Properties

Label 225.2.h.c.136.1
Level $225$
Weight $2$
Character 225.136
Analytic conductor $1.797$
Analytic rank $0$
Dimension $8$
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] = [225,2,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), 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: \(1.79663404548\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 75)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 136.1
Root \(-0.0272949 + 1.41395i\) of defining polynomial
Character \(\chi\) \(=\) 225.136
Dual form 225.2.h.c.91.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38048 + 1.00297i) q^{2} +(0.281722 - 0.867051i) q^{4} +(1.02729 - 1.98612i) q^{5} -3.94243 q^{7} +(-0.573870 - 1.76619i) q^{8} +O(q^{10})\) \(q+(-1.38048 + 1.00297i) q^{2} +(0.281722 - 0.867051i) q^{4} +(1.02729 - 1.98612i) q^{5} -3.94243 q^{7} +(-0.573870 - 1.76619i) q^{8} +(0.573870 + 3.77214i) q^{10} +(-4.78023 + 3.47304i) q^{11} +(-2.66220 - 1.93420i) q^{13} +(5.44243 - 3.95416i) q^{14} +(4.03877 + 2.93434i) q^{16} +(-0.836312 - 2.57390i) q^{17} +(-0.728704 - 2.24272i) q^{19} +(-1.43265 - 1.45025i) q^{20} +(3.11562 - 9.58890i) q^{22} +(-0.472705 + 0.343440i) q^{23} +(-2.88933 - 4.08066i) q^{25} +5.61505 q^{26} +(-1.11067 + 3.41829i) q^{28} +(1.20877 - 3.72022i) q^{29} +(0.837233 + 2.57674i) q^{31} -4.80433 q^{32} +(3.73607 + 2.71441i) q^{34} +(-4.05004 + 7.83013i) q^{35} +(0.0168692 + 0.0122562i) q^{37} +(3.25535 + 2.36515i) q^{38} +(-4.09740 - 0.674625i) q^{40} +(1.19098 + 0.865300i) q^{41} +1.27279 q^{43} +(1.66461 + 5.12314i) q^{44} +(0.308096 - 0.948222i) q^{46} +(-1.67907 + 5.16764i) q^{47} +8.54276 q^{49} +(8.08145 + 2.73533i) q^{50} +(-2.42705 + 1.76336i) q^{52} +(-0.870050 + 2.67774i) q^{53} +(1.98716 + 13.0619i) q^{55} +(2.26244 + 6.96308i) q^{56} +(2.06260 + 6.34804i) q^{58} +(-3.79456 - 2.75691i) q^{59} +(-4.51538 + 3.28061i) q^{61} +(-3.74018 - 2.71740i) q^{62} +(-1.44528 + 1.05006i) q^{64} +(-6.57641 + 3.30045i) q^{65} +(1.86361 + 5.73559i) q^{67} -2.46731 q^{68} +(-2.26244 - 14.8714i) q^{70} +(2.50346 - 7.70487i) q^{71} +(-10.7734 + 7.82730i) q^{73} -0.0355801 q^{74} -2.14984 q^{76} +(18.8457 - 13.6922i) q^{77} +(5.14971 - 15.8492i) q^{79} +(9.97696 - 5.00705i) q^{80} -2.51200 q^{82} +(-0.241540 - 0.743385i) q^{83} +(-5.97122 - 0.983144i) q^{85} +(-1.75705 + 1.27657i) q^{86} +(8.87728 + 6.44972i) q^{88} +(-2.80994 + 2.04154i) q^{89} +(10.4955 + 7.62545i) q^{91} +(0.164609 + 0.506614i) q^{92} +(-2.86510 - 8.81786i) q^{94} +(-5.20290 - 0.856643i) q^{95} +(-0.758460 + 2.33430i) q^{97} +(-11.7931 + 8.56817i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} + q^{4} + 5 q^{5} + 4 q^{7} - 16 q^{11} - 8 q^{13} + 8 q^{14} - 17 q^{16} + q^{17} - 5 q^{19} + 10 q^{20} + 13 q^{22} - 7 q^{23} - 15 q^{25} - 6 q^{26} - 17 q^{28} - 5 q^{29} - 19 q^{31} - 24 q^{32} + 12 q^{34} + 10 q^{35} - q^{37} + 10 q^{38} + 25 q^{40} + 14 q^{41} + 32 q^{43} + 3 q^{44} + 16 q^{46} + q^{47} + 16 q^{49} - 10 q^{50} - 6 q^{52} + 3 q^{53} + 15 q^{55} + 15 q^{56} + 5 q^{58} - 30 q^{59} - 14 q^{61} + 17 q^{62} - 44 q^{64} - 25 q^{65} + 4 q^{67} + 22 q^{68} - 15 q^{70} - 21 q^{71} + 2 q^{73} + 38 q^{74} + 80 q^{76} + 37 q^{77} - 30 q^{79} + 50 q^{80} - 12 q^{82} - 2 q^{83} - 30 q^{85} + 34 q^{86} + 70 q^{88} + 21 q^{91} - 9 q^{92} - 33 q^{94} - 65 q^{95} - 6 q^{97} - 73 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{4}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38048 + 1.00297i −0.976144 + 0.709210i −0.956844 0.290604i \(-0.906144\pi\)
−0.0193004 + 0.999814i \(0.506144\pi\)
\(3\) 0 0
\(4\) 0.281722 0.867051i 0.140861 0.433526i
\(5\) 1.02729 1.98612i 0.459420 0.888219i
\(6\) 0 0
\(7\) −3.94243 −1.49010 −0.745049 0.667009i \(-0.767574\pi\)
−0.745049 + 0.667009i \(0.767574\pi\)
\(8\) −0.573870 1.76619i −0.202894 0.624442i
\(9\) 0 0
\(10\) 0.573870 + 3.77214i 0.181474 + 1.19286i
\(11\) −4.78023 + 3.47304i −1.44129 + 1.04716i −0.453524 + 0.891244i \(0.649833\pi\)
−0.987770 + 0.155918i \(0.950167\pi\)
\(12\) 0 0
\(13\) −2.66220 1.93420i −0.738361 0.536451i 0.153836 0.988096i \(-0.450837\pi\)
−0.892197 + 0.451646i \(0.850837\pi\)
\(14\) 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 \(-0.206440\pi\)
\(18\) 0 0
\(19\) −0.728704 2.24272i −0.167176 0.514515i 0.832014 0.554755i \(-0.187188\pi\)
−0.999190 + 0.0402396i \(0.987188\pi\)
\(20\) −1.43265 1.45025i −0.320351 0.324286i
\(21\) 0 0
\(22\) 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 \(0.319403\pi\)
\(24\) 0 0
\(25\) −2.88933 4.08066i −0.577866 0.816132i
\(26\) 5.61505 1.10120
\(27\) 0 0
\(28\) −1.11067 + 3.41829i −0.209897 + 0.645996i
\(29\) 1.20877 3.72022i 0.224464 0.690828i −0.773882 0.633330i \(-0.781688\pi\)
0.998346 0.0574980i \(-0.0183123\pi\)
\(30\) 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
\(33\) 0 0
\(34\) 3.73607 + 2.71441i 0.640730 + 0.465518i
\(35\) −4.05004 + 7.83013i −0.684581 + 1.32353i
\(36\) 0 0
\(37\) 0.0168692 + 0.0122562i 0.00277328 + 0.00201490i 0.589171 0.808008i \(-0.299454\pi\)
−0.586398 + 0.810023i \(0.699454\pi\)
\(38\) 3.25535 + 2.36515i 0.528087 + 0.383678i
\(39\) 0 0
\(40\) −4.09740 0.674625i −0.647855 0.106668i
\(41\) 1.19098 + 0.865300i 0.186000 + 0.135137i 0.676889 0.736085i \(-0.263328\pi\)
−0.490889 + 0.871222i \(0.663328\pi\)
\(42\) 0 0
\(43\) 1.27279 0.194098 0.0970491 0.995280i \(-0.469060\pi\)
0.0970491 + 0.995280i \(0.469060\pi\)
\(44\) 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 \(0.970299\pi\)
\(48\) 0 0
\(49\) 8.54276 1.22039
\(50\) 8.08145 + 2.73533i 1.14289 + 0.386833i
\(51\) 0 0
\(52\) −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 0
\(55\) 1.98716 + 13.0619i 0.267949 + 1.76127i
\(56\) 2.26244 + 6.96308i 0.302332 + 0.930481i
\(57\) 0 0
\(58\) 2.06260 + 6.34804i 0.270833 + 0.833539i
\(59\) −3.79456 2.75691i −0.494009 0.358919i 0.312715 0.949847i \(-0.398762\pi\)
−0.806724 + 0.590928i \(0.798762\pi\)
\(60\) 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
\(63\) 0 0
\(64\) −1.44528 + 1.05006i −0.180660 + 0.131257i
\(65\) −6.57641 + 3.30045i −0.815704 + 0.409370i
\(66\) 0 0
\(67\) 1.86361 + 5.73559i 0.227676 + 0.700714i 0.998009 + 0.0630725i \(0.0200899\pi\)
−0.770333 + 0.637642i \(0.779910\pi\)
\(68\) −2.46731 −0.299206
\(69\) 0 0
\(70\) −2.26244 14.8714i −0.270414 1.77747i
\(71\) 2.50346 7.70487i 0.297106 0.914400i −0.685399 0.728167i \(-0.740372\pi\)
0.982506 0.186232i \(-0.0596277\pi\)
\(72\) 0 0
\(73\) −10.7734 + 7.82730i −1.26093 + 0.916116i −0.998803 0.0489187i \(-0.984422\pi\)
−0.262123 + 0.965035i \(0.584422\pi\)
\(74\) −0.0355801 −0.00413611
\(75\) 0 0
\(76\) −2.14984 −0.246604
\(77\) 18.8457 13.6922i 2.14767 1.56037i
\(78\) 0 0
\(79\) 5.14971 15.8492i 0.579388 1.78317i −0.0413379 0.999145i \(-0.513162\pi\)
0.620726 0.784028i \(-0.286838\pi\)
\(80\) 9.97696 5.00705i 1.11546 0.559805i
\(81\) 0 0
\(82\) −2.51200 −0.277404
\(83\) −0.241540 0.743385i −0.0265125 0.0815971i 0.936925 0.349531i \(-0.113659\pi\)
−0.963437 + 0.267934i \(0.913659\pi\)
\(84\) 0 0
\(85\) −5.97122 0.983144i −0.647669 0.106637i
\(86\) −1.75705 + 1.27657i −0.189468 + 0.137656i
\(87\) 0 0
\(88\) 8.87728 + 6.44972i 0.946322 + 0.687543i
\(89\) −2.80994 + 2.04154i −0.297853 + 0.216403i −0.726667 0.686990i \(-0.758932\pi\)
0.428814 + 0.903393i \(0.358932\pi\)
\(90\) 0 0
\(91\) 10.4955 + 7.62545i 1.10023 + 0.799364i
\(92\) 0.164609 + 0.506614i 0.0171617 + 0.0528182i
\(93\) 0 0
\(94\) −2.86510 8.81786i −0.295512 0.909493i
\(95\) −5.20290 0.856643i −0.533806 0.0878897i
\(96\) 0 0
\(97\) −0.758460 + 2.33430i −0.0770099 + 0.237012i −0.982149 0.188103i \(-0.939766\pi\)
0.905139 + 0.425115i \(0.139766\pi\)
\(98\) −11.7931 + 8.56817i −1.19128 + 0.865515i
\(99\) 0 0
\(100\) −4.35213 + 1.35559i −0.435213 + 0.135559i
\(101\) 6.87495 0.684083 0.342042 0.939685i \(-0.388882\pi\)
0.342042 + 0.939685i \(0.388882\pi\)
\(102\) 0 0
\(103\) 3.63192 11.1779i 0.357864 1.10139i −0.596466 0.802638i \(-0.703429\pi\)
0.954330 0.298754i \(-0.0965710\pi\)
\(104\) −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 0
\(109\) 1.10130 + 0.800139i 0.105485 + 0.0766394i 0.639277 0.768976i \(-0.279234\pi\)
−0.533792 + 0.845616i \(0.679234\pi\)
\(110\) −15.8440 16.0386i −1.51067 1.52922i
\(111\) 0 0
\(112\) −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 \(0.867627\pi\)
\(114\) 0 0
\(115\) 0.196506 + 1.29166i 0.0183242 + 0.120448i
\(116\) −2.88508 2.09614i −0.267873 0.194621i
\(117\) 0 0
\(118\) 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
\(123\) 0 0
\(124\) 2.47003 0.221815
\(125\) −11.0729 + 1.54651i −0.990387 + 0.138324i
\(126\) 0 0
\(127\) 10.9563 7.96023i 0.972216 0.706356i 0.0162606 0.999868i \(-0.494824\pi\)
0.955956 + 0.293511i \(0.0948239\pi\)
\(128\) 3.91123 12.0375i 0.345708 1.06398i
\(129\) 0 0
\(130\) 5.76832 11.1522i 0.505915 0.978109i
\(131\) −1.41912 4.36759i −0.123989 0.381599i 0.869727 0.493534i \(-0.164295\pi\)
−0.993716 + 0.111935i \(0.964295\pi\)
\(132\) 0 0
\(133\) 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 0
\(139\) −14.7550 + 10.7201i −1.25150 + 0.909269i −0.998308 0.0581460i \(-0.981481\pi\)
−0.253194 + 0.967416i \(0.581481\pi\)
\(140\) 5.64814 + 5.71751i 0.477355 + 0.483218i
\(141\) 0 0
\(142\) 4.27182 + 13.1473i 0.358483 + 1.10330i
\(143\) 19.4435 1.62595
\(144\) 0 0
\(145\) −6.14703 6.22253i −0.510483 0.516753i
\(146\) 7.02177 21.6108i 0.581126 1.78852i
\(147\) 0 0
\(148\) 0.0153792 0.0111736i 0.00126416 0.000918465i
\(149\) −14.7323 −1.20692 −0.603458 0.797394i \(-0.706211\pi\)
−0.603458 + 0.797394i \(0.706211\pi\)
\(150\) 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 0
\(154\) −12.2831 + 37.8036i −0.989803 + 3.04630i
\(155\) 5.97779 + 0.984226i 0.480148 + 0.0790549i
\(156\) 0 0
\(157\) 17.9105 1.42942 0.714708 0.699423i \(-0.246560\pi\)
0.714708 + 0.699423i \(0.246560\pi\)
\(158\) 8.78728 + 27.0445i 0.699078 + 2.15154i
\(159\) 0 0
\(160\) −4.93547 + 9.54197i −0.390183 + 0.754359i
\(161\) 1.86361 1.35399i 0.146873 0.106709i
\(162\) 0 0
\(163\) −17.6041 12.7901i −1.37886 1.00180i −0.996986 0.0775819i \(-0.975280\pi\)
−0.381870 0.924216i \(-0.624720\pi\)
\(164\) 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 \(0.561167\pi\)
\(168\) 0 0
\(169\) −0.671052 2.06529i −0.0516194 0.158868i
\(170\) 9.22919 4.63177i 0.707846 0.355241i
\(171\) 0 0
\(172\) 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 \(0.136694\pi\)
\(174\) 0 0
\(175\) 11.3910 + 16.0877i 0.861077 + 1.21612i
\(176\) −29.4974 −2.22345
\(177\) 0 0
\(178\) 1.83144 5.63659i 0.137272 0.422480i
\(179\) 1.98716 6.11586i 0.148528 0.457121i −0.848920 0.528521i \(-0.822747\pi\)
0.997448 + 0.0714002i \(0.0227468\pi\)
\(180\) 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
\(183\) 0 0
\(184\) 0.877852 + 0.637797i 0.0647161 + 0.0470190i
\(185\) 0.0416718 0.0209135i 0.00306377 0.00153759i
\(186\) 0 0
\(187\) 12.9370 + 9.39931i 0.946050 + 0.687346i
\(188\) 4.00758 + 2.91168i 0.292283 + 0.212356i
\(189\) 0 0
\(190\) 8.04167 4.03580i 0.583404 0.292788i
\(191\) 5.43095 + 3.94582i 0.392970 + 0.285509i 0.766671 0.642040i \(-0.221912\pi\)
−0.373702 + 0.927549i \(0.621912\pi\)
\(192\) 0 0
\(193\) 4.82817 0.347539 0.173769 0.984786i \(-0.444405\pi\)
0.173769 + 0.984786i \(0.444405\pi\)
\(194\) −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 \(-0.0712477\pi\)
\(198\) 0 0
\(199\) −8.72608 −0.618575 −0.309288 0.950969i \(-0.600091\pi\)
−0.309288 + 0.950969i \(0.600091\pi\)
\(200\) −5.54912 + 7.44487i −0.392382 + 0.526432i
\(201\) 0 0
\(202\) −9.49071 + 6.89540i −0.667764 + 0.485159i
\(203\) −4.76550 + 14.6667i −0.334473 + 1.02940i
\(204\) 0 0
\(205\) 2.94208 1.47651i 0.205484 0.103124i
\(206\) 6.19738 + 19.0736i 0.431792 + 1.32892i
\(207\) 0 0
\(208\) −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
\(213\) 0 0
\(214\) 7.82426 5.68466i 0.534856 0.388595i
\(215\) 1.30753 2.52790i 0.0891726 0.172402i
\(216\) 0 0
\(217\) −3.30073 10.1586i −0.224068 0.689611i
\(218\) −2.32283 −0.157322
\(219\) 0 0
\(220\) 11.8852 + 1.95687i 0.801300 + 0.131932i
\(221\) −2.75202 + 8.46984i −0.185121 + 0.569743i
\(222\) 0 0
\(223\) 0.246494 0.179088i 0.0165064 0.0119926i −0.579501 0.814971i \(-0.696753\pi\)
0.596008 + 0.802979i \(0.296753\pi\)
\(224\) 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 0
\(229\) 3.74812 11.5355i 0.247682 0.762288i −0.747501 0.664260i \(-0.768747\pi\)
0.995184 0.0980277i \(-0.0312534\pi\)
\(230\) −1.56678 1.58602i −0.103310 0.104579i
\(231\) 0 0
\(232\) −7.26430 −0.476924
\(233\) −6.21132 19.1165i −0.406917 1.25236i −0.919284 0.393595i \(-0.871231\pi\)
0.512367 0.858766i \(-0.328769\pi\)
\(234\) 0 0
\(235\) 8.53864 + 8.64351i 0.557000 + 0.563841i
\(236\) −3.45939 + 2.51340i −0.225187 + 0.163608i
\(237\) 0 0
\(238\) −14.7292 10.7014i −0.954751 0.693667i
\(239\) 14.2902 10.3825i 0.924358 0.671585i −0.0202473 0.999795i \(-0.506445\pi\)
0.944605 + 0.328210i \(0.106445\pi\)
\(240\) 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
\(243\) 0 0
\(244\) 1.57238 + 4.83929i 0.100661 + 0.309804i
\(245\) 8.77593 16.9669i 0.560674 1.08398i
\(246\) 0 0
\(247\) −2.39791 + 7.38002i −0.152576 + 0.469580i
\(248\) 4.07055 2.95742i 0.258480 0.187797i
\(249\) 0 0
\(250\) 13.7347 13.2407i 0.868659 0.837417i
\(251\) −1.89396 −0.119546 −0.0597729 0.998212i \(-0.519038\pi\)
−0.0597729 + 0.998212i \(0.519038\pi\)
\(252\) 0 0
\(253\) 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 0
\(259\) −0.0665056 0.0483191i −0.00413245 0.00300240i
\(260\) 1.00894 + 6.63190i 0.0625715 + 0.411293i
\(261\) 0 0
\(262\) 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 \(0.907967\pi\)
\(264\) 0 0
\(265\) 4.42451 + 4.47885i 0.271795 + 0.275134i
\(266\) −12.8340 9.32443i −0.786902 0.571718i
\(267\) 0 0
\(268\) 5.49807 0.335848
\(269\) −5.61321 17.2757i −0.342244 1.05332i −0.963043 0.269348i \(-0.913192\pi\)
0.620799 0.783970i \(-0.286808\pi\)
\(270\) 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
\(273\) 0 0
\(274\) −26.0425 −1.57329
\(275\) 27.9840 + 9.47173i 1.68750 + 0.571167i
\(276\) 0 0
\(277\) −6.67837 + 4.85212i −0.401264 + 0.291535i −0.770056 0.637977i \(-0.779772\pi\)
0.368792 + 0.929512i \(0.379772\pi\)
\(278\) 9.61690 29.5978i 0.576783 1.77516i
\(279\) 0 0
\(280\) 16.1537 + 2.65966i 0.965368 + 0.158945i
\(281\) −0.395941 1.21858i −0.0236199 0.0726944i 0.938552 0.345138i \(-0.112168\pi\)
−0.962172 + 0.272444i \(0.912168\pi\)
\(282\) 0 0
\(283\) 0.825484 + 2.54058i 0.0490699 + 0.151022i 0.972589 0.232531i \(-0.0747006\pi\)
−0.923519 + 0.383552i \(0.874701\pi\)
\(284\) −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
\(288\) 0 0
\(289\) 7.82773 5.68718i 0.460455 0.334540i
\(290\) 14.7269 + 2.42474i 0.864792 + 0.142385i
\(291\) 0 0
\(292\) 3.75158 + 11.5462i 0.219545 + 0.675689i
\(293\) −17.6605 −1.03174 −0.515870 0.856667i \(-0.672531\pi\)
−0.515870 + 0.856667i \(0.672531\pi\)
\(294\) 0 0
\(295\) −9.37368 + 4.70428i −0.545757 + 0.273894i
\(296\) 0.0119660 0.0368276i 0.000695511 0.00214056i
\(297\) 0 0
\(298\) 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
\(303\) 0 0
\(304\) 3.63783 11.1961i 0.208644 0.642140i
\(305\) 1.87706 + 12.3382i 0.107480 + 0.706485i
\(306\) 0 0
\(307\) −28.5593 −1.62997 −0.814983 0.579484i \(-0.803254\pi\)
−0.814983 + 0.579484i \(0.803254\pi\)
\(308\) −6.56260 20.1976i −0.373939 1.15087i
\(309\) 0 0
\(310\) −9.23935 + 4.63687i −0.524760 + 0.263357i
\(311\) −23.7271 + 17.2388i −1.34544 + 0.977521i −0.346217 + 0.938154i \(0.612534\pi\)
−0.999225 + 0.0393664i \(0.987466\pi\)
\(312\) 0 0
\(313\) 14.1523 + 10.2823i 0.799937 + 0.581189i 0.910896 0.412637i \(-0.135392\pi\)
−0.110958 + 0.993825i \(0.535392\pi\)
\(314\) −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 \(0.935091\pi\)
\(318\) 0 0
\(319\) 7.14227 + 21.9816i 0.399890 + 1.23074i
\(320\) 0.600809 + 3.94921i 0.0335862 + 0.220768i
\(321\) 0 0
\(322\) −1.21465 + 3.73830i −0.0676897 + 0.208327i
\(323\) −5.16312 + 3.75123i −0.287284 + 0.208724i
\(324\) 0 0
\(325\) −0.200840 + 16.4521i −0.0111406 + 0.912596i
\(326\) 37.1301 2.05645
\(327\) 0 0
\(328\) 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 0
\(334\) −31.2029 22.6702i −1.70734 1.24046i
\(335\) 13.3060 + 2.19080i 0.726986 + 0.119696i
\(336\) 0 0
\(337\) 11.3647 + 8.25697i 0.619077 + 0.449786i 0.852599 0.522566i \(-0.175025\pi\)
−0.233522 + 0.972352i \(0.575025\pi\)
\(338\) 2.99780 + 2.17803i 0.163059 + 0.118469i
\(339\) 0 0
\(340\) −2.53466 + 4.90038i −0.137461 + 0.265760i
\(341\) −12.9513 9.40966i −0.701351 0.509562i
\(342\) 0 0
\(343\) −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 \(0.0911944\pi\)
\(348\) 0 0
\(349\) 21.5626 1.15422 0.577109 0.816667i \(-0.304181\pi\)
0.577109 + 0.816667i \(0.304181\pi\)
\(350\) −31.8605 10.7838i −1.70302 0.576420i
\(351\) 0 0
\(352\) 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 \(0.160993\pi\)
\(354\) 0 0
\(355\) −12.7310 12.8873i −0.675690 0.683989i
\(356\) 0.978498 + 3.01151i 0.0518603 + 0.159610i
\(357\) 0 0
\(358\) 3.39082 + 10.4359i 0.179210 + 0.551553i
\(359\) 21.9663 + 15.9595i 1.15934 + 0.842308i 0.989694 0.143198i \(-0.0457385\pi\)
0.169643 + 0.985506i \(0.445738\pi\)
\(360\) 0 0
\(361\) 10.8725 7.89936i 0.572239 0.415756i
\(362\) −20.3028 14.7508i −1.06709 0.775285i
\(363\) 0 0
\(364\) 9.56848 6.95191i 0.501525 0.364379i
\(365\) 4.47853 + 29.4381i 0.234417 + 1.54086i
\(366\) 0 0
\(367\) 6.62605 + 20.3929i 0.345877 + 1.06450i 0.961113 + 0.276157i \(0.0890608\pi\)
−0.615236 + 0.788343i \(0.710939\pi\)
\(368\) −2.91692 −0.152055
\(369\) 0 0
\(370\) −0.0365513 + 0.0706663i −0.00190021 + 0.00367377i
\(371\) 3.43011 10.5568i 0.178083 0.548082i
\(372\) 0 0
\(373\) −5.17021 + 3.75638i −0.267703 + 0.194498i −0.713536 0.700618i \(-0.752908\pi\)
0.445833 + 0.895116i \(0.352908\pi\)
\(374\) −27.2865 −1.41095
\(375\) 0 0
\(376\) 10.0906 0.520383
\(377\) −10.4136 + 7.56596i −0.536330 + 0.389667i
\(378\) 0 0
\(379\) −0.0477946 + 0.147097i −0.00245504 + 0.00755585i −0.952277 0.305237i \(-0.901264\pi\)
0.949821 + 0.312792i \(0.101264\pi\)
\(380\) −2.20852 + 4.26985i −0.113295 + 0.219038i
\(381\) 0 0
\(382\) −11.4549 −0.586081
\(383\) 1.31489 + 4.04682i 0.0671878 + 0.206783i 0.979014 0.203794i \(-0.0653273\pi\)
−0.911826 + 0.410577i \(0.865327\pi\)
\(384\) 0 0
\(385\) −7.83425 51.4958i −0.399270 2.62447i
\(386\) −6.66517 + 4.84253i −0.339248 + 0.246478i
\(387\) 0 0
\(388\) 1.81028 + 1.31525i 0.0919032 + 0.0667716i
\(389\) −16.4782 + 11.9721i −0.835479 + 0.607011i −0.921104 0.389316i \(-0.872711\pi\)
0.0856250 + 0.996327i \(0.472711\pi\)
\(390\) 0 0
\(391\) 1.27931 + 0.929474i 0.0646975 + 0.0470055i
\(392\) −4.90243 15.0881i −0.247610 0.762066i
\(393\) 0 0
\(394\) 7.58465 + 23.3431i 0.382109 + 1.17601i
\(395\) −26.1881 26.5097i −1.31767 1.33385i
\(396\) 0 0
\(397\) −0.604795 + 1.86137i −0.0303538 + 0.0934194i −0.965086 0.261934i \(-0.915640\pi\)
0.934732 + 0.355354i \(0.115640\pi\)
\(398\) 12.0461 8.75203i 0.603818 0.438700i
\(399\) 0 0
\(400\) 0.304690 24.9591i 0.0152345 1.24796i
\(401\) 32.8337 1.63964 0.819818 0.572624i \(-0.194075\pi\)
0.819818 + 0.572624i \(0.194075\pi\)
\(402\) 0 0
\(403\) 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
\(408\) 0 0
\(409\) 32.0180 + 23.2624i 1.58319 + 1.15025i 0.912923 + 0.408132i \(0.133820\pi\)
0.670265 + 0.742122i \(0.266180\pi\)
\(410\) −2.58056 + 4.98912i −0.127445 + 0.246395i
\(411\) 0 0
\(412\) −8.66863 6.29813i −0.427073 0.310287i
\(413\) 14.9598 + 10.8689i 0.736123 + 0.534825i
\(414\) 0 0
\(415\) −1.72458 0.283948i −0.0846564 0.0139384i
\(416\) 12.7901 + 9.29254i 0.627086 + 0.455604i
\(417\) 0 0
\(418\) −23.7756 −1.16290
\(419\) −6.04421 18.6022i −0.295279 0.908776i −0.983128 0.182921i \(-0.941445\pi\)
0.687848 0.725854i \(-0.258555\pi\)
\(420\) 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
\(423\) 0 0
\(424\) 5.22869 0.253928
\(425\) −8.08684 + 10.8496i −0.392269 + 0.526281i
\(426\) 0 0
\(427\) 17.8016 12.9336i 0.861478 0.625901i
\(428\) −1.59675 + 4.91428i −0.0771816 + 0.237540i
\(429\) 0 0
\(430\) 0.730414 + 4.80113i 0.0352237 + 0.231531i
\(431\) −4.24497 13.0647i −0.204473 0.629304i −0.999735 0.0230370i \(-0.992666\pi\)
0.795261 0.606267i \(-0.207334\pi\)
\(432\) 0 0
\(433\) −3.83964 11.8172i −0.184522 0.567899i 0.815418 0.578872i \(-0.196507\pi\)
−0.999940 + 0.0109734i \(0.996507\pi\)
\(434\) 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
\(438\) 0 0
\(439\) −8.87118 + 6.44529i −0.423399 + 0.307617i −0.779004 0.627019i \(-0.784275\pi\)
0.355605 + 0.934636i \(0.384275\pi\)
\(440\) 21.9295 11.0056i 1.04545 0.524670i
\(441\) 0 0
\(442\) −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 0
\(445\) 1.16810 + 7.67813i 0.0553734 + 0.363978i
\(446\) −0.160658 + 0.494454i −0.00760737 + 0.0234131i
\(447\) 0 0
\(448\) 5.69791 4.13977i 0.269201 0.195586i
\(449\) 32.9503 1.55502 0.777511 0.628869i \(-0.216482\pi\)
0.777511 + 0.628869i \(0.216482\pi\)
\(450\) 0 0
\(451\) −8.69840 −0.409592
\(452\) −7.88130 + 5.72610i −0.370705 + 0.269333i
\(453\) 0 0
\(454\) 5.04738 15.5342i 0.236885 0.729058i
\(455\) 25.9270 13.0118i 1.21548 0.610002i
\(456\) 0 0
\(457\) −22.8800 −1.07028 −0.535142 0.844762i \(-0.679742\pi\)
−0.535142 + 0.844762i \(0.679742\pi\)
\(458\) 6.39564 + 19.6838i 0.298849 + 0.919762i
\(459\) 0 0
\(460\) 1.17530 + 0.193509i 0.0547985 + 0.00902243i
\(461\) 9.74259 7.07841i 0.453758 0.329674i −0.337320 0.941390i \(-0.609520\pi\)
0.791078 + 0.611716i \(0.209520\pi\)
\(462\) 0 0
\(463\) 22.0054 + 15.9878i 1.02268 + 0.743018i 0.966830 0.255421i \(-0.0822141\pi\)
0.0558471 + 0.998439i \(0.482214\pi\)
\(464\) 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 \(0.870924\pi\)
\(468\) 0 0
\(469\) −7.34714 22.6122i −0.339259 1.04413i
\(470\) −20.4566 3.36812i −0.943593 0.155360i
\(471\) 0 0
\(472\) −2.69164 + 8.28402i −0.123893 + 0.381303i
\(473\) −6.08421 + 4.42044i −0.279752 + 0.203252i
\(474\) 0 0
\(475\) −7.04630 + 9.45355i −0.323307 + 0.433758i
\(476\) 9.72721 0.445846
\(477\) 0 0
\(478\) −9.31397 + 28.6655i −0.426011 + 1.31113i
\(479\) −6.16466 + 18.9729i −0.281670 + 0.866893i 0.705706 + 0.708504i \(0.250630\pi\)
−0.987377 + 0.158388i \(0.949370\pi\)
\(480\) 0 0
\(481\) −0.0212032 0.0652567i −0.000966783 0.00297545i
\(482\) 50.4038 2.29583
\(483\) 0 0
\(484\) −17.6370 12.8140i −0.801680 0.582455i
\(485\) 3.85703 + 3.90440i 0.175139 + 0.177290i
\(486\) 0 0
\(487\) 8.90102 + 6.46697i 0.403344 + 0.293046i 0.770902 0.636954i \(-0.219806\pi\)
−0.367558 + 0.930001i \(0.619806\pi\)
\(488\) 8.38543 + 6.09237i 0.379591 + 0.275789i
\(489\) 0 0
\(490\) 4.90243 + 32.2245i 0.221469 + 1.45575i
\(491\) −26.9348 19.5693i −1.21555 0.883151i −0.219830 0.975538i \(-0.570550\pi\)
−0.995723 + 0.0923876i \(0.970550\pi\)
\(492\) 0 0
\(493\) −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
\(498\) 0 0
\(499\) −41.1448 −1.84189 −0.920946 0.389690i \(-0.872582\pi\)
−0.920946 + 0.389690i \(0.872582\pi\)
\(500\) −1.77856 + 10.0364i −0.0795398 + 0.448843i
\(501\) 0 0
\(502\) 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 \(0.846380\pi\)
\(504\) 0 0
\(505\) 7.06260 13.6545i 0.314282 0.607616i
\(506\) 1.82044 + 5.60275i 0.0809286 + 0.249073i
\(507\) 0 0
\(508\) −3.81529 11.7423i −0.169276 0.520979i
\(509\) −21.9206 15.9262i −0.971612 0.705918i −0.0157938 0.999875i \(-0.505028\pi\)
−0.955818 + 0.293958i \(0.905028\pi\)
\(510\) 0 0
\(511\) 42.4732 30.8586i 1.87890 1.36510i
\(512\) −4.40295 3.19893i −0.194585 0.141374i
\(513\) 0 0
\(514\) 30.5376 22.1869i 1.34696 0.978622i
\(515\) −18.4696 18.6964i −0.813868 0.823864i
\(516\) 0 0
\(517\) −9.92109 30.5340i −0.436329 1.34288i
\(518\) 0.140272 0.00616321
\(519\) 0 0
\(520\) 9.60322 + 9.72117i 0.421129 + 0.426301i
\(521\) −8.02073 + 24.6853i −0.351395 + 1.08148i 0.606676 + 0.794949i \(0.292503\pi\)
−0.958071 + 0.286532i \(0.907497\pi\)
\(522\) 0 0
\(523\) 1.45123 1.05438i 0.0634577 0.0461047i −0.555604 0.831447i \(-0.687513\pi\)
0.619062 + 0.785342i \(0.287513\pi\)
\(524\) −4.18673 −0.182898
\(525\) 0 0
\(526\) 33.6414 1.46684
\(527\) 5.93209 4.30991i 0.258406 0.187743i
\(528\) 0 0
\(529\) −7.00189 + 21.5496i −0.304430 + 0.936939i
\(530\) −10.6001 1.74528i −0.460439 0.0758100i
\(531\) 0 0
\(532\) 8.47561 0.367464
\(533\) −1.49697 4.60720i −0.0648410 0.199560i
\(534\) 0 0
\(535\) −5.82250 + 11.2569i −0.251729 + 0.486679i
\(536\) 9.06068 6.58297i 0.391362 0.284341i
\(537\) 0 0
\(538\) 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
\(543\) 0 0
\(544\) 4.01792 + 12.3659i 0.172267 + 0.530183i
\(545\) 2.72053 1.36533i 0.116535 0.0584842i
\(546\) 0 0
\(547\) 6.02174 18.5330i 0.257471 0.792414i −0.735862 0.677132i \(-0.763223\pi\)
0.993333 0.115283i \(-0.0367774\pi\)
\(548\) 11.2566 8.17841i 0.480859 0.349364i
\(549\) 0 0
\(550\) −48.1311 + 14.9917i −2.05232 + 0.639249i
\(551\) −9.22425 −0.392966
\(552\) 0 0
\(553\) −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 \(0.311650\pi\)
\(558\) 0 0
\(559\) −3.38841 2.46182i −0.143314 0.104124i
\(560\) −39.3335 + 19.7399i −1.66214 + 0.834165i
\(561\) 0 0
\(562\) 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 \(0.417824\pi\)
\(564\) 0 0
\(565\) −21.3554 + 10.7175i −0.898429 + 0.450887i
\(566\) −3.68770 2.67927i −0.155005 0.112618i
\(567\) 0 0
\(568\) −15.0449 −0.631271
\(569\) 11.2118 + 34.5065i 0.470025 + 1.44659i 0.852552 + 0.522643i \(0.175054\pi\)
−0.382527 + 0.923944i \(0.624946\pi\)
\(570\) 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
\(573\) 0 0
\(574\) 9.90337 0.413359
\(575\) 2.76726 + 0.936635i 0.115403 + 0.0390604i
\(576\) 0 0
\(577\) 5.56961 4.04656i 0.231866 0.168461i −0.465786 0.884898i \(-0.654228\pi\)
0.697652 + 0.716437i \(0.254228\pi\)
\(578\) −5.10190 + 15.7020i −0.212211 + 0.653118i
\(579\) 0 0
\(580\) −7.12701 + 3.57677i −0.295933 + 0.148517i
\(581\) 0.952256 + 2.93074i 0.0395062 + 0.121588i
\(582\) 0 0
\(583\) −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 \(0.798370\pi\)
\(588\) 0 0
\(589\) 5.16880 3.75536i 0.212977 0.154737i
\(590\) 8.22186 15.8957i 0.338489 0.654416i
\(591\) 0 0
\(592\) 0.0321670 + 0.0989998i 0.00132206 + 0.00406887i
\(593\) −5.82561 −0.239229 −0.119615 0.992820i \(-0.538166\pi\)
−0.119615 + 0.992820i \(0.538166\pi\)
\(594\) 0 0
\(595\) 23.5411 + 3.87597i 0.965091 + 0.158899i
\(596\) −4.15041 + 12.7737i −0.170008 + 0.523230i
\(597\) 0 0
\(598\) −2.65426 + 1.92844i −0.108541 + 0.0788596i
\(599\) 27.1527 1.10943 0.554715 0.832040i \(-0.312827\pi\)
0.554715 + 0.832040i \(0.312827\pi\)
\(600\) 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
\(603\) 0 0
\(604\) −4.91194 + 15.1174i −0.199864 + 0.615118i
\(605\) −37.5777 38.0393i −1.52775 1.54652i
\(606\) 0 0
\(607\) 1.46424 0.0594318 0.0297159 0.999558i \(-0.490540\pi\)
0.0297159 + 0.999558i \(0.490540\pi\)
\(608\) 3.50094 + 10.7748i 0.141982 + 0.436975i
\(609\) 0 0
\(610\) −14.9662 15.1500i −0.605963 0.613405i
\(611\) 14.4653 10.5096i 0.585202 0.425174i
\(612\) 0 0
\(613\) −28.0814 20.4023i −1.13420 0.824041i −0.147896 0.989003i \(-0.547250\pi\)
−0.986300 + 0.164962i \(0.947250\pi\)
\(614\) 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 \(-0.419504\pi\)
\(618\) 0 0
\(619\) −5.79758 17.8431i −0.233025 0.717176i −0.997377 0.0723776i \(-0.976941\pi\)
0.764353 0.644798i \(-0.223059\pi\)
\(620\) 2.53745 4.90577i 0.101906 0.197021i
\(621\) 0 0
\(622\) 15.4647 47.5954i 0.620077 1.90840i
\(623\) 11.0780 8.04863i 0.443830 0.322461i
\(624\) 0 0
\(625\) −8.30354 + 23.5807i −0.332142 + 0.943230i
\(626\) −29.8498 −1.19304
\(627\) 0 0
\(628\) 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 0
\(634\) 5.40820 + 3.92928i 0.214787 + 0.156052i
\(635\) −4.55459 29.9380i −0.180743 1.18806i
\(636\) 0 0
\(637\) −22.7425 16.5234i −0.901091 0.654681i
\(638\) −31.9068 23.1816i −1.26320 0.917769i
\(639\) 0 0
\(640\) −19.8900 20.1343i −0.786221 0.795877i
\(641\) −1.46647 1.06546i −0.0579223 0.0420830i 0.558447 0.829540i \(-0.311397\pi\)
−0.616370 + 0.787457i \(0.711397\pi\)
\(642\) 0 0
\(643\) 45.7391 1.80377 0.901886 0.431974i \(-0.142183\pi\)
0.901886 + 0.431974i \(0.142183\pi\)
\(644\) −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 \(-0.0684101\pi\)
\(648\) 0 0
\(649\) 27.7137 1.08786
\(650\) −16.2237 22.9131i −0.636348 0.898726i
\(651\) 0 0
\(652\) −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 0
\(655\) −10.1324 1.66827i −0.395906 0.0651848i
\(656\) 2.27103 + 6.98950i 0.0886687 + 0.272894i
\(657\) 0 0
\(658\) 11.2954 + 34.7638i 0.440342 + 1.35523i
\(659\) −25.9633 18.8635i −1.01139 0.734816i −0.0468880 0.998900i \(-0.514930\pi\)
−0.964500 + 0.264084i \(0.914930\pi\)
\(660\) 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
\(663\) 0 0
\(664\) −1.17435 + 0.853212i −0.0455734 + 0.0331110i
\(665\) 20.5121 + 3.37725i 0.795424 + 0.130964i
\(666\) 0 0
\(667\) 0.706281 + 2.17371i 0.0273473 + 0.0841663i
\(668\) 20.6065 0.797289
\(669\) 0 0
\(670\) −20.5660 + 10.3213i −0.794533 + 0.398745i
\(671\) 10.1908 31.3642i 0.393413 1.21080i
\(672\) 0 0
\(673\) −27.6367 + 20.0792i −1.06531 + 0.773997i −0.975064 0.221922i \(-0.928767\pi\)
−0.0902506 + 0.995919i \(0.528767\pi\)
\(674\) −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 \(0.243582\pi\)
\(678\) 0 0
\(679\) 2.99017 9.20281i 0.114752 0.353171i
\(680\) 1.69028 + 11.1105i 0.0648194 + 0.426068i
\(681\) 0 0
\(682\) 27.3166 1.04601
\(683\) −6.02604 18.5463i −0.230580 0.709653i −0.997677 0.0681215i \(-0.978299\pi\)
0.767097 0.641531i \(-0.221701\pi\)
\(684\) 0 0
\(685\) 30.5013 15.3074i 1.16539 0.584866i
\(686\) 8.39634 6.10030i 0.320574 0.232910i
\(687\) 0 0
\(688\) 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
\(693\) 0 0
\(694\) 0.543375 + 1.67234i 0.0206262 + 0.0634810i
\(695\) 6.13371 + 40.3179i 0.232665 + 1.52934i
\(696\) 0 0
\(697\) 1.23116 3.78914i 0.0466337 0.143524i
\(698\) −29.7666 + 21.6267i −1.12668 + 0.818583i
\(699\) 0 0
\(700\) 17.1580 5.34431i 0.648510 0.201996i
\(701\) 20.4085 0.770820 0.385410 0.922745i \(-0.374060\pi\)
0.385410 + 0.922745i \(0.374060\pi\)
\(702\) 0 0
\(703\) 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
\(708\) 0 0
\(709\) −13.3334 9.68727i −0.500746 0.363813i 0.308556 0.951206i \(-0.400154\pi\)
−0.809302 + 0.587393i \(0.800154\pi\)
\(710\) 30.5005 + 5.02182i 1.14466 + 0.188466i
\(711\) 0 0
\(712\) 5.21829 + 3.79131i 0.195564 + 0.142085i
\(713\) −1.28072 0.930497i −0.0479633 0.0348474i
\(714\) 0 0
\(715\) 19.9742 38.6171i 0.746992 1.44420i
\(716\) −4.74294 3.44595i −0.177252 0.128781i
\(717\) 0 0
\(718\) −46.3309 −1.72905
\(719\) −9.60466 29.5601i −0.358193 1.10241i −0.954135 0.299378i \(-0.903221\pi\)
0.595941 0.803028i \(-0.296779\pi\)
\(720\) 0 0
\(721\) −14.3186 + 44.0681i −0.533253 + 1.64118i
\(722\) −7.08642 + 21.8098i −0.263729 + 0.811675i
\(723\) 0 0
\(724\) 13.4080 0.498305
\(725\) −18.6735 + 5.81636i −0.693516 + 0.216014i
\(726\) 0 0
\(727\) 0.771033 0.560188i 0.0285960 0.0207762i −0.573395 0.819279i \(-0.694374\pi\)
0.601991 + 0.798503i \(0.294374\pi\)
\(728\) 7.44492 22.9131i 0.275927 0.849217i
\(729\) 0 0
\(730\) −35.7082 36.1467i −1.32162 1.33785i
\(731\) −1.06445 3.27603i −0.0393700 0.121168i
\(732\) 0 0
\(733\) −4.75118 14.6226i −0.175489 0.540099i 0.824167 0.566347i \(-0.191644\pi\)
−0.999655 + 0.0262485i \(0.991644\pi\)
\(734\) −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
\(738\) 0 0
\(739\) −4.20110 + 3.05228i −0.154540 + 0.112280i −0.662368 0.749179i \(-0.730449\pi\)
0.507828 + 0.861458i \(0.330449\pi\)
\(740\) −0.00639318 0.0420234i −0.000235018 0.00154481i
\(741\) 0 0
\(742\) 5.85301 + 18.0137i 0.214871 + 0.661305i
\(743\) 42.3399 1.55330 0.776650 0.629932i \(-0.216917\pi\)
0.776650 + 0.629932i \(0.216917\pi\)
\(744\) 0 0
\(745\) −15.1344 + 29.2601i −0.554482 + 1.07201i
\(746\) 3.36980 10.3712i 0.123377 0.379716i
\(747\) 0 0
\(748\) 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 0
\(754\) 6.78733 20.8892i 0.247180 0.760741i
\(755\) −17.9113 + 34.6288i −0.651860 + 1.26027i
\(756\) 0 0
\(757\) −9.27680 −0.337171 −0.168585 0.985687i \(-0.553920\pi\)
−0.168585 + 0.985687i \(0.553920\pi\)
\(758\) −0.0815549 0.251000i −0.00296221 0.00911674i
\(759\) 0 0
\(760\) 1.47279 + 9.68091i 0.0534238 + 0.351163i
\(761\) −14.0868 + 10.2346i −0.510644 + 0.371005i −0.813068 0.582169i \(-0.802204\pi\)
0.302424 + 0.953174i \(0.402204\pi\)
\(762\) 0 0
\(763\) −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
\(768\) 0 0
\(769\) −7.16648 22.0562i −0.258430 0.795365i −0.993134 0.116978i \(-0.962679\pi\)
0.734705 0.678387i \(-0.237321\pi\)
\(770\) 62.4640 + 63.2312i 2.25105 + 2.27869i
\(771\) 0 0
\(772\) 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 \(0.331582\pi\)
\(774\) 0 0
\(775\) 8.09574 10.8615i 0.290808 0.390157i
\(776\) 4.55807 0.163625
\(777\) 0 0
\(778\) 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
\(783\) 0 0
\(784\) 34.5023 + 25.0674i 1.23222 + 0.895263i
\(785\) 18.3994 35.5724i 0.656703 1.26963i
\(786\) 0 0
\(787\) −20.8703 15.1632i −0.743946 0.540509i 0.149998 0.988686i \(-0.452073\pi\)
−0.893944 + 0.448178i \(0.852073\pi\)
\(788\) −10.6091 7.70795i −0.377933 0.274584i
\(789\) 0 0
\(790\) 62.7406 + 10.3301i 2.23221 + 0.367527i
\(791\) 34.0819 + 24.7619i 1.21181 + 0.880433i
\(792\) 0 0
\(793\) 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 \(0.120930\pi\)
\(798\) 0 0
\(799\) 14.7052 0.520233
\(800\) 13.8813 + 19.6048i 0.490778 + 0.693136i
\(801\) 0 0
\(802\) −45.3261 + 32.9313i −1.60052 + 1.16285i
\(803\) 24.3146 74.8326i 0.858043 2.64079i
\(804\) 0 0
\(805\) −0.774709 5.09229i −0.0273049 0.179480i
\(806\) 4.70111 + 14.4685i 0.165589 + 0.509632i
\(807\) 0 0
\(808\) −3.94533 12.1425i −0.138796 0.427171i
\(809\) 30.3414 + 22.0443i 1.06675 + 0.775037i 0.975325 0.220776i \(-0.0708588\pi\)
0.0914219 + 0.995812i \(0.470859\pi\)
\(810\) 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
\(813\) 0 0
\(814\) 0.170081 0.123571i 0.00596135 0.00433117i
\(815\) −43.4872 + 21.8245i −1.52329 + 0.764480i
\(816\) 0 0
\(817\) −0.927484 2.85450i −0.0324486 0.0998664i
\(818\) −67.5317 −2.36119
\(819\) 0 0
\(820\) −0.451366 2.96690i −0.0157624 0.103609i
\(821\) −13.9216 + 42.8462i −0.485866 + 1.49534i 0.344857 + 0.938655i \(0.387927\pi\)
−0.830723 + 0.556686i \(0.812073\pi\)
\(822\) 0 0
\(823\) 33.5397 24.3680i 1.16912 0.849415i 0.178217 0.983991i \(-0.442967\pi\)
0.990903 + 0.134576i \(0.0429672\pi\)
\(824\) −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 0
\(829\) 7.45527 22.9450i 0.258932 0.796911i −0.734097 0.679044i \(-0.762394\pi\)
0.993029 0.117867i \(-0.0376056\pi\)
\(830\) 2.66554 1.33773i 0.0925221 0.0464333i
\(831\) 0 0
\(832\) 5.87864 0.203805
\(833\) −7.14441 21.9882i −0.247539 0.761847i
\(834\) 0 0
\(835\) 49.8703 + 8.21101i 1.72583 + 0.284154i
\(836\) 10.2768 7.46650i 0.355429 0.258234i
\(837\) 0 0
\(838\) 27.0014 + 19.6177i 0.932748 + 0.677681i
\(839\) −14.3890 + 10.4542i −0.496763 + 0.360919i −0.807779 0.589485i \(-0.799331\pi\)
0.311016 + 0.950405i \(0.399331\pi\)
\(840\) 0 0
\(841\) 11.0826 + 8.05197i 0.382158 + 0.277654i
\(842\) −21.2671 65.4534i −0.732913 2.25567i
\(843\) 0 0
\(844\) 0.838452 + 2.58049i 0.0288607 + 0.0888242i
\(845\) −4.79127 0.788869i −0.164825 0.0271379i
\(846\) 0 0
\(847\) −29.1322 + 89.6598i −1.00100 + 3.08075i
\(848\) −11.3713 + 8.26176i −0.390493 + 0.283710i
\(849\) 0 0
\(850\) 0.281854 23.0884i 0.00966750 0.791927i
\(851\) −0.0121834 −0.000417642
\(852\) 0 0
\(853\) 3.96878 12.2147i 0.135889 0.418222i −0.859839 0.510566i \(-0.829436\pi\)
0.995727 + 0.0923439i \(0.0294359\pi\)
\(854\) −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 \(0.414143\pi\)
\(858\) 0 0
\(859\) −3.90628 2.83808i −0.133281 0.0968340i 0.519147 0.854685i \(-0.326250\pi\)
−0.652428 + 0.757851i \(0.726250\pi\)
\(860\) −1.82346 1.84586i −0.0621796 0.0629433i
\(861\) 0 0
\(862\) 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 \(0.771878\pi\)
\(864\) 0 0
\(865\) −4.34235 28.5430i −0.147644 0.970490i
\(866\) 17.1529 + 12.4623i 0.582879 + 0.423486i
\(867\) 0 0
\(868\) −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
\(873\) 0 0
\(874\) −2.35111 −0.0795274
\(875\) 43.6540 6.09702i 1.47577 0.206117i
\(876\) 0 0
\(877\) −5.05840 + 3.67515i −0.170810 + 0.124101i −0.669906 0.742446i \(-0.733666\pi\)
0.499096 + 0.866547i \(0.333666\pi\)
\(878\) 5.78199 17.7951i 0.195133 0.600557i
\(879\) 0 0
\(880\) −30.3025 + 58.5852i −1.02150 + 1.97491i
\(881\) 5.18532 + 15.9588i 0.174698 + 0.537665i 0.999620 0.0275821i \(-0.00878076\pi\)
−0.824922 + 0.565247i \(0.808781\pi\)
\(882\) 0 0
\(883\) 5.01740 + 15.4420i 0.168849 + 0.519664i 0.999299 0.0374289i \(-0.0119168\pi\)
−0.830450 + 0.557093i \(0.811917\pi\)
\(884\) 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 0
\(889\) −43.1945 + 31.3827i −1.44870 + 1.05254i
\(890\) −9.31351 9.42790i −0.312190 0.316024i
\(891\) 0 0
\(892\) −0.0858359 0.264176i −0.00287400 0.00884526i
\(893\) 12.8131 0.428774
\(894\) 0 0
\(895\) −10.1054 10.2295i −0.337787 0.341936i
\(896\) −15.4198 + 47.4572i −0.515138 + 1.58543i
\(897\) 0 0
\(898\) −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
\(903\) 0 0
\(904\) −6.13219 + 18.8729i −0.203953 + 0.627704i
\(905\) 32.4491 + 5.34265i 1.07865 + 0.177596i
\(906\) 0 0
\(907\) 9.00465 0.298995 0.149497 0.988762i \(-0.452234\pi\)
0.149497 + 0.988762i \(0.452234\pi\)
\(908\) 2.69670 + 8.29960i 0.0894933 + 0.275432i
\(909\) 0 0
\(910\) −22.7412 + 43.9666i −0.753863 + 1.45748i
\(911\) 24.2303 17.6044i 0.802786 0.583258i −0.108944 0.994048i \(-0.534747\pi\)
0.911730 + 0.410789i \(0.134747\pi\)
\(912\) 0 0
\(913\) 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
\(918\) 0 0
\(919\) 2.76125 + 8.49826i 0.0910853 + 0.280332i 0.986214 0.165477i \(-0.0529162\pi\)
−0.895128 + 0.445808i \(0.852916\pi\)
\(920\) 2.16855 1.08831i 0.0714951 0.0358806i
\(921\) 0 0
\(922\) −6.34995 + 19.5431i −0.209125 + 0.643619i
\(923\) −21.5675 + 15.6697i −0.709902 + 0.515774i
\(924\) 0 0
\(925\) 0.00127263 0.104249i 4.18439e−5 0.00342770i
\(926\) −46.4133 −1.52524
\(927\) 0 0
\(928\) −5.80735 + 17.8732i −0.190636 + 0.586716i
\(929\) 12.8117 39.4304i 0.420339 1.29367i −0.487048 0.873375i \(-0.661926\pi\)
0.907387 0.420296i \(-0.138074\pi\)
\(930\) 0 0
\(931\) −6.22514 19.1590i −0.204021 0.627911i
\(932\) −18.3248 −0.600250
\(933\) 0 0
\(934\) −5.44243 3.95416i −0.178082 0.129384i
\(935\) 31.9583 16.0386i 1.04515 0.524519i
\(936\) 0 0
\(937\) −16.8749 12.2603i −0.551278 0.400527i 0.276978 0.960876i \(-0.410667\pi\)
−0.828256 + 0.560349i \(0.810667\pi\)
\(938\) 32.8220 + 23.8466i 1.07168 + 0.778618i
\(939\) 0 0
\(940\) 9.89989 4.96837i 0.322899 0.162050i
\(941\) 2.97219 + 2.15942i 0.0968905 + 0.0703951i 0.635176 0.772368i \(-0.280928\pi\)
−0.538285 + 0.842763i \(0.680928\pi\)
\(942\) 0 0
\(943\) −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 \(-0.0722270\pi\)
\(948\) 0 0
\(949\) 43.8204 1.42247
\(950\) 0.245588 20.1177i 0.00796791 0.652703i
\(951\) 0 0
\(952\) 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 \(0.963789\pi\)
\(954\) 0 0
\(955\) 13.4160 6.73299i 0.434133 0.217875i
\(956\) −4.97625 15.3153i −0.160943 0.495333i
\(957\) 0 0
\(958\) −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
\(963\) 0 0
\(964\) −21.7865 + 15.8288i −0.701697 + 0.509813i
\(965\) 4.95995 9.58931i 0.159666 0.308691i
\(966\) 0 0
\(967\) −8.96663 27.5965i −0.288347 0.887442i −0.985375 0.170398i \(-0.945495\pi\)
0.697028 0.717044i \(-0.254505\pi\)
\(968\) −44.4077 −1.42732
\(969\) 0 0
\(970\) −9.24056 1.52143i −0.296696 0.0488502i
\(971\) 1.16588 3.58821i 0.0374149 0.115151i −0.930605 0.366026i \(-0.880718\pi\)
0.968020 + 0.250875i \(0.0807182\pi\)
\(972\) 0 0
\(973\) 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 \(0.100177\pi\)
\(978\) 0 0
\(979\) 6.34180 19.5181i 0.202685 0.623800i
\(980\) −12.2388 12.3891i −0.390955 0.395757i
\(981\) 0 0
\(982\) 56.8104 1.81289
\(983\) −7.28128 22.4095i −0.232237 0.714752i −0.997476 0.0710055i \(-0.977379\pi\)
0.765239 0.643746i \(-0.222621\pi\)
\(984\) 0 0
\(985\) −22.6040 22.8816i −0.720223 0.729068i
\(986\) 14.6143 10.6179i 0.465413 0.338143i
\(987\) 0 0
\(988\) 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
\(993\) 0 0
\(994\) −16.8413 51.8323i −0.534175 1.64402i
\(995\) −8.96425 + 17.3310i −0.284186 + 0.549430i
\(996\) 0 0
\(997\) 13.5733 41.7742i 0.429870 1.32300i −0.468384 0.883525i \(-0.655164\pi\)
0.898254 0.439478i \(-0.144836\pi\)
\(998\) 56.7993 41.2671i 1.79795 1.30629i
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 225.2.h.c.136.1 8
3.2 odd 2 75.2.g.b.61.2 yes 8
15.2 even 4 375.2.i.b.199.3 16
15.8 even 4 375.2.i.b.199.2 16
15.14 odd 2 375.2.g.b.301.1 8
25.4 even 10 5625.2.a.n.1.1 4
25.16 even 5 inner 225.2.h.c.91.1 8
25.21 even 5 5625.2.a.i.1.4 4
75.29 odd 10 1875.2.a.e.1.4 4
75.38 even 20 375.2.i.b.49.3 16
75.41 odd 10 75.2.g.b.16.2 8
75.47 even 20 1875.2.b.c.1249.3 8
75.53 even 20 1875.2.b.c.1249.6 8
75.59 odd 10 375.2.g.b.76.1 8
75.62 even 20 375.2.i.b.49.2 16
75.71 odd 10 1875.2.a.h.1.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.2.g.b.16.2 8 75.41 odd 10
75.2.g.b.61.2 yes 8 3.2 odd 2
225.2.h.c.91.1 8 25.16 even 5 inner
225.2.h.c.136.1 8 1.1 even 1 trivial
375.2.g.b.76.1 8 75.59 odd 10
375.2.g.b.301.1 8 15.14 odd 2
375.2.i.b.49.2 16 75.62 even 20
375.2.i.b.49.3 16 75.38 even 20
375.2.i.b.199.2 16 15.8 even 4
375.2.i.b.199.3 16 15.2 even 4
1875.2.a.e.1.4 4 75.29 odd 10
1875.2.a.h.1.1 4 75.71 odd 10
1875.2.b.c.1249.3 8 75.47 even 20
1875.2.b.c.1249.6 8 75.53 even 20
5625.2.a.i.1.4 4 25.21 even 5
5625.2.a.n.1.1 4 25.4 even 10