0.513993 + 0.373438i −0.814336 0.580394i \(-0.802899\pi\)
0.300343 + 0.953831i \(0.402899\pi\)
\(228\) 0.664339 2.04462i 0.0439969 0.135409i
\(229\) 3.74812 11.5355i 0.247682 0.762288i −0.747501 0.664260i \(-0.768747\pi\)
0.995184 0.0980277i \(-0.0312534\pi\)
\(230\) 0 0
\(231\) 7.19843 + 22.1545i 0.473622 + 1.45766i
\(232\) 7.26430 0.476924
\(233\) −6.21132 19.1165i −0.406917 1.25236i −0.919284 0.393595i \(-0.871231\pi\)
0.512367 0.858766i \(-0.328769\pi\)
\(234\) 4.54267 + 3.30045i 0.296964 + 0.215757i
\(235\) 0 0
\(236\) 3.45939 2.51340i 0.225187 0.163608i
\(237\) 13.4821 + 9.79534i 0.875758 + 0.636275i
\(238\) 14.7292 + 10.7014i 0.954751 + 0.693667i
\(239\) −14.2902 + 10.3825i −0.924358 + 0.671585i −0.944605 0.328210i \(-0.893555\pi\)
0.0202473 + 0.999795i \(0.493555\pi\)
\(240\) 0 0
\(241\) −23.8973 17.3624i −1.53936 1.11841i −0.950733 0.310010i \(-0.899668\pi\)
−0.588630 0.808403i \(-0.700332\pi\)
\(242\) 12.6090 + 38.8066i 0.810538 + 2.49458i
\(243\) −1.00000 −0.0641500
\(244\) 1.57238 + 4.83929i 0.100661 + 0.309804i
\(245\) 0 0
\(246\) −0.776250 + 2.38905i −0.0494919 + 0.152320i
\(247\) 2.39791 7.38002i 0.152576 0.469580i
\(248\) 4.07055 2.95742i 0.258480 0.187797i
\(249\) 0.781641 0.0495345
\(250\) 0 0
\(251\) 1.89396 0.119546 0.0597729 0.998212i \(-0.480962\pi\)
0.0597729 + 0.998212i \(0.480962\pi\)
\(252\) −2.90777 + 2.11262i −0.183172 + 0.133083i
\(253\) −1.06686 + 3.28345i −0.0670727 + 0.206429i
\(254\) 7.14103 21.9778i 0.448068 1.37901i
\(255\) 0 0
\(256\) 5.56989 + 17.1424i 0.348118 + 1.07140i
\(257\) −22.1211 −1.37988 −0.689938 0.723869i \(-0.742362\pi\)
−0.689938 + 0.723869i \(0.742362\pi\)
\(258\) 0.671134 + 2.06554i 0.0417830 + 0.128595i
\(259\) −0.0665056 0.0483191i −0.00413245 0.00300240i
\(260\) 0 0
\(261\) 3.16461 2.29922i 0.195884 0.142318i
\(262\) −6.33964 4.60602i −0.391664 0.284561i
\(263\) −15.9500 11.5884i −0.983520 0.714569i −0.0250272 0.999687i \(-0.507967\pi\)
−0.958492 + 0.285118i \(0.907967\pi\)
\(264\) 8.87728 6.44972i 0.546359 0.396953i
\(265\) 0 0
\(266\) 12.8340 + 9.32443i 0.786902 + 0.571718i
\(267\) 1.07330 + 3.30328i 0.0656849 + 0.202157i
\(268\) −5.49807 −0.335848
\(269\) 5.61321 + 17.2757i 0.342244 + 1.05332i 0.963043 + 0.269348i \(0.0868082\pi\)
−0.620799 + 0.783970i \(0.713192\pi\)
\(270\) 0 0
\(271\) 6.97436 21.4649i 0.423662 1.30390i −0.480608 0.876936i \(-0.659584\pi\)
0.904270 0.426962i \(-0.140416\pi\)
\(272\) 4.17503 12.8494i 0.253149 0.779111i
\(273\) −10.4955 + 7.62545i −0.635218 + 0.461513i
\(274\) −26.0425 −1.57329
\(275\) 0 0
\(276\) −0.532686 −0.0320639
\(277\) 6.67837 4.85212i 0.401264 0.291535i −0.368792 0.929512i \(-0.620228\pi\)
0.770056 + 0.637977i \(0.220228\pi\)
\(278\) 9.61690 29.5978i 0.576783 1.77516i
\(279\) 0.837233 2.57674i 0.0501238 0.154265i
\(280\) 0 0
\(281\) 0.395941 + 1.21858i 0.0236199 + 0.0726944i 0.962172 0.272444i \(-0.0878320\pi\)
−0.938552 + 0.345138i \(0.887832\pi\)
\(282\) 9.27165 0.552119
\(283\) −0.825484 2.54058i −0.0490699 0.151022i 0.923519 0.383552i \(-0.125299\pi\)
−0.972589 + 0.232531i \(0.925299\pi\)
\(284\) 5.97524 + 4.34126i 0.354565 + 0.257607i
\(285\) 0 0
\(286\) −26.8413 + 19.5013i −1.58716 + 1.15314i
\(287\) −4.69537 3.41138i −0.277159 0.201368i
\(288\) 3.88679 + 2.82392i 0.229031 + 0.166401i
\(289\) 7.82773 5.68718i 0.460455 0.334540i
\(290\) 0 0
\(291\) 1.98567 + 1.44268i 0.116402 + 0.0845712i
\(292\) −3.75158 11.5462i −0.219545 0.675689i
\(293\) −17.6605 −1.03174 −0.515870 0.856667i \(-0.672531\pi\)
−0.515870 + 0.856667i \(0.672531\pi\)
\(294\) −4.50455 13.8636i −0.262711 0.808541i
\(295\) 0 0
\(296\) −0.0119660 + 0.0368276i −0.000695511 + 0.00214056i
\(297\) 1.82589 5.61950i 0.105949 0.326076i
\(298\) −20.3376 + 14.7761i −1.17812 + 0.855958i
\(299\) −1.92272 −0.111194
\(300\) 0 0
\(301\) −5.01787 −0.289225
\(302\) 24.0692 17.4873i 1.38503 1.00628i
\(303\) 2.12448 6.53847i 0.122048 0.375625i
\(304\) 3.63783 11.1961i 0.208644 0.642140i
\(305\) 0 0
\(306\) −1.42705 4.39201i −0.0815791 0.251075i
\(307\) 28.5593 1.62997 0.814983 0.579484i \(-0.196746\pi\)
0.814983 + 0.579484i \(0.196746\pi\)
\(308\) −6.56260 20.1976i −0.373939 1.15087i
\(309\) −9.50850 6.90833i −0.540920 0.393001i
\(310\) 0 0
\(311\) 23.7271 17.2388i 1.34544 0.977521i 0.346217 0.938154i \(-0.387466\pi\)
0.999225 0.0393664i \(-0.0125340\pi\)
\(312\) 4.94392 + 3.59197i 0.279894 + 0.203355i
\(313\) −14.1523 10.2823i −0.799937 0.581189i 0.110958 0.993825i \(-0.464608\pi\)
−0.910896 + 0.412637i \(0.864608\pi\)
\(314\) 24.7251 17.9638i 1.39532 1.01376i
\(315\) 0 0
\(316\) −12.2913 8.93013i −0.691438 0.502359i
\(317\) −1.21061 3.72589i −0.0679949 0.209267i 0.911286 0.411775i \(-0.135091\pi\)
−0.979281 + 0.202508i \(0.935091\pi\)
\(318\) 4.80433 0.269414
\(319\) 7.14227 + 21.9816i 0.399890 + 1.23074i
\(320\) 0 0
\(321\) 1.75145 5.39040i 0.0977562 0.300863i
\(322\) 1.21465 3.73830i 0.0676897 0.208327i
\(323\) −5.16312 + 3.75123i −0.287284 + 0.208724i
\(324\) 0.911672 0.0506484
\(325\) 0 0
\(326\) −37.1301 −2.05645
\(327\) −1.10130 + 0.800139i −0.0609018 + 0.0442478i
\(328\) −0.844815 + 2.60007i −0.0466471 + 0.143565i
\(329\) −6.61961 + 20.3731i −0.364951 + 1.12320i
\(330\) 0 0
\(331\) −5.42429 16.6942i −0.298146 0.917599i −0.982147 0.188117i \(-0.939762\pi\)
0.684001 0.729481i \(-0.260238\pi\)
\(332\) −0.712600 −0.0391090
\(333\) 0.00644345 + 0.0198309i 0.000353099 + 0.00108673i
\(334\) −31.2029 22.6702i −1.70734 1.24046i
\(335\) 0 0
\(336\) −15.9226 + 11.5684i −0.868648 + 0.631110i
\(337\) −11.3647 8.25697i −0.619077 0.449786i 0.233522 0.972352i \(-0.424975\pi\)
−0.852599 + 0.522566i \(0.824975\pi\)
\(338\) 2.99780 + 2.17803i 0.163059 + 0.118469i
\(339\) 8.64489 6.28088i 0.469526 0.341131i
\(340\) 0 0
\(341\) 12.9513 + 9.40966i 0.701351 + 0.509562i
\(342\) −1.24343 3.82689i −0.0672371 0.206935i
\(343\) 6.08221 0.328408
\(344\) 0.730414 + 2.24798i 0.0393813 + 0.121203i
\(345\) 0 0
\(346\) −6.80826 + 20.9537i −0.366014 + 1.12648i
\(347\) 0.318440 0.980059i 0.0170948 0.0526123i −0.942145 0.335205i \(-0.891194\pi\)
0.959240 + 0.282593i \(0.0911944\pi\)
\(348\) −2.88508 + 2.09614i −0.154657 + 0.112365i
\(349\) 21.5626 1.15422 0.577109 0.816667i \(-0.304181\pi\)
0.577109 + 0.816667i \(0.304181\pi\)
\(350\) 0 0
\(351\) 3.29066 0.175642
\(352\) −22.9658 + 16.6857i −1.22408 + 0.889348i
\(353\) −2.21140 + 6.80599i −0.117701 + 0.362246i −0.992501 0.122238i \(-0.960993\pi\)
0.874800 + 0.484485i \(0.160993\pi\)
\(354\) 2.47319 7.61169i 0.131448 0.404557i
\(355\) 0 0
\(356\) −0.978498 3.01151i −0.0518603 0.159610i
\(357\) 10.6696 0.564697
\(358\) −3.39082 10.4359i −0.179210 0.551553i
\(359\) −21.9663 15.9595i −1.15934 0.842308i −0.169643 0.985506i \(-0.554262\pi\)
−0.989694 + 0.143198i \(0.954262\pi\)
\(360\) 0 0
\(361\) 10.8725 7.89936i 0.572239 0.415756i
\(362\) −20.3028 14.7508i −1.06709 0.775285i
\(363\) 19.3457 + 14.0555i 1.01539 + 0.737722i
\(364\) 9.56848 6.95191i 0.501525 0.364379i
\(365\) 0 0
\(366\) 7.70487 + 5.59792i 0.402740 + 0.292608i
\(367\) −6.62605 20.3929i −0.345877 1.06450i −0.961113 0.276157i \(-0.910939\pi\)
0.615236 0.788343i \(-0.289061\pi\)
\(368\) −2.91692 −0.152055
\(369\) 0.454915 + 1.40008i 0.0236819 + 0.0728855i
\(370\) 0 0
\(371\) −3.43011 + 10.5568i −0.178083 + 0.548082i
\(372\) −0.763282 + 2.34914i −0.0395743 + 0.121797i
\(373\) 5.17021 3.75638i 0.267703 0.194498i −0.445833 0.895116i \(-0.647092\pi\)
0.713536 + 0.700618i \(0.247092\pi\)
\(374\) 27.2865 1.41095
\(375\) 0 0
\(376\) 10.0906 0.520383
\(377\) −10.4136 + 7.56596i −0.536330 + 0.389667i
\(378\) −2.07882 + 6.39796i −0.106923 + 0.329076i
\(379\) −0.0477946 + 0.147097i −0.00245504 + 0.00755585i −0.952277 0.305237i \(-0.901264\pi\)
0.949821 + 0.312792i \(0.101264\pi\)
\(380\) 0 0
\(381\) −4.18494 12.8799i −0.214401 0.659859i
\(382\) 11.4549 0.586081
\(383\) 1.31489 + 4.04682i 0.0671878 + 0.206783i 0.979014 0.203794i \(-0.0653273\pi\)
−0.911826 + 0.410577i \(0.865327\pi\)
\(384\) 10.2397 + 7.43961i 0.522545 + 0.379651i
\(385\) 0 0
\(386\) 6.66517 4.84253i 0.339248 0.246478i
\(387\) 1.02971 + 0.748125i 0.0523429 + 0.0380293i
\(388\) −1.81028 1.31525i −0.0919032 0.0667716i
\(389\) 16.4782 11.9721i 0.835479 0.607011i −0.0856250 0.996327i \(-0.527289\pi\)
0.921104 + 0.389316i \(0.127289\pi\)
\(390\) 0 0
\(391\) 1.27931 + 0.929474i 0.0646975 + 0.0470055i
\(392\) −4.90243 15.0881i −0.247610 0.762066i
\(393\) −4.59236 −0.231654
\(394\) 7.58465 + 23.3431i 0.382109 + 1.17601i
\(395\) 0 0
\(396\) −1.66461 + 5.12314i −0.0836497 + 0.257447i
\(397\) 0.604795 1.86137i 0.0303538 0.0934194i −0.934732 0.355354i \(-0.884360\pi\)
0.965086 + 0.261934i \(0.0843604\pi\)
\(398\) 12.0461 8.75203i 0.603818 0.438700i
\(399\) 9.29678 0.465421
\(400\) 0 0
\(401\) −32.8337 −1.63964 −0.819818 0.572624i \(-0.805925\pi\)
−0.819818 + 0.572624i \(0.805925\pi\)
\(402\) −8.32532 + 6.04870i −0.415229 + 0.301682i
\(403\) −2.75505 + 8.47916i −0.137239 + 0.422377i
\(404\) −1.93683 + 5.96094i −0.0963607 + 0.296568i
\(405\) 0 0
\(406\) −8.13167 25.0267i −0.403568 1.24206i
\(407\) −0.123205 −0.00610704
\(408\) −1.55310 4.77995i −0.0768899 0.236643i
\(409\) 32.0180 + 23.2624i 1.58319 + 1.15025i 0.912923 + 0.408132i \(0.133820\pi\)
0.670265 + 0.742122i \(0.266180\pi\)
\(410\) 0 0
\(411\) −12.3472 + 8.97078i −0.609043 + 0.442496i
\(412\) 8.66863 + 6.29813i 0.427073 + 0.310287i
\(413\) 14.9598 + 10.8689i 0.736123 + 0.534825i
\(414\) −0.806606 + 0.586034i −0.0396425 + 0.0288020i
\(415\) 0 0
\(416\) −12.7901 9.29254i −0.627086 0.455604i
\(417\) −5.63591 17.3455i −0.275991 0.849414i
\(418\) 23.7756 1.16290
\(419\) 6.04421 + 18.6022i 0.295279 + 0.908776i 0.983128 + 0.182921i \(0.0585554\pi\)
−0.687848 + 0.725854i \(0.741445\pi\)
\(420\) 0 0
\(421\) −12.4634 + 38.3584i −0.607430 + 1.86948i −0.128292 + 0.991736i \(0.540949\pi\)
−0.479138 + 0.877740i \(0.659051\pi\)
\(422\) 1.56932 4.82987i 0.0763932 0.235114i
\(423\) 4.39586 3.19378i 0.213734 0.155287i
\(424\) 5.22869 0.253928
\(425\) 0 0
\(426\) 13.8239 0.669769
\(427\) −17.8016 + 12.9336i −0.861478 + 0.625901i
\(428\) −1.59675 + 4.91428i −0.0771816 + 0.237540i
\(429\) −6.00837 + 18.4919i −0.290087 + 0.892795i
\(430\) 0 0
\(431\) 4.24497 + 13.0647i 0.204473 + 0.629304i 0.999735 + 0.0230370i \(0.00733356\pi\)
−0.795261 + 0.606267i \(0.792666\pi\)
\(432\) 4.99220 0.240187
\(433\) 3.83964 + 11.8172i 0.184522 + 0.567899i 0.999940 0.0109734i \(-0.00349301\pi\)
−0.815418 + 0.578872i \(0.803493\pi\)
\(434\) −14.7454 10.7132i −0.707802 0.514248i
\(435\) 0 0
\(436\) 1.00402 0.729464i 0.0480839 0.0349350i
\(437\) 1.11470 + 0.809879i 0.0533234 + 0.0387417i
\(438\) −18.3832 13.3562i −0.878385 0.638184i
\(439\) −8.87118 + 6.44529i −0.423399 + 0.307617i −0.779004 0.627019i \(-0.784275\pi\)
0.355605 + 0.934636i \(0.384275\pi\)
\(440\) 0 0
\(441\) −6.91123 5.02131i −0.329106 0.239110i
\(442\) 4.69594 + 14.4526i 0.223363 + 0.687440i
\(443\) −8.13187 −0.386357 −0.193178 0.981164i \(-0.561880\pi\)
−0.193178 + 0.981164i \(0.561880\pi\)
\(444\) −0.00587431 0.0180793i −0.000278783 0.000858005i
\(445\) 0 0
\(446\) 0.160658 0.494454i 0.00760737 0.0234131i
\(447\) −4.55253 + 14.0112i −0.215327 + 0.662709i
\(448\) −5.69791 + 4.13977i −0.269201 + 0.195586i
\(449\) −32.9503 −1.55502 −0.777511 0.628869i \(-0.783518\pi\)
−0.777511 + 0.628869i \(0.783518\pi\)
\(450\) 0 0
\(451\) −8.69840 −0.409592
\(452\) −7.88130 + 5.72610i −0.370705 + 0.269333i
\(453\) 5.38784 16.5821i 0.253143 0.779093i
\(454\) 5.04738 15.5342i 0.236885 0.729058i
\(455\) 0 0
\(456\) −1.35326 4.16491i −0.0633723 0.195040i
\(457\) 22.8800 1.07028 0.535142 0.844762i \(-0.320258\pi\)
0.535142 + 0.844762i \(0.320258\pi\)
\(458\) 6.39564 + 19.6838i 0.298849 + 0.919762i
\(459\) −2.18949 1.59076i −0.102197 0.0742503i
\(460\) 0 0
\(461\) −9.74259 + 7.07841i −0.453758 + 0.329674i −0.791078 0.611716i \(-0.790480\pi\)
0.337320 + 0.941390i \(0.390480\pi\)
\(462\) −32.1576 23.3639i −1.49611 1.08699i
\(463\) −22.0054 15.9878i −1.02268 0.743018i −0.0558471 0.998439i \(-0.517786\pi\)
−0.966830 + 0.255421i \(0.917786\pi\)
\(464\) −15.7984 + 11.4782i −0.733420 + 0.532861i
\(465\) 0 0
\(466\) 27.7479 + 20.1600i 1.28540 + 0.933895i
\(467\) 1.21828 + 3.74947i 0.0563752 + 0.173505i 0.975279 0.220976i \(-0.0709243\pi\)
−0.918904 + 0.394481i \(0.870924\pi\)
\(468\) −3.00000 −0.138675
\(469\) −7.34714 22.6122i −0.339259 1.04413i
\(470\) 0 0
\(471\) 5.53466 17.0339i 0.255024 0.784882i
\(472\) 2.69164 8.28402i 0.123893 0.381303i
\(473\) −6.08421 + 4.42044i −0.279752 + 0.203252i
\(474\) −28.4362 −1.30612
\(475\) 0 0
\(476\) −9.72721 −0.445846
\(477\) 2.27782 1.65493i 0.104294 0.0757742i
\(478\) 9.31397 28.6655i 0.426011 1.31113i
\(479\) 6.16466 18.9729i 0.281670 0.866893i −0.705706 0.708504i \(-0.749370\pi\)
0.987377 0.158388i \(-0.0506298\pi\)
\(480\) 0 0
\(481\) −0.0212032 0.0652567i −0.000966783 0.00297545i
\(482\) 50.4038 2.29583
\(483\) −0.711834 2.19080i −0.0323896 0.0996849i
\(484\) −17.6370 12.8140i −0.801680 0.582455i
\(485\) 0 0
\(486\) 1.38048 1.00297i 0.0626197 0.0454958i
\(487\) −8.90102 6.46697i −0.403344 0.293046i 0.367558 0.930001i \(-0.380194\pi\)
−0.770902 + 0.636954i \(0.780194\pi\)
\(488\) 8.38543 + 6.09237i 0.379591 + 0.275789i
\(489\) −17.6041 + 12.7901i −0.796083 + 0.578388i
\(490\) 0 0
\(491\) 26.9348 + 19.5693i 1.21555 + 0.883151i 0.995723 0.0923876i \(-0.0294499\pi\)
0.219830 + 0.975538i \(0.429450\pi\)
\(492\) −0.414733 1.27642i −0.0186976 0.0575453i
\(493\) 10.5864 0.476788
\(494\) 4.09171 + 12.5930i 0.184095 + 0.566585i
\(495\) 0 0
\(496\) −4.17963 + 12.8636i −0.187671 + 0.577592i
\(497\) −9.86973 + 30.3759i −0.442718 + 1.36255i
\(498\) −1.07904 + 0.783966i −0.0483528 + 0.0351303i
\(499\) −41.1448 −1.84189 −0.920946 0.389690i \(-0.872582\pi\)
−0.920946 + 0.389690i \(0.872582\pi\)
\(500\) 0 0
\(501\) −22.6030 −1.00983
\(502\) −2.61457 + 1.89960i −0.116694 + 0.0847832i
\(503\) −9.91207 + 30.5062i −0.441958 + 1.36021i 0.443829 + 0.896112i \(0.353620\pi\)
−0.885786 + 0.464094i \(0.846380\pi\)
\(504\) −2.26244 + 6.96308i −0.100777 + 0.310160i
\(505\) 0 0
\(506\) −1.82044 5.60275i −0.0809286 0.249073i
\(507\) 2.17157 0.0964429
\(508\) 3.81529 + 11.7423i 0.169276 + 0.520979i
\(509\) 21.9206 + 15.9262i 0.971612 + 0.705918i 0.955818 0.293958i \(-0.0949725\pi\)
0.0157938 + 0.999875i \(0.494972\pi\)
\(510\) 0 0
\(511\) 42.4732 30.8586i 1.87890 1.36510i
\(512\) −4.40295 3.19893i −0.194585 0.141374i
\(513\) −1.90777 1.38608i −0.0842301 0.0611968i
\(514\) 30.5376 22.1869i 1.34696 0.978622i
\(515\) 0 0
\(516\) −0.938754 0.682045i −0.0413263 0.0300253i
\(517\) 9.92109 + 30.5340i 0.436329 + 1.34288i
\(518\) 0.140272 0.00616321
\(519\) 3.98993 + 12.2797i 0.175138 + 0.539020i
\(520\) 0 0
\(521\) 8.02073 24.6853i 0.351395 1.08148i −0.606676 0.794949i \(-0.707497\pi\)
0.958071 0.286532i \(-0.0925026\pi\)
\(522\) −2.06260 + 6.34804i −0.0902778 + 0.277846i
\(523\) −1.45123 + 1.05438i −0.0634577 + 0.0461047i −0.619062 0.785342i \(-0.712487\pi\)
0.555604 + 0.831447i \(0.312487\pi\)
\(524\) 4.18673 0.182898
\(525\) 0 0
\(526\) 33.6414 1.46684
\(527\) 5.93209 4.30991i 0.258406 0.187743i
\(528\) −9.11519 + 28.0537i −0.396688 + 1.22088i
\(529\) −7.00189 + 21.5496i −0.304430 + 0.936939i
\(530\) 0 0
\(531\) −1.44939 4.46077i −0.0628983 0.193581i
\(532\) −8.47561 −0.367464
\(533\) −1.49697 4.60720i −0.0648410 0.199560i
\(534\) −4.79477 3.48361i −0.207490 0.150750i
\(535\) 0 0
\(536\) −9.06068 + 6.58297i −0.391362 + 0.284341i
\(537\) −5.20246 3.77981i −0.224503 0.163111i
\(538\) −25.0760 18.2188i −1.08110 0.785467i
\(539\) 40.8364 29.6693i 1.75895 1.27795i
\(540\) 0 0
\(541\) 6.01538 + 4.37043i 0.258621 + 0.187899i 0.709539 0.704666i \(-0.248903\pi\)
−0.450918 + 0.892566i \(0.648903\pi\)
\(542\) 11.9008 + 36.6268i 0.511182 + 1.57326i
\(543\) −14.7071 −0.631141
\(544\) 4.01792 + 12.3659i 0.172267 + 0.530183i
\(545\) 0 0
\(546\) 6.84070 21.0535i 0.292755 0.901007i
\(547\) −6.02174 + 18.5330i −0.257471 + 0.792414i 0.735862 + 0.677132i \(0.236777\pi\)
−0.993333 + 0.115283i \(0.963223\pi\)
\(548\) 11.2566 8.17841i 0.480859 0.349364i
\(549\) 5.58132 0.238205
\(550\) 0 0
\(551\) 9.22425 0.392966
\(552\) −0.877852 + 0.637797i −0.0373639 + 0.0271464i
\(553\) 20.3024 62.4843i 0.863345 2.65710i
\(554\) −4.35277 + 13.3965i −0.184932 + 0.569161i
\(555\) 0 0
\(556\) 5.13810 + 15.8134i 0.217904 + 0.670639i
\(557\) 26.3285 1.11557 0.557787 0.829984i \(-0.311650\pi\)
0.557787 + 0.829984i \(0.311650\pi\)
\(558\) 1.42862 + 4.39685i 0.0604784 + 0.186133i
\(559\) −3.38841 2.46182i −0.143314 0.104124i
\(560\) 0 0
\(561\) 12.9370 9.39931i 0.546202 0.396839i
\(562\) −1.76879 1.28510i −0.0746120 0.0542088i
\(563\) 29.7482 + 21.6134i 1.25374 + 0.910895i 0.998433 0.0559656i \(-0.0178237\pi\)
0.255306 + 0.966860i \(0.417824\pi\)
\(564\) −4.00758 + 2.91168i −0.168749 + 0.122604i
\(565\) 0 0
\(566\) 3.68770 + 2.67927i 0.155005 + 0.112618i
\(567\) 1.21828 + 3.74947i 0.0511629 + 0.157463i
\(568\) 15.0449 0.631271
\(569\) −11.2118 34.5065i −0.470025 1.44659i −0.852552 0.522643i \(-0.824946\pi\)
0.382527 0.923944i \(-0.375054\pi\)
\(570\) 0 0
\(571\) −1.03966 + 3.19975i −0.0435085 + 0.133906i −0.970451 0.241298i \(-0.922427\pi\)
0.926943 + 0.375203i \(0.122427\pi\)
\(572\) 5.47766 16.8585i 0.229032 0.704889i
\(573\) 5.43095 3.94582i 0.226881 0.164839i
\(574\) 9.90337 0.413359
\(575\) 0 0
\(576\) 1.78646 0.0744359
\(577\) −5.56961 + 4.04656i −0.231866 + 0.168461i −0.697652 0.716437i \(-0.745772\pi\)
0.465786 + 0.884898i \(0.345772\pi\)
\(578\) −5.10190 + 15.7020i −0.212211 + 0.653118i
\(579\) 1.49199 4.59186i 0.0620048 0.190831i
\(580\) 0 0
\(581\) −0.952256 2.93074i −0.0395062 0.121588i
\(582\) −4.18814 −0.173604
\(583\) 5.14086 + 15.8219i 0.212913 + 0.655278i
\(584\) −20.0070 14.5359i −0.827895 0.601501i
\(585\) 0 0
\(586\) 24.3800 17.7131i 1.00713 0.731720i
\(587\) −11.9230 8.66258i −0.492116 0.357543i 0.313882 0.949462i \(-0.398370\pi\)
−0.805997 + 0.591919i \(0.798370\pi\)
\(588\) 6.30078 + 4.57778i 0.259840 + 0.188785i
\(589\) 5.16880 3.75536i 0.212977 0.154737i
\(590\) 0 0
\(591\) 11.6370 + 8.45474i 0.478680 + 0.347782i
\(592\) −0.0321670 0.0989998i −0.00132206 0.00406887i
\(593\) −5.82561 −0.239229 −0.119615 0.992820i \(-0.538166\pi\)
−0.119615 + 0.992820i \(0.538166\pi\)
\(594\) 3.11562 + 9.58890i 0.127836 + 0.393437i
\(595\) 0 0
\(596\) 4.15041 12.7737i 0.170008 0.523230i
\(597\) 2.69651 8.29899i 0.110361 0.339655i
\(598\) 2.65426 1.92844i 0.108541 0.0788596i
\(599\) −27.1527 −1.10943 −0.554715 0.832040i \(-0.687173\pi\)
−0.554715 + 0.832040i \(0.687173\pi\)
\(600\) 0 0
\(601\) 20.9140 0.853101 0.426551 0.904464i \(-0.359729\pi\)
0.426551 + 0.904464i \(0.359729\pi\)
\(602\) 6.92705 5.03280i 0.282326 0.205121i
\(603\) −1.86361 + 5.73559i −0.0758919 + 0.233571i
\(604\) −4.91194 + 15.1174i −0.199864 + 0.615118i
\(605\) 0 0
\(606\) 3.62513 + 11.1570i 0.147261 + 0.453222i
\(607\) −1.46424 −0.0594318 −0.0297159 0.999558i \(-0.509460\pi\)
−0.0297159 + 0.999558i \(0.509460\pi\)
\(608\) 3.50094 + 10.7748i 0.141982 + 0.436975i
\(609\) −12.4762 9.06453i −0.505563 0.367313i
\(610\) 0 0
\(611\) −14.4653 + 10.5096i −0.585202 + 0.425174i
\(612\) 1.99610 + 1.45025i 0.0806875 + 0.0586229i
\(613\) 28.0814 + 20.4023i 1.13420 + 0.824041i 0.986300 0.164962i \(-0.0527501\pi\)
0.147896 + 0.989003i \(0.452750\pi\)
\(614\) −39.4255 + 28.6443i −1.59108 + 1.15599i
\(615\) 0 0
\(616\) −34.9981 25.4276i −1.41011 1.02451i
\(617\) −12.9490 39.8529i −0.521307 1.60442i −0.771506 0.636222i \(-0.780496\pi\)
0.250199 0.968194i \(-0.419504\pi\)
\(618\) 20.0551 0.806736
\(619\) −5.79758 17.8431i −0.233025 0.717176i −0.997377 0.0723776i \(-0.976941\pi\)
0.764353 0.644798i \(-0.223059\pi\)
\(620\) 0 0
\(621\) −0.180557 + 0.555698i −0.00724551 + 0.0222994i
\(622\) −15.4647 + 47.5954i −0.620077 + 1.90840i
\(623\) 11.0780 8.04863i 0.443830 0.322461i
\(624\) −16.4276 −0.657631
\(625\) 0 0
\(626\) 29.8498 1.19304
\(627\) 11.2724 8.18990i 0.450177 0.327073i
\(628\) −5.04579 + 15.5294i −0.201349 + 0.619689i
\(629\) −0.0174383 + 0.0536696i −0.000695311 + 0.00213995i
\(630\) 0 0
\(631\) 3.05583 + 9.40488i 0.121651 + 0.374402i 0.993276 0.115770i \(-0.0369337\pi\)
−0.871625 + 0.490173i \(0.836934\pi\)
\(632\) −30.9479 −1.23104
\(633\) −0.919687 2.83050i −0.0365543 0.112502i
\(634\) 5.40820 + 3.92928i 0.214787 + 0.156052i
\(635\) 0 0
\(636\) −2.07663 + 1.50876i −0.0823436 + 0.0598261i
\(637\) 22.7425 + 16.5234i 0.901091 + 0.654681i
\(638\) −31.9068 23.1816i −1.26320 0.917769i
\(639\) 6.55415 4.76187i 0.259278 0.188377i
\(640\) 0 0
\(641\) 1.46647 + 1.06546i 0.0579223 + 0.0420830i 0.616370 0.787457i \(-0.288603\pi\)
−0.558447 + 0.829540i \(0.688603\pi\)
\(642\) 2.98860 + 9.19797i 0.117951 + 0.363015i
\(643\) −45.7391 −1.80377 −0.901886 0.431974i \(-0.857817\pi\)
−0.901886 + 0.431974i \(0.857817\pi\)
\(644\) 0.648959 + 1.99729i 0.0255726 + 0.0787043i
\(645\) 0 0
\(646\) 3.36518 10.3570i 0.132401 0.407489i
\(647\) 7.93466 24.4204i 0.311944 0.960064i −0.665050 0.746798i \(-0.731590\pi\)
0.976994 0.213266i \(-0.0684101\pi\)
\(648\) 1.50241 1.09157i 0.0590203 0.0428807i
\(649\) 27.7137 1.08786
\(650\) 0 0
\(651\) −10.6814 −0.418637
\(652\) 16.0491 11.6604i 0.628532 0.456655i
\(653\) −11.1148 + 34.2079i −0.434957 + 1.33866i 0.458173 + 0.888863i \(0.348504\pi\)
−0.893130 + 0.449798i \(0.851496\pi\)
\(654\) 0.717795 2.20914i 0.0280680 0.0863844i
\(655\) 0 0
\(656\) −2.27103 6.98950i −0.0886687 0.272894i
\(657\) −13.3166 −0.519530
\(658\) −11.2954 34.7638i −0.440342 1.35523i
\(659\) 25.9633 + 18.8635i 1.01139 + 0.734816i 0.964500 0.264084i \(-0.0850696\pi\)
0.0468880 + 0.998900i \(0.485070\pi\)
\(660\) 0 0
\(661\) −13.1113 + 9.52591i −0.509970 + 0.370515i −0.812812 0.582526i \(-0.802064\pi\)
0.302842 + 0.953041i \(0.402064\pi\)
\(662\) 24.2320 + 17.6056i 0.941803 + 0.684260i
\(663\) 7.20487 + 5.23465i 0.279814 + 0.203297i
\(664\) −1.17435 + 0.853212i −0.0455734 + 0.0331110i
\(665\) 0 0
\(666\) −0.0287849 0.0209135i −0.00111539 0.000810381i
\(667\) −0.706281 2.17371i −0.0273473 0.0841663i
\(668\) 20.6065 0.797289
\(669\) −0.0941522 0.289771i −0.00364014 0.0112032i
\(670\) 0 0
\(671\) −10.1908 + 31.3642i −0.393413 + 1.21080i
\(672\) 5.85301 18.0137i 0.225785 0.694895i
\(673\) 27.6367 20.0792i 1.06531 0.773997i 0.0902506 0.995919i \(-0.471233\pi\)
0.975064 + 0.221922i \(0.0712332\pi\)
\(674\) 23.9703 0.923301
\(675\) 0 0
\(676\) −1.97976 −0.0761446
\(677\) 7.42284 5.39301i 0.285283 0.207270i −0.435935 0.899978i \(-0.643582\pi\)
0.721218 + 0.692708i \(0.243582\pi\)
\(678\) −5.63450 + 17.3412i −0.216392 + 0.665985i
\(679\) 2.99017 9.20281i 0.114752 0.353171i
\(680\) 0 0
\(681\) −2.95798 9.10372i −0.113350 0.348855i
\(682\) −27.3166 −1.04601
\(683\) −6.02604 18.5463i −0.230580 0.709653i −0.997677 0.0681215i \(-0.978299\pi\)
0.767097 0.641531i \(-0.221701\pi\)
\(684\) 1.73926 + 1.26365i 0.0665023 + 0.0483168i
\(685\) 0 0
\(686\) −8.39634 + 6.10030i −0.320574 + 0.232910i
\(687\) 9.81269 + 7.12934i 0.374378 + 0.272001i
\(688\) −5.14050 3.73479i −0.195980 0.142387i
\(689\) −7.49553 + 5.44582i −0.285557 + 0.207469i
\(690\) 0 0
\(691\) −23.4986 17.0727i −0.893927 0.649476i 0.0429718 0.999076i \(-0.486317\pi\)
−0.936899 + 0.349600i \(0.886317\pi\)
\(692\) −3.63750 11.1951i −0.138277 0.425573i
\(693\) −23.2946 −0.884889
\(694\) 0.543375 + 1.67234i 0.0206262 + 0.0634810i
\(695\) 0 0
\(696\) −2.24479 + 6.90876i −0.0850886 + 0.261876i
\(697\) −1.23116 + 3.78914i −0.0466337 + 0.143524i
\(698\) −29.7666 + 21.6267i −1.12668 + 0.818583i
\(699\) 20.1002 0.760261
\(700\) 0 0
\(701\) −20.4085 −0.770820 −0.385410 0.922745i \(-0.625940\pi\)
−0.385410 + 0.922745i \(0.625940\pi\)
\(702\) −4.54267 + 3.30045i −0.171452 + 0.124567i
\(703\) −0.0151945 + 0.0467640i −0.000573073 + 0.00176374i
\(704\) −3.26188 + 10.0390i −0.122937 + 0.378360i
\(705\) 0 0
\(706\) −3.77345 11.6135i −0.142016 0.437079i
\(707\) −27.1040 −1.01935
\(708\) 1.32137 + 4.06676i 0.0496601 + 0.152838i
\(709\) −13.3334 9.68727i −0.500746 0.363813i 0.308556 0.951206i \(-0.400154\pi\)
−0.809302 + 0.587393i \(0.800154\pi\)
\(710\) 0 0
\(711\) −13.4821 + 9.79534i −0.505619 + 0.367354i
\(712\) −5.21829 3.79131i −0.195564 0.142085i
\(713\) −1.28072 0.930497i −0.0479633 0.0348474i
\(714\) −14.7292 + 10.7014i −0.551226 + 0.400489i
\(715\) 0 0
\(716\) 4.74294 + 3.44595i 0.177252 + 0.128781i
\(717\) −5.45838 16.7992i −0.203847 0.627376i
\(718\) 46.3309 1.72905
\(719\) 9.60466 + 29.5601i 0.358193 + 1.10241i 0.954135 + 0.299378i \(0.0967791\pi\)
−0.595941 + 0.803028i \(0.703221\pi\)
\(720\) 0 0
\(721\) −14.3186 + 44.0681i −0.533253 + 1.64118i
\(722\) −7.08642 + 21.8098i −0.263729 + 0.811675i
\(723\) 23.8973 17.3624i 0.888752 0.645716i
\(724\) 13.4080 0.498305
\(725\) 0 0
\(726\) −40.8036 −1.51436
\(727\) −0.771033 + 0.560188i −0.0285960 + 0.0207762i −0.601991 0.798503i \(-0.705626\pi\)
0.573395 + 0.819279i \(0.305626\pi\)
\(728\) 7.44492 22.9131i 0.275927 0.849217i
\(729\) 0.309017 0.951057i 0.0114451 0.0352243i
\(730\) 0 0
\(731\) 1.06445 + 3.27603i 0.0393700 + 0.121168i
\(732\) −5.08833 −0.188070
\(733\) 4.75118 + 14.6226i 0.175489 + 0.540099i 0.999655 0.0262485i \(-0.00835612\pi\)
−0.824167 + 0.566347i \(0.808356\pi\)
\(734\) 29.6006 + 21.5061i 1.09258 + 0.793806i
\(735\) 0 0
\(736\) 2.27103 1.65000i 0.0837114 0.0608199i
\(737\) −28.8284 20.9451i −1.06191 0.771522i
\(738\) −2.03225 1.47651i −0.0748081 0.0543513i
\(739\) −4.20110 + 3.05228i −0.154540 + 0.112280i −0.662368 0.749179i \(-0.730449\pi\)
0.507828 + 0.861458i \(0.330449\pi\)
\(740\) 0 0
\(741\) 6.27782 + 4.56110i 0.230622 + 0.167556i
\(742\) −5.85301 18.0137i −0.214871 0.661305i
\(743\) 42.3399 1.55330 0.776650 0.629932i \(-0.216917\pi\)
0.776650 + 0.629932i \(0.216917\pi\)
\(744\) 1.55481 + 4.78521i 0.0570021 + 0.175434i
\(745\) 0 0
\(746\) −3.36980 + 10.3712i −0.123377 + 0.379716i
\(747\) −0.241540 + 0.743385i −0.00883750 + 0.0271990i
\(748\) −11.7943 + 8.56909i −0.431244 + 0.313317i
\(749\) −22.3449 −0.816465
\(750\) 0 0
\(751\) 22.2461 0.811773 0.405887 0.913923i \(-0.366963\pi\)
0.405887 + 0.913923i \(0.366963\pi\)
\(752\) −21.9450 + 15.9440i −0.800251 + 0.581416i
\(753\) −0.585267 + 1.80127i −0.0213283 + 0.0656418i
\(754\) 6.78733 20.8892i 0.247180 0.760741i
\(755\) 0 0
\(756\) −1.11067 3.41829i −0.0403947 0.124322i
\(757\) 9.27680 0.337171 0.168585 0.985687i \(-0.446080\pi\)
0.168585 + 0.985687i \(0.446080\pi\)
\(758\) −0.0815549 0.251000i −0.00296221 0.00911674i
\(759\) −2.79307 2.02928i −0.101382 0.0736583i
\(760\) 0 0
\(761\) 14.0868 10.2346i 0.510644 0.371005i −0.302424 0.953174i \(-0.597796\pi\)
0.813068 + 0.582169i \(0.197796\pi\)
\(762\) 18.6954 + 13.5830i 0.677265 + 0.492062i
\(763\) 4.34178 + 3.15449i 0.157183 + 0.114200i
\(764\) −4.95125 + 3.59729i −0.179130 + 0.130145i
\(765\) 0 0
\(766\) −5.87403 4.26773i −0.212237 0.154200i
\(767\) 4.76945 + 14.6789i 0.172215 + 0.530023i
\(768\) −18.0245 −0.650404
\(769\) −7.16648 22.0562i −0.258430 0.795365i −0.993134 0.116978i \(-0.962679\pi\)
0.734705 0.678387i \(-0.237321\pi\)
\(770\) 0 0
\(771\) 6.83579 21.0384i 0.246185 0.757680i
\(772\) −1.36020 + 4.18627i −0.0489547 + 0.150667i
\(773\) −4.45605 + 3.23751i −0.160273 + 0.116445i −0.665031 0.746816i \(-0.731582\pi\)
0.504758 + 0.863261i \(0.331582\pi\)
\(774\) −2.17183 −0.0780650
\(775\) 0 0
\(776\) −4.55807 −0.163625
\(777\) 0.0665056 0.0483191i 0.00238587 0.00173344i
\(778\) −10.7401 + 33.0545i −0.385049 + 1.18506i
\(779\) −1.07275 + 3.30159i −0.0384353 + 0.118292i
\(780\) 0 0
\(781\) 14.7922 + 45.5257i 0.529306 + 1.62904i
\(782\) −2.69830 −0.0964909
\(783\) 1.20877 + 3.72022i 0.0431980 + 0.132950i
\(784\) 34.5023 + 25.0674i 1.23222 + 0.895263i
\(785\) 0 0
\(786\) 6.33964 4.60602i 0.226128 0.164291i
\(787\) 20.8703 + 15.1632i 0.743946 + 0.540509i 0.893944 0.448178i \(-0.147927\pi\)
−0.149998 + 0.988686i \(0.547927\pi\)
\(788\) −10.6091 7.70795i −0.377933 0.274584i
\(789\) 15.9500 11.5884i 0.567835 0.412556i
\(790\) 0 0
\(791\) −34.0819 24.7619i −1.21181 0.880433i
\(792\) 3.39082 + 10.4359i 0.120488 + 0.370823i
\(793\) −18.3662 −0.652203
\(794\) 1.03200 + 3.17617i 0.0366243 + 0.112718i
\(795\) 0 0
\(796\) −2.45833 + 7.56596i −0.0871331 + 0.268168i
\(797\) −1.14642 + 3.52831i −0.0406082 + 0.124979i −0.969305 0.245860i \(-0.920930\pi\)
0.928697 + 0.370839i \(0.120930\pi\)
\(798\) −12.8340 + 9.32443i −0.454318 + 0.330081i
\(799\) 14.7052 0.520233
\(800\) 0 0
\(801\) −3.47327 −0.122722
\(802\) 45.3261 32.9313i 1.60052 1.16285i
\(803\) 24.3146 74.8326i 0.858043 2.64079i
\(804\) 1.69900 5.22898i 0.0599190 0.184412i
\(805\) 0 0
\(806\) −4.70111 14.4685i −0.165589 0.509632i
\(807\) −18.1647 −0.639429
\(808\) 3.94533 + 12.1425i 0.138796 + 0.427171i
\(809\) −30.3414 22.0443i −1.06675 0.775037i −0.0914219 0.995812i \(-0.529141\pi\)
−0.975325 + 0.220776i \(0.929141\pi\)
\(810\) 0 0
\(811\) −36.9041 + 26.8124i −1.29588 + 0.941509i −0.999906 0.0136877i \(-0.995643\pi\)
−0.295970 + 0.955197i \(0.595643\pi\)
\(812\) 11.3742 + 8.26387i 0.399158 + 0.290005i
\(813\) 18.2591 + 13.2660i 0.640375 + 0.465260i
\(814\) 0.170081 0.123571i 0.00596135 0.00433117i
\(815\) 0 0
\(816\) 10.9304 + 7.94139i 0.382640 + 0.278004i
\(817\) 0.927484 + 2.85450i 0.0324486 + 0.0998664i
\(818\) −67.5317 −2.36119
\(819\) −4.00894 12.3382i −0.140084 0.431133i
\(820\) 0 0
\(821\) 13.9216 42.8462i 0.485866 1.49534i −0.344857 0.938655i \(-0.612073\pi\)
0.830723 0.556686i \(-0.187927\pi\)
\(822\) 8.04758 24.7679i 0.280691 0.863880i
\(823\) −33.5397 + 24.3680i −1.16912 + 0.849415i −0.990903 0.134576i \(-0.957033\pi\)
−0.178217 + 0.983991i \(0.557033\pi\)
\(824\) 21.8266 0.760364
\(825\) 0 0
\(826\) −31.5529 −1.09786
\(827\) −31.3035 + 22.7434i −1.08853 + 0.790864i −0.979151 0.203136i \(-0.934887\pi\)
−0.109380 + 0.994000i \(0.534887\pi\)
\(828\) 0.164609 0.506614i 0.00572056 0.0176061i
\(829\) 7.45527 22.9450i 0.258932 0.796911i −0.734097 0.679044i \(-0.762394\pi\)
0.993029 0.117867i \(-0.0376056\pi\)
\(830\) 0 0
\(831\) 2.55091 + 7.85089i 0.0884901 + 0.272344i
\(832\) −5.87864 −0.203805
\(833\) −7.14441 21.9882i −0.247539 0.761847i
\(834\) 25.1774 + 18.2924i 0.871821 + 0.633415i
\(835\) 0 0
\(836\) −10.2768 + 7.46650i −0.355429 + 0.258234i
\(837\) 2.19190 + 1.59251i 0.0757633 + 0.0550452i
\(838\) −27.0014 19.6177i −0.932748 0.677681i
\(839\) 14.3890 10.4542i 0.496763 0.360919i −0.311016 0.950405i \(-0.600669\pi\)
0.807779 + 0.589485i \(0.200669\pi\)
\(840\) 0 0
\(841\) 11.0826 + 8.05197i 0.382158 + 0.277654i
\(842\) −21.2671 65.4534i −0.732913 2.25567i
\(843\) −1.28129 −0.0441300
\(844\) 0.838452 + 2.58049i 0.0288607 + 0.0888242i
\(845\) 0 0
\(846\) −2.86510 + 8.81786i −0.0985041 + 0.303164i
\(847\) 29.1322 89.6598i 1.00100 3.08075i
\(848\) −11.3713 + 8.26176i −0.390493 + 0.283710i
\(849\) 2.67132 0.0916796
\(850\) 0 0
\(851\) 0.0121834 0.000417642
\(852\) −5.97524 + 4.34126i −0.204708 + 0.148729i
\(853\) −3.96878 + 12.2147i −0.135889 + 0.418222i −0.995727 0.0923439i \(-0.970564\pi\)
0.859839 + 0.510566i \(0.170564\pi\)
\(854\) 11.6026 35.7090i 0.397032 1.22194i
\(855\) 0 0
\(856\) 3.25258 + 10.0104i 0.111171 + 0.342149i
\(857\) 15.6015 0.532936 0.266468 0.963844i \(-0.414143\pi\)
0.266468 + 0.963844i \(0.414143\pi\)
\(858\) −10.2524 31.5538i −0.350013 1.07723i
\(859\) −3.90628 2.83808i −0.133281 0.0968340i 0.519147 0.854685i \(-0.326250\pi\)
−0.652428 + 0.757851i \(0.726250\pi\)
\(860\) 0 0
\(861\) 4.69537 3.41138i 0.160018 0.116260i
\(862\) −18.9636 13.7779i −0.645904 0.469276i
\(863\) −10.6425 7.73222i −0.362274 0.263208i 0.391726 0.920082i \(-0.371878\pi\)
−0.754000 + 0.656874i \(0.771878\pi\)
\(864\) −3.88679 + 2.82392i −0.132231 + 0.0960716i
\(865\) 0 0
\(866\) −17.1529 12.4623i −0.582879 0.423486i
\(867\) 2.98993 + 9.20205i 0.101543 + 0.312518i
\(868\) 9.73792 0.330527
\(869\) −30.4281 93.6480i −1.03220 3.17679i
\(870\) 0 0
\(871\) 6.13249 18.8739i 0.207792 0.639517i
\(872\) 0.781196 2.40427i 0.0264546 0.0814190i
\(873\) −1.98567 + 1.44268i −0.0672049 + 0.0488272i
\(874\) −2.35111 −0.0795274
\(875\) 0 0
\(876\) 12.1404 0.410185
\(877\) 5.05840 3.67515i 0.170810 0.124101i −0.499096 0.866547i \(-0.666334\pi\)
0.669906 + 0.742446i \(0.266334\pi\)
\(878\) 5.78199 17.7951i 0.195133 0.600557i
\(879\) 5.45741 16.7962i 0.184074 0.566521i
\(880\) 0 0
\(881\) −5.18532 15.9588i −0.174698 0.537665i 0.824922 0.565247i \(-0.191219\pi\)
−0.999620 + 0.0275821i \(0.991219\pi\)
\(882\) 14.5770 0.490834
\(883\) −5.01740 15.4420i −0.168849 0.519664i 0.830450 0.557093i \(-0.188083\pi\)
−0.999299 + 0.0374289i \(0.988083\pi\)
\(884\) −6.56848 4.77228i −0.220922 0.160509i
\(885\) 0 0
\(886\) 11.2259 8.15606i 0.377140 0.274008i
\(887\) 46.6700 + 33.9078i 1.56703 + 1.13851i 0.929935 + 0.367723i \(0.119863\pi\)
0.637091 + 0.770788i \(0.280137\pi\)
\(888\) −0.0313275 0.0227607i −0.00105128 0.000763800i
\(889\) −43.1945 + 31.3827i −1.44870 + 1.05254i
\(890\) 0 0
\(891\) 4.78023 + 3.47304i 0.160144 + 0.116351i
\(892\) 0.0858359 + 0.264176i 0.00287400 + 0.00884526i
\(893\) 12.8131 0.428774
\(894\) −7.76827 23.9083i −0.259810 0.799612i
\(895\) 0 0
\(896\) 15.4198 47.4572i 0.515138 1.58543i
\(897\) 0.594152 1.82861i 0.0198382 0.0610556i
\(898\) 45.4871 33.0483i 1.51793 1.10284i
\(899\) −10.5981 −0.353465
\(900\) 0 0
\(901\) 7.61988 0.253855
\(902\) 12.0079 8.72427i 0.399820 0.290486i
\(903\) 1.55061 4.77228i 0.0516010 0.158812i
\(904\) −6.13219 + 18.8729i −0.203953 + 0.627704i
\(905\) 0 0
\(906\) 9.19361 + 28.2950i 0.305437 + 0.940039i
\(907\) −9.00465 −0.298995 −0.149497 0.988762i \(-0.547766\pi\)
−0.149497 + 0.988762i \(0.547766\pi\)
\(908\) 2.69670 + 8.29960i 0.0894933 + 0.275432i
\(909\) 5.56195 + 4.04100i 0.184478 + 0.134031i
\(910\) 0 0
\(911\) −24.2303 + 17.6044i −0.802786 + 0.583258i −0.911730 0.410789i \(-0.865253\pi\)
0.108944 + 0.994048i \(0.465253\pi\)
\(912\) 9.52397 + 6.91957i 0.315370 + 0.229130i
\(913\) −3.73642 2.71467i −0.123658 0.0898425i
\(914\) −31.5853 + 22.9481i −1.04475 + 0.759056i
\(915\) 0 0
\(916\) −8.94596 6.49962i −0.295583 0.214753i
\(917\) 5.59477 + 17.2189i 0.184756 + 0.568619i
\(918\) 4.61803 0.152418
\(919\) 2.76125 + 8.49826i 0.0910853 + 0.280332i 0.986214 0.165477i \(-0.0529162\pi\)
−0.895128 + 0.445808i \(0.852916\pi\)
\(920\) 0 0
\(921\) −8.82532 + 27.1615i −0.290804 + 0.895003i
\(922\) 6.34995 19.5431i 0.209125 0.643619i
\(923\) −21.5675 + 15.6697i −0.709902 + 0.515774i
\(924\) 21.2370 0.698647
\(925\) 0 0
\(926\) 46.4133 1.52524
\(927\) 9.50850 6.90833i 0.312300 0.226899i
\(928\) 5.80735 17.8732i 0.190636 0.586716i
\(929\) −12.8117 + 39.4304i −0.420339 + 1.29367i 0.487048 + 0.873375i \(0.338074\pi\)
−0.907387 + 0.420296i \(0.861926\pi\)
\(930\) 0 0
\(931\) −6.22514 19.1590i −0.204021 0.627911i
\(932\) −18.3248 −0.600250
\(933\) 9.06296 + 27.8929i 0.296708 + 0.913173i
\(934\) −5.44243 3.95416i −0.178082 0.129384i
\(935\) 0 0
\(936\) −4.94392 + 3.59197i −0.161597 + 0.117407i
\(937\) 16.8749 + 12.2603i 0.551278 + 0.400527i 0.828256 0.560349i \(-0.189333\pi\)
−0.276978 + 0.960876i \(0.589333\pi\)
\(938\) 32.8220 + 23.8466i 1.07168 + 0.778618i
\(939\) 14.1523 10.2823i 0.461844 0.335549i
\(940\) 0 0
\(941\) −2.97219 2.15942i −0.0968905 0.0703951i 0.538285 0.842763i \(-0.319072\pi\)
−0.635176 + 0.772368i \(0.719072\pi\)
\(942\) 9.44413 + 29.0661i 0.307706 + 0.947023i
\(943\) 0.860163 0.0280107
\(944\) 7.23565 + 22.2691i 0.235500 + 0.724796i
\(945\) 0 0
\(946\) 3.96552 12.2046i 0.128930 0.396807i
\(947\) 9.79575 30.1482i 0.318319 0.979685i −0.656048 0.754719i \(-0.727773\pi\)
0.974367 0.224966i \(-0.0722270\pi\)
\(948\) 12.2913 8.93013i 0.399202 0.290037i
\(949\) 43.8204 1.42247
\(950\) 0 0
\(951\) 3.91763 0.127038
\(952\) −16.0302 + 11.6466i −0.519541 + 0.377469i
\(953\) −7.91746 + 24.3674i −0.256472 + 0.789339i 0.737064 + 0.675822i \(0.236211\pi\)
−0.993536 + 0.113516i \(0.963789\pi\)
\(954\) −1.48462 + 4.56919i −0.0480664 + 0.147933i
\(955\) 0 0
\(956\) 4.97625 + 15.3153i 0.160943 + 0.495333i
\(957\) −23.1129 −0.747133
\(958\) 10.5191 + 32.3746i 0.339858 + 1.04598i
\(959\) 48.6781 + 35.3667i 1.57190 + 1.14205i
\(960\) 0 0
\(961\) 19.1409 13.9067i 0.617449 0.448603i
\(962\) 0.0947214 + 0.0688191i 0.00305394 + 0.00221882i
\(963\) 4.58535 + 3.33145i 0.147761 + 0.107354i
\(964\) −21.7865 + 15.8288i −0.701697 + 0.509813i
\(965\) 0 0
\(966\) 3.17999 + 2.31040i 0.102314 + 0.0743358i
\(967\) 8.96663 + 27.5965i 0.288347 + 0.887442i 0.985375 + 0.170398i \(0.0545054\pi\)
−0.697028 + 0.717044i \(0.745495\pi\)
\(968\) −44.4077 −1.42732
\(969\) −1.97214 6.06961i −0.0633541 0.194984i
\(970\) 0 0
\(971\) −1.16588 + 3.58821i −0.0374149 + 0.115151i −0.968020 0.250875i \(-0.919282\pi\)
0.930605 + 0.366026i \(0.119282\pi\)
\(972\) −0.281722 + 0.867051i −0.00903624 + 0.0278107i
\(973\) −58.1705 + 42.2634i −1.86486 + 1.35490i
\(974\) 18.7739 0.601553
\(975\) 0 0
\(976\) −27.8630 −0.891874
\(977\) 29.7044 21.5815i 0.950329 0.690455i −0.000555441 1.00000i \(-0.500177\pi\)
0.950885 + 0.309545i \(0.100177\pi\)
\(978\) 11.4738 35.3128i 0.366893 1.12918i
\(979\) 6.34180 19.5181i 0.202685 0.623800i
\(980\) 0 0
\(981\) −0.420658 1.29465i −0.0134306 0.0413350i
\(982\) −56.8104 −1.81289
\(983\) −7.28128 22.4095i −0.232237 0.714752i −0.997476 0.0710055i \(-0.977379\pi\)
0.765239 0.643746i \(-0.222621\pi\)
\(984\) −2.21175 1.60693i −0.0705081 0.0512271i
\(985\) 0 0
\(986\) −14.6143 + 10.6179i −0.465413 + 0.338143i
\(987\) −17.3304 12.5912i −0.551631 0.400784i
\(988\) −5.72331 4.15823i −0.182083 0.132291i
\(989\) 0.601653 0.437126i 0.0191314 0.0138998i
\(990\) 0 0
\(991\) −23.5727 17.1266i −0.748812 0.544044i 0.146646 0.989189i \(-0.453152\pi\)
−0.895458 + 0.445145i \(0.853152\pi\)
\(992\) −4.02235 12.3795i −0.127710 0.393050i
\(993\) 17.5534 0.557039
\(994\) −16.8413 51.8323i −0.534175 1.64402i
\(995\) 0 0
\(996\) 0.220205 0.677723i 0.00697748 0.0214745i
\(997\) −13.5733 + 41.7742i −0.429870 + 1.32300i 0.468384 + 0.883525i \(0.344836\pi\)
−0.898254 + 0.439478i \(0.855164\pi\)
\(998\) 56.7993 41.2671i 1.79795 1.30629i
\(999\) −0.0208515 −0.000659711
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 375.2.g.b.301.1 8
5.2 odd 4 375.2.i.b.199.2 16
5.3 odd 4 375.2.i.b.199.3 16
5.4 even 2 75.2.g.b.61.2 yes 8
15.14 odd 2 225.2.h.c.136.1 8
25.3 odd 20 1875.2.b.c.1249.3 8
25.4 even 10 1875.2.a.h.1.1 4
25.9 even 10 75.2.g.b.16.2 8
25.12 odd 20 375.2.i.b.49.3 16
25.13 odd 20 375.2.i.b.49.2 16
25.16 even 5 inner 375.2.g.b.76.1 8
25.21 even 5 1875.2.a.e.1.4 4
25.22 odd 20 1875.2.b.c.1249.6 8
75.29 odd 10 5625.2.a.i.1.4 4
75.59 odd 10 225.2.h.c.91.1 8
75.71 odd 10 5625.2.a.n.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.b.16.2 8 25.9 even 10
75.2.g.b.61.2 yes 8 5.4 even 2
225.2.h.c.91.1 8 75.59 odd 10
225.2.h.c.136.1 8 15.14 odd 2
375.2.g.b.76.1 8 25.16 even 5 inner
375.2.g.b.301.1 8 1.1 even 1 trivial
375.2.i.b.49.2 16 25.13 odd 20
375.2.i.b.49.3 16 25.12 odd 20
375.2.i.b.199.2 16 5.2 odd 4
375.2.i.b.199.3 16 5.3 odd 4
1875.2.a.e.1.4 4 25.21 even 5
1875.2.a.h.1.1 4 25.4 even 10
1875.2.b.c.1249.3 8 25.3 odd 20
1875.2.b.c.1249.6 8 25.22 odd 20
5625.2.a.i.1.4 4 75.29 odd 10
5625.2.a.n.1.1 4 75.71 odd 10