Properties

Label 575.2.k.a.26.1
Level $575$
Weight $2$
Character 575.26
Analytic conductor $4.591$
Analytic rank $0$
Dimension $10$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [575,2,Mod(26,575)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(575, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 16]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("575.26");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 575 = 5^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 575.k (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.59139811622\)
Analytic rank: \(0\)
Dimension: \(10\)
Coefficient field: \(\Q(\zeta_{22})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 115)
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 26.1
Root \(-0.415415 - 0.909632i\) of defining polynomial
Character \(\chi\) \(=\) 575.26
Dual form 575.2.k.a.376.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0125459 + 0.0872586i) q^{2} +(0.415415 - 0.909632i) q^{3} +(1.91153 - 0.561276i) q^{4} +(0.0845850 + 0.0248364i) q^{6} +(1.30075 - 0.835939i) q^{7} +(0.146201 + 0.320135i) q^{8} +(1.30972 + 1.51150i) q^{9} +(0.289532 - 2.01374i) q^{11} +(0.283524 - 1.97195i) q^{12} +(-1.80075 - 1.15727i) q^{13} +(0.0892619 + 0.103014i) q^{14} +(3.32584 - 2.13739i) q^{16} +(4.18251 + 1.22809i) q^{17} +(-0.115460 + 0.133248i) q^{18} +(-7.12381 + 2.09174i) q^{19} +(-0.220047 - 1.53046i) q^{21} +0.179348 q^{22} +(2.79310 + 3.89854i) q^{23} +0.351939 q^{24} +(0.0783898 - 0.171650i) q^{26} +(4.79746 - 1.40866i) q^{27} +(2.01722 - 2.32800i) q^{28} +(-4.30111 - 1.26292i) q^{29} +(-0.376329 - 0.824045i) q^{31} +(0.689173 + 0.795348i) q^{32} +(-1.71148 - 1.09990i) q^{33} +(-0.0546886 + 0.380367i) q^{34} +(3.35194 + 2.15416i) q^{36} +(-7.26571 - 8.38507i) q^{37} +(-0.271897 - 0.595371i) q^{38} +(-1.80075 + 1.15727i) q^{39} +(3.95750 - 4.56720i) q^{41} +(0.130785 - 0.0384020i) q^{42} +(-2.24116 + 4.90745i) q^{43} +(-0.576814 - 4.01183i) q^{44} +(-0.305139 + 0.292633i) q^{46} +2.72825 q^{47} +(-0.562632 - 3.91319i) q^{48} +(-1.91476 + 4.19273i) q^{49} +(2.85459 - 3.29437i) q^{51} +(-4.09173 - 1.20144i) q^{52} +(0.230732 - 0.148283i) q^{53} +(0.183106 + 0.400947i) q^{54} +(0.457783 + 0.294199i) q^{56} +(-1.05662 + 7.34898i) q^{57} +(0.0562393 - 0.391153i) q^{58} +(6.74757 + 4.33640i) q^{59} +(-1.33718 - 2.92802i) q^{61} +(0.0671837 - 0.0431763i) q^{62} +(2.96714 + 0.871230i) q^{63} +(5.11714 - 5.90549i) q^{64} +(0.0745040 - 0.163141i) q^{66} +(-0.279610 - 1.94473i) q^{67} +8.68428 q^{68} +(4.70653 - 0.921186i) q^{69} +(1.58700 + 11.0378i) q^{71} +(-0.292401 + 0.640269i) q^{72} +(-9.95039 + 2.92170i) q^{73} +(0.640515 - 0.739194i) q^{74} +(-12.4433 + 7.99684i) q^{76} +(-1.30675 - 2.86139i) q^{77} +(-0.123574 - 0.142612i) q^{78} +(2.70849 + 1.74064i) q^{79} +(-0.142315 + 0.989821i) q^{81} +(0.448178 + 0.288027i) q^{82} +(-2.85563 - 3.29557i) q^{83} +(-1.27964 - 2.80202i) q^{84} +(-0.456334 - 0.133992i) q^{86} +(-2.93553 + 3.38779i) q^{87} +(0.686997 - 0.201720i) q^{88} +(0.266861 - 0.584343i) q^{89} -3.30972 q^{91} +(7.52725 + 5.88446i) q^{92} -0.905910 q^{93} +(0.0342284 + 0.238063i) q^{94} +(1.00977 - 0.296494i) q^{96} +(-3.62848 + 4.18748i) q^{97} +(-0.389875 - 0.114478i) q^{98} +(3.42297 - 2.19981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 5 q^{2} - q^{3} - q^{4} + 6 q^{6} - 5 q^{7} + 16 q^{8} + 2 q^{9} + 8 q^{11} - q^{12} - 3 q^{14} + 5 q^{16} + 23 q^{17} + 10 q^{18} - 13 q^{19} + 6 q^{21} - 4 q^{22} + 21 q^{23} - 6 q^{24} + 11 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).

\(n\) \(51\) \(277\)
\(\chi(n)\) \(e\left(\frac{8}{11}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0125459 + 0.0872586i 0.00887129 + 0.0617012i 0.993776 0.111395i \(-0.0355319\pi\)
−0.984905 + 0.173096i \(0.944623\pi\)
\(3\) 0.415415 0.909632i 0.239840 0.525176i −0.750986 0.660318i \(-0.770422\pi\)
0.990826 + 0.135141i \(0.0431489\pi\)
\(4\) 1.91153 0.561276i 0.955765 0.280638i
\(5\) 0 0
\(6\) 0.0845850 + 0.0248364i 0.0345317 + 0.0101394i
\(7\) 1.30075 0.835939i 0.491636 0.315955i −0.271227 0.962515i \(-0.587429\pi\)
0.762863 + 0.646560i \(0.223793\pi\)
\(8\) 0.146201 + 0.320135i 0.0516897 + 0.113185i
\(9\) 1.30972 + 1.51150i 0.436574 + 0.503833i
\(10\) 0 0
\(11\) 0.289532 2.01374i 0.0872971 0.607165i −0.898468 0.439038i \(-0.855319\pi\)
0.985765 0.168126i \(-0.0537717\pi\)
\(12\) 0.283524 1.97195i 0.0818462 0.569253i
\(13\) −1.80075 1.15727i −0.499437 0.320969i 0.266554 0.963820i \(-0.414115\pi\)
−0.765991 + 0.642851i \(0.777751\pi\)
\(14\) 0.0892619 + 0.103014i 0.0238563 + 0.0275316i
\(15\) 0 0
\(16\) 3.32584 2.13739i 0.831460 0.534347i
\(17\) 4.18251 + 1.22809i 1.01441 + 0.297857i 0.746355 0.665548i \(-0.231802\pi\)
0.268052 + 0.963405i \(0.413620\pi\)
\(18\) −0.115460 + 0.133248i −0.0272141 + 0.0314068i
\(19\) −7.12381 + 2.09174i −1.63431 + 0.479878i −0.964814 0.262935i \(-0.915310\pi\)
−0.669499 + 0.742813i \(0.733491\pi\)
\(20\) 0 0
\(21\) −0.220047 1.53046i −0.0480182 0.333974i
\(22\) 0.179348 0.0382372
\(23\) 2.79310 + 3.89854i 0.582402 + 0.812901i
\(24\) 0.351939 0.0718392
\(25\) 0 0
\(26\) 0.0783898 0.171650i 0.0153735 0.0336633i
\(27\) 4.79746 1.40866i 0.923273 0.271097i
\(28\) 2.01722 2.32800i 0.381219 0.439951i
\(29\) −4.30111 1.26292i −0.798695 0.234518i −0.143177 0.989697i \(-0.545732\pi\)
−0.655519 + 0.755179i \(0.727550\pi\)
\(30\) 0 0
\(31\) −0.376329 0.824045i −0.0675906 0.148003i 0.872822 0.488039i \(-0.162288\pi\)
−0.940412 + 0.340037i \(0.889561\pi\)
\(32\) 0.689173 + 0.795348i 0.121830 + 0.140599i
\(33\) −1.71148 1.09990i −0.297931 0.191469i
\(34\) −0.0546886 + 0.380367i −0.00937901 + 0.0652325i
\(35\) 0 0
\(36\) 3.35194 + 2.15416i 0.558656 + 0.359027i
\(37\) −7.26571 8.38507i −1.19447 1.37850i −0.907227 0.420641i \(-0.861805\pi\)
−0.287248 0.957856i \(-0.592740\pi\)
\(38\) −0.271897 0.595371i −0.0441075 0.0965819i
\(39\) −1.80075 + 1.15727i −0.288350 + 0.185311i
\(40\) 0 0
\(41\) 3.95750 4.56720i 0.618058 0.713277i −0.357279 0.933998i \(-0.616295\pi\)
0.975337 + 0.220720i \(0.0708408\pi\)
\(42\) 0.130785 0.0384020i 0.0201806 0.00592556i
\(43\) −2.24116 + 4.90745i −0.341773 + 0.748379i −0.999990 0.00444961i \(-0.998584\pi\)
0.658217 + 0.752828i \(0.271311\pi\)
\(44\) −0.576814 4.01183i −0.0869579 0.604806i
\(45\) 0 0
\(46\) −0.305139 + 0.292633i −0.0449903 + 0.0431464i
\(47\) 2.72825 0.397956 0.198978 0.980004i \(-0.436238\pi\)
0.198978 + 0.980004i \(0.436238\pi\)
\(48\) −0.562632 3.91319i −0.0812089 0.564821i
\(49\) −1.91476 + 4.19273i −0.273537 + 0.598962i
\(50\) 0 0
\(51\) 2.85459 3.29437i 0.399723 0.461305i
\(52\) −4.09173 1.20144i −0.567420 0.166610i
\(53\) 0.230732 0.148283i 0.0316935 0.0203682i −0.524698 0.851288i \(-0.675822\pi\)
0.556392 + 0.830920i \(0.312185\pi\)
\(54\) 0.183106 + 0.400947i 0.0249176 + 0.0545620i
\(55\) 0 0
\(56\) 0.457783 + 0.294199i 0.0611738 + 0.0393140i
\(57\) −1.05662 + 7.34898i −0.139953 + 0.973396i
\(58\) 0.0562393 0.391153i 0.00738458 0.0513609i
\(59\) 6.74757 + 4.33640i 0.878458 + 0.564551i 0.900329 0.435210i \(-0.143326\pi\)
−0.0218707 + 0.999761i \(0.506962\pi\)
\(60\) 0 0
\(61\) −1.33718 2.92802i −0.171208 0.374894i 0.804505 0.593946i \(-0.202431\pi\)
−0.975713 + 0.219052i \(0.929704\pi\)
\(62\) 0.0671837 0.0431763i 0.00853233 0.00548340i
\(63\) 2.96714 + 0.871230i 0.373824 + 0.109765i
\(64\) 5.11714 5.90549i 0.639642 0.738187i
\(65\) 0 0
\(66\) 0.0745040 0.163141i 0.00917081 0.0200813i
\(67\) −0.279610 1.94473i −0.0341598 0.237587i 0.965587 0.260080i \(-0.0837488\pi\)
−0.999747 + 0.0224928i \(0.992840\pi\)
\(68\) 8.68428 1.05312
\(69\) 4.70653 0.921186i 0.566600 0.110898i
\(70\) 0 0
\(71\) 1.58700 + 11.0378i 0.188342 + 1.30995i 0.836301 + 0.548271i \(0.184714\pi\)
−0.647959 + 0.761675i \(0.724377\pi\)
\(72\) −0.292401 + 0.640269i −0.0344598 + 0.0754564i
\(73\) −9.95039 + 2.92170i −1.16461 + 0.341959i −0.806221 0.591615i \(-0.798491\pi\)
−0.358385 + 0.933574i \(0.616672\pi\)
\(74\) 0.640515 0.739194i 0.0744584 0.0859295i
\(75\) 0 0
\(76\) −12.4433 + 7.99684i −1.42735 + 0.917300i
\(77\) −1.30675 2.86139i −0.148919 0.326086i
\(78\) −0.123574 0.142612i −0.0139920 0.0161476i
\(79\) 2.70849 + 1.74064i 0.304729 + 0.195837i 0.684064 0.729422i \(-0.260211\pi\)
−0.379335 + 0.925259i \(0.623847\pi\)
\(80\) 0 0
\(81\) −0.142315 + 0.989821i −0.0158128 + 0.109980i
\(82\) 0.448178 + 0.288027i 0.0494930 + 0.0318072i
\(83\) −2.85563 3.29557i −0.313446 0.361736i 0.577065 0.816698i \(-0.304198\pi\)
−0.890510 + 0.454963i \(0.849653\pi\)
\(84\) −1.27964 2.80202i −0.139620 0.305725i
\(85\) 0 0
\(86\) −0.456334 0.133992i −0.0492078 0.0144487i
\(87\) −2.93553 + 3.38779i −0.314722 + 0.363209i
\(88\) 0.686997 0.201720i 0.0732341 0.0215035i
\(89\) 0.266861 0.584343i 0.0282872 0.0619403i −0.894961 0.446144i \(-0.852797\pi\)
0.923248 + 0.384204i \(0.125524\pi\)
\(90\) 0 0
\(91\) −3.30972 −0.346953
\(92\) 7.52725 + 5.88446i 0.784770 + 0.613498i
\(93\) −0.905910 −0.0939385
\(94\) 0.0342284 + 0.238063i 0.00353038 + 0.0245544i
\(95\) 0 0
\(96\) 1.00977 0.296494i 0.103059 0.0302608i
\(97\) −3.62848 + 4.18748i −0.368416 + 0.425175i −0.909442 0.415831i \(-0.863491\pi\)
0.541026 + 0.841006i \(0.318036\pi\)
\(98\) −0.389875 0.114478i −0.0393833 0.0115640i
\(99\) 3.42297 2.19981i 0.344021 0.221089i
\(100\) 0 0
\(101\) −2.94535 3.39912i −0.293073 0.338225i 0.590049 0.807367i \(-0.299108\pi\)
−0.883122 + 0.469143i \(0.844563\pi\)
\(102\) 0.323276 + 0.207757i 0.0320091 + 0.0205710i
\(103\) 1.38513 9.63380i 0.136481 0.949247i −0.800367 0.599510i \(-0.795362\pi\)
0.936848 0.349737i \(-0.113729\pi\)
\(104\) 0.107212 0.745675i 0.0105130 0.0731194i
\(105\) 0 0
\(106\) 0.0158337 + 0.0182730i 0.00153790 + 0.00177483i
\(107\) 3.07272 + 6.72833i 0.297051 + 0.650452i 0.998031 0.0627299i \(-0.0199807\pi\)
−0.700979 + 0.713182i \(0.747253\pi\)
\(108\) 8.37985 5.38540i 0.806351 0.518210i
\(109\) −9.99029 2.93341i −0.956897 0.280970i −0.234241 0.972179i \(-0.575260\pi\)
−0.722656 + 0.691208i \(0.757079\pi\)
\(110\) 0 0
\(111\) −10.6456 + 3.12583i −1.01044 + 0.296691i
\(112\) 2.53935 5.56040i 0.239946 0.525408i
\(113\) 2.78825 + 19.3927i 0.262297 + 1.82431i 0.515486 + 0.856898i \(0.327611\pi\)
−0.253189 + 0.967417i \(0.581480\pi\)
\(114\) −0.654518 −0.0613012
\(115\) 0 0
\(116\) −8.93053 −0.829179
\(117\) −0.609264 4.23753i −0.0563265 0.391760i
\(118\) −0.293734 + 0.643187i −0.0270404 + 0.0592102i
\(119\) 6.46699 1.89888i 0.592828 0.174070i
\(120\) 0 0
\(121\) 6.58311 + 1.93298i 0.598465 + 0.175725i
\(122\) 0.238719 0.153415i 0.0216126 0.0138896i
\(123\) −2.51047 5.49716i −0.226361 0.495662i
\(124\) −1.18188 1.36396i −0.106136 0.122487i
\(125\) 0 0
\(126\) −0.0387969 + 0.269839i −0.00345631 + 0.0240391i
\(127\) −2.49696 + 17.3667i −0.221569 + 1.54105i 0.510536 + 0.859856i \(0.329447\pi\)
−0.732105 + 0.681192i \(0.761462\pi\)
\(128\) 2.35017 + 1.51036i 0.207727 + 0.133498i
\(129\) 3.53296 + 4.07725i 0.311060 + 0.358982i
\(130\) 0 0
\(131\) −10.9767 + 7.05427i −0.959035 + 0.616334i −0.923731 0.383043i \(-0.874876\pi\)
−0.0353039 + 0.999377i \(0.511240\pi\)
\(132\) −3.88890 1.14188i −0.338486 0.0993883i
\(133\) −7.51770 + 8.67589i −0.651867 + 0.752295i
\(134\) 0.166187 0.0487968i 0.0143563 0.00421540i
\(135\) 0 0
\(136\) 0.218329 + 1.51851i 0.0187216 + 0.130211i
\(137\) −21.5268 −1.83916 −0.919580 0.392903i \(-0.871471\pi\)
−0.919580 + 0.392903i \(0.871471\pi\)
\(138\) 0.139429 + 0.399128i 0.0118690 + 0.0339760i
\(139\) −16.3719 −1.38864 −0.694322 0.719665i \(-0.744295\pi\)
−0.694322 + 0.719665i \(0.744295\pi\)
\(140\) 0 0
\(141\) 1.13336 2.48170i 0.0954458 0.208997i
\(142\) −0.943233 + 0.276958i −0.0791544 + 0.0232418i
\(143\) −2.85181 + 3.29117i −0.238480 + 0.275221i
\(144\) 7.58658 + 2.22762i 0.632215 + 0.185635i
\(145\) 0 0
\(146\) −0.379780 0.831602i −0.0314308 0.0688239i
\(147\) 3.01843 + 3.48345i 0.248956 + 0.287310i
\(148\) −18.5950 11.9502i −1.52850 0.982304i
\(149\) −2.74972 + 19.1247i −0.225266 + 1.56676i 0.492399 + 0.870370i \(0.336120\pi\)
−0.717665 + 0.696389i \(0.754789\pi\)
\(150\) 0 0
\(151\) 16.8366 + 10.8202i 1.37015 + 0.880539i 0.998849 0.0479750i \(-0.0152768\pi\)
0.371297 + 0.928514i \(0.378913\pi\)
\(152\) −1.71114 1.97476i −0.138792 0.160174i
\(153\) 3.62165 + 7.93032i 0.292793 + 0.641128i
\(154\) 0.233287 0.149924i 0.0187988 0.0120812i
\(155\) 0 0
\(156\) −2.79263 + 3.22287i −0.223590 + 0.258036i
\(157\) 5.54048 1.62683i 0.442179 0.129835i −0.0530620 0.998591i \(-0.516898\pi\)
0.495241 + 0.868756i \(0.335080\pi\)
\(158\) −0.117905 + 0.258177i −0.00938006 + 0.0205395i
\(159\) −0.0390330 0.271480i −0.00309552 0.0215298i
\(160\) 0 0
\(161\) 6.89206 + 2.73614i 0.543170 + 0.215638i
\(162\) −0.0881559 −0.00692618
\(163\) 1.25289 + 8.71401i 0.0981335 + 0.682534i 0.978197 + 0.207678i \(0.0665906\pi\)
−0.880064 + 0.474856i \(0.842500\pi\)
\(164\) 5.00143 10.9516i 0.390546 0.855176i
\(165\) 0 0
\(166\) 0.251740 0.290524i 0.0195388 0.0225490i
\(167\) −18.7367 5.50159i −1.44989 0.425726i −0.540384 0.841418i \(-0.681721\pi\)
−0.909505 + 0.415692i \(0.863539\pi\)
\(168\) 0.457783 0.294199i 0.0353187 0.0226980i
\(169\) −3.49698 7.65732i −0.268998 0.589024i
\(170\) 0 0
\(171\) −12.4919 8.02803i −0.955276 0.613919i
\(172\) −1.52960 + 10.6386i −0.116631 + 0.811188i
\(173\) 3.07149 21.3627i 0.233521 1.62417i −0.449155 0.893454i \(-0.648275\pi\)
0.682676 0.730721i \(-0.260816\pi\)
\(174\) −0.332443 0.213648i −0.0252024 0.0161966i
\(175\) 0 0
\(176\) −3.34120 7.31621i −0.251852 0.551480i
\(177\) 6.74757 4.33640i 0.507178 0.325944i
\(178\) 0.0543370 + 0.0159548i 0.00407273 + 0.00119586i
\(179\) 10.0553 11.6044i 0.751567 0.867354i −0.243152 0.969988i \(-0.578182\pi\)
0.994719 + 0.102634i \(0.0327270\pi\)
\(180\) 0 0
\(181\) 0.340209 0.744955i 0.0252876 0.0553720i −0.896567 0.442909i \(-0.853947\pi\)
0.921854 + 0.387537i \(0.126674\pi\)
\(182\) −0.0415234 0.288802i −0.00307792 0.0214074i
\(183\) −3.21890 −0.237948
\(184\) −0.839703 + 1.46414i −0.0619037 + 0.107938i
\(185\) 0 0
\(186\) −0.0113655 0.0790485i −0.000833356 0.00579612i
\(187\) 3.68403 8.06690i 0.269403 0.589910i
\(188\) 5.21513 1.53130i 0.380353 0.111682i
\(189\) 5.06273 5.84270i 0.368259 0.424994i
\(190\) 0 0
\(191\) −3.58868 + 2.30630i −0.259668 + 0.166878i −0.663997 0.747735i \(-0.731141\pi\)
0.404329 + 0.914613i \(0.367505\pi\)
\(192\) −3.24609 7.10794i −0.234266 0.512972i
\(193\) 3.16580 + 3.65352i 0.227879 + 0.262986i 0.858162 0.513379i \(-0.171607\pi\)
−0.630283 + 0.776366i \(0.717061\pi\)
\(194\) −0.410917 0.264080i −0.0295021 0.0189598i
\(195\) 0 0
\(196\) −1.30684 + 9.08924i −0.0933454 + 0.649232i
\(197\) 0.220925 + 0.141980i 0.0157403 + 0.0101157i 0.548487 0.836159i \(-0.315204\pi\)
−0.532747 + 0.846275i \(0.678840\pi\)
\(198\) 0.234896 + 0.271085i 0.0166934 + 0.0192652i
\(199\) −1.79719 3.93530i −0.127399 0.278966i 0.835175 0.549985i \(-0.185367\pi\)
−0.962574 + 0.271019i \(0.912639\pi\)
\(200\) 0 0
\(201\) −1.88514 0.553528i −0.132968 0.0390429i
\(202\) 0.259650 0.299652i 0.0182689 0.0210835i
\(203\) −6.65037 + 1.95273i −0.466765 + 0.137054i
\(204\) 3.60758 7.89950i 0.252581 0.553076i
\(205\) 0 0
\(206\) 0.858010 0.0597804
\(207\) −2.23445 + 9.32777i −0.155305 + 0.648325i
\(208\) −8.46252 −0.586770
\(209\) 2.14964 + 14.9511i 0.148694 + 1.03419i
\(210\) 0 0
\(211\) 6.30147 1.85028i 0.433811 0.127378i −0.0575338 0.998344i \(-0.518324\pi\)
0.491345 + 0.870965i \(0.336506\pi\)
\(212\) 0.357824 0.412951i 0.0245755 0.0283616i
\(213\) 10.6996 + 3.14169i 0.733125 + 0.215265i
\(214\) −0.548554 + 0.352535i −0.0374984 + 0.0240988i
\(215\) 0 0
\(216\) 1.15235 + 1.32989i 0.0784077 + 0.0904874i
\(217\) −1.17836 0.757286i −0.0799923 0.0514079i
\(218\) 0.130629 0.908542i 0.00884728 0.0615342i
\(219\) −1.47587 + 10.2649i −0.0997301 + 0.693638i
\(220\) 0 0
\(221\) −6.11040 7.05178i −0.411030 0.474354i
\(222\) −0.406315 0.889705i −0.0272701 0.0597131i
\(223\) 7.74566 4.97783i 0.518688 0.333340i −0.254965 0.966950i \(-0.582064\pi\)
0.773653 + 0.633610i \(0.218428\pi\)
\(224\) 1.56130 + 0.458439i 0.104319 + 0.0306308i
\(225\) 0 0
\(226\) −1.65720 + 0.486598i −0.110235 + 0.0323680i
\(227\) 3.68538 8.06985i 0.244607 0.535615i −0.747012 0.664810i \(-0.768512\pi\)
0.991619 + 0.129196i \(0.0412396\pi\)
\(228\) 2.10504 + 14.6408i 0.139409 + 0.969614i
\(229\) −8.38484 −0.554086 −0.277043 0.960858i \(-0.589354\pi\)
−0.277043 + 0.960858i \(0.589354\pi\)
\(230\) 0 0
\(231\) −3.14566 −0.206969
\(232\) −0.224520 1.56157i −0.0147405 0.102522i
\(233\) 9.97561 21.8435i 0.653524 1.43102i −0.234911 0.972017i \(-0.575480\pi\)
0.888435 0.459002i \(-0.151793\pi\)
\(234\) 0.362117 0.106327i 0.0236723 0.00695082i
\(235\) 0 0
\(236\) 15.3321 + 4.50191i 0.998034 + 0.293049i
\(237\) 2.70849 1.74064i 0.175935 0.113067i
\(238\) 0.246828 + 0.540478i 0.0159995 + 0.0350340i
\(239\) 7.35914 + 8.49290i 0.476023 + 0.549360i 0.942077 0.335396i \(-0.108870\pi\)
−0.466054 + 0.884756i \(0.654325\pi\)
\(240\) 0 0
\(241\) 4.00004 27.8209i 0.257665 1.79210i −0.291689 0.956513i \(-0.594217\pi\)
0.549355 0.835589i \(-0.314874\pi\)
\(242\) −0.0860778 + 0.598684i −0.00553329 + 0.0384849i
\(243\) 13.4601 + 8.65025i 0.863463 + 0.554914i
\(244\) −4.19948 4.84646i −0.268844 0.310263i
\(245\) 0 0
\(246\) 0.448178 0.288027i 0.0285748 0.0183639i
\(247\) 15.2489 + 4.47747i 0.970262 + 0.284895i
\(248\) 0.208786 0.240952i 0.0132579 0.0153004i
\(249\) −4.18403 + 1.22854i −0.265152 + 0.0778556i
\(250\) 0 0
\(251\) 3.91272 + 27.2135i 0.246969 + 1.71770i 0.615541 + 0.788105i \(0.288938\pi\)
−0.368572 + 0.929599i \(0.620153\pi\)
\(252\) 6.16077 0.388092
\(253\) 8.65932 4.49583i 0.544407 0.282650i
\(254\) −1.54672 −0.0970501
\(255\) 0 0
\(256\) 6.38987 13.9919i 0.399367 0.874492i
\(257\) 17.0432 5.00435i 1.06313 0.312163i 0.297018 0.954872i \(-0.404008\pi\)
0.766110 + 0.642709i \(0.222190\pi\)
\(258\) −0.311451 + 0.359434i −0.0193901 + 0.0223774i
\(259\) −16.4603 4.83317i −1.02279 0.300318i
\(260\) 0 0
\(261\) −3.72435 8.15519i −0.230531 0.504794i
\(262\) −0.753257 0.869305i −0.0465364 0.0537059i
\(263\) 7.35320 + 4.72561i 0.453417 + 0.291394i 0.747348 0.664433i \(-0.231327\pi\)
−0.293930 + 0.955827i \(0.594963\pi\)
\(264\) 0.101897 0.708712i 0.00627135 0.0436182i
\(265\) 0 0
\(266\) −0.851362 0.547137i −0.0522004 0.0335471i
\(267\) −0.420680 0.485490i −0.0257452 0.0297115i
\(268\) −1.62601 3.56047i −0.0993246 0.217491i
\(269\) 2.46553 1.58450i 0.150326 0.0966086i −0.463316 0.886193i \(-0.653340\pi\)
0.613642 + 0.789585i \(0.289704\pi\)
\(270\) 0 0
\(271\) 4.29616 4.95803i 0.260973 0.301179i −0.610108 0.792318i \(-0.708874\pi\)
0.871081 + 0.491139i \(0.163419\pi\)
\(272\) 16.5353 4.85519i 1.00260 0.294389i
\(273\) −1.37491 + 3.01063i −0.0832132 + 0.182212i
\(274\) −0.270073 1.87840i −0.0163157 0.113478i
\(275\) 0 0
\(276\) 8.47963 4.40253i 0.510414 0.265001i
\(277\) 22.7888 1.36924 0.684622 0.728898i \(-0.259967\pi\)
0.684622 + 0.728898i \(0.259967\pi\)
\(278\) −0.205400 1.42859i −0.0123191 0.0856809i
\(279\) 0.752658 1.64809i 0.0450604 0.0986686i
\(280\) 0 0
\(281\) 9.32744 10.7644i 0.556429 0.642153i −0.405940 0.913900i \(-0.633056\pi\)
0.962369 + 0.271747i \(0.0876013\pi\)
\(282\) 0.230769 + 0.0677599i 0.0137421 + 0.00403504i
\(283\) −19.9441 + 12.8173i −1.18555 + 0.761910i −0.976399 0.215973i \(-0.930708\pi\)
−0.209155 + 0.977882i \(0.567071\pi\)
\(284\) 9.22884 + 20.2083i 0.547631 + 1.19914i
\(285\) 0 0
\(286\) −0.322961 0.207554i −0.0190971 0.0122730i
\(287\) 1.32981 9.24901i 0.0784960 0.545952i
\(288\) −0.299543 + 2.08337i −0.0176507 + 0.122764i
\(289\) 1.68384 + 1.08214i 0.0990493 + 0.0636551i
\(290\) 0 0
\(291\) 2.30175 + 5.04012i 0.134931 + 0.295457i
\(292\) −17.3806 + 11.1698i −1.01712 + 0.653664i
\(293\) −4.10110 1.20419i −0.239589 0.0703497i 0.159734 0.987160i \(-0.448936\pi\)
−0.399323 + 0.916810i \(0.630755\pi\)
\(294\) −0.266092 + 0.307087i −0.0155188 + 0.0179097i
\(295\) 0 0
\(296\) 1.62210 3.55191i 0.0942827 0.206450i
\(297\) −1.44766 10.0687i −0.0840017 0.584245i
\(298\) −1.70330 −0.0986692
\(299\) −0.518014 10.2526i −0.0299575 0.592926i
\(300\) 0 0
\(301\) 1.18715 + 8.25681i 0.0684262 + 0.475915i
\(302\) −0.732929 + 1.60489i −0.0421753 + 0.0923511i
\(303\) −4.31549 + 1.26714i −0.247918 + 0.0727954i
\(304\) −19.2218 + 22.1831i −1.10244 + 1.27229i
\(305\) 0 0
\(306\) −0.646552 + 0.415514i −0.0369609 + 0.0237533i
\(307\) 3.71586 + 8.13661i 0.212076 + 0.464381i 0.985536 0.169463i \(-0.0542034\pi\)
−0.773461 + 0.633844i \(0.781476\pi\)
\(308\) −4.10393 4.73619i −0.233843 0.269869i
\(309\) −8.18781 5.26199i −0.465788 0.299344i
\(310\) 0 0
\(311\) 3.32224 23.1067i 0.188387 1.31026i −0.647798 0.761812i \(-0.724310\pi\)
0.836185 0.548447i \(-0.184781\pi\)
\(312\) −0.633752 0.407288i −0.0358792 0.0230581i
\(313\) −14.7416 17.0127i −0.833244 0.961615i 0.166457 0.986049i \(-0.446767\pi\)
−0.999701 + 0.0244337i \(0.992222\pi\)
\(314\) 0.211465 + 0.463045i 0.0119337 + 0.0261311i
\(315\) 0 0
\(316\) 6.15434 + 1.80708i 0.346209 + 0.101656i
\(317\) 8.34970 9.63606i 0.468966 0.541215i −0.471158 0.882049i \(-0.656164\pi\)
0.940124 + 0.340834i \(0.110709\pi\)
\(318\) 0.0231993 0.00681193i 0.00130095 0.000381994i
\(319\) −3.78849 + 8.29564i −0.212115 + 0.464467i
\(320\) 0 0
\(321\) 7.39676 0.412847
\(322\) −0.152285 + 0.635719i −0.00848651 + 0.0354272i
\(323\) −32.3642 −1.80079
\(324\) 0.283524 + 1.97195i 0.0157513 + 0.109553i
\(325\) 0 0
\(326\) −0.744654 + 0.218650i −0.0412426 + 0.0121099i
\(327\) −6.81845 + 7.86891i −0.377061 + 0.435151i
\(328\) 2.04071 + 0.599206i 0.112679 + 0.0330856i
\(329\) 3.54876 2.28065i 0.195650 0.125736i
\(330\) 0 0
\(331\) 10.7382 + 12.3926i 0.590227 + 0.681158i 0.969771 0.244015i \(-0.0784647\pi\)
−0.379545 + 0.925173i \(0.623919\pi\)
\(332\) −7.30834 4.69678i −0.401097 0.257769i
\(333\) 3.15798 21.9642i 0.173056 1.20363i
\(334\) 0.244993 1.70396i 0.0134054 0.0932366i
\(335\) 0 0
\(336\) −4.00303 4.61974i −0.218383 0.252028i
\(337\) −11.3983 24.9589i −0.620907 1.35960i −0.914858 0.403776i \(-0.867697\pi\)
0.293951 0.955821i \(-0.405030\pi\)
\(338\) 0.624294 0.401210i 0.0339571 0.0218229i
\(339\) 18.7985 + 5.51975i 1.02100 + 0.299792i
\(340\) 0 0
\(341\) −1.76837 + 0.519240i −0.0957626 + 0.0281184i
\(342\) 0.543793 1.19074i 0.0294050 0.0643879i
\(343\) 2.55459 + 17.7675i 0.137935 + 0.959357i
\(344\) −1.89870 −0.102371
\(345\) 0 0
\(346\) 1.90261 0.102285
\(347\) 0.858953 + 5.97415i 0.0461110 + 0.320709i 0.999802 + 0.0199196i \(0.00634104\pi\)
−0.953691 + 0.300789i \(0.902750\pi\)
\(348\) −3.70988 + 8.12350i −0.198870 + 0.435465i
\(349\) −8.00915 + 2.35170i −0.428720 + 0.125883i −0.488972 0.872300i \(-0.662628\pi\)
0.0602518 + 0.998183i \(0.480810\pi\)
\(350\) 0 0
\(351\) −10.2692 3.01532i −0.548130 0.160946i
\(352\) 1.80116 1.15753i 0.0960021 0.0616968i
\(353\) 10.8642 + 23.7892i 0.578242 + 1.26617i 0.942291 + 0.334794i \(0.108667\pi\)
−0.364049 + 0.931380i \(0.618606\pi\)
\(354\) 0.463042 + 0.534379i 0.0246104 + 0.0284019i
\(355\) 0 0
\(356\) 0.182134 1.26677i 0.00965310 0.0671388i
\(357\) 0.959204 6.67141i 0.0507664 0.353088i
\(358\) 1.13874 + 0.731822i 0.0601841 + 0.0386780i
\(359\) −3.70672 4.27779i −0.195633 0.225773i 0.649454 0.760401i \(-0.274997\pi\)
−0.845088 + 0.534628i \(0.820452\pi\)
\(360\) 0 0
\(361\) 30.3894 19.5301i 1.59944 1.02790i
\(362\) 0.0692719 + 0.0203401i 0.00364085 + 0.00106905i
\(363\) 4.49302 5.18522i 0.235822 0.272154i
\(364\) −6.32663 + 1.85767i −0.331605 + 0.0973682i
\(365\) 0 0
\(366\) −0.0403840 0.280877i −0.00211091 0.0146817i
\(367\) 12.3147 0.642822 0.321411 0.946940i \(-0.395843\pi\)
0.321411 + 0.946940i \(0.395843\pi\)
\(368\) 17.6221 + 6.99596i 0.918615 + 0.364690i
\(369\) 12.0866 0.629201
\(370\) 0 0
\(371\) 0.176169 0.385756i 0.00914624 0.0200275i
\(372\) −1.73167 + 0.508465i −0.0897831 + 0.0263627i
\(373\) 19.0734 22.0119i 0.987585 1.13973i −0.00260397 0.999997i \(-0.500829\pi\)
0.990189 0.139737i \(-0.0446257\pi\)
\(374\) 0.750126 + 0.220257i 0.0387881 + 0.0113892i
\(375\) 0 0
\(376\) 0.398872 + 0.873407i 0.0205702 + 0.0450426i
\(377\) 6.28366 + 7.25173i 0.323625 + 0.373483i
\(378\) 0.573343 + 0.368465i 0.0294896 + 0.0189518i
\(379\) 4.74698 33.0160i 0.243836 1.69592i −0.388683 0.921372i \(-0.627070\pi\)
0.632519 0.774545i \(-0.282021\pi\)
\(380\) 0 0
\(381\) 14.7601 + 9.48571i 0.756181 + 0.485968i
\(382\) −0.246268 0.284209i −0.0126002 0.0145414i
\(383\) −12.9139 28.2775i −0.659870 1.44491i −0.882643 0.470044i \(-0.844238\pi\)
0.222773 0.974870i \(-0.428489\pi\)
\(384\) 2.35017 1.51036i 0.119931 0.0770753i
\(385\) 0 0
\(386\) −0.279084 + 0.322080i −0.0142050 + 0.0163934i
\(387\) −10.3529 + 3.03988i −0.526267 + 0.154526i
\(388\) −4.58560 + 10.0411i −0.232799 + 0.509758i
\(389\) 1.80544 + 12.5571i 0.0915394 + 0.636670i 0.983005 + 0.183581i \(0.0587690\pi\)
−0.891465 + 0.453089i \(0.850322\pi\)
\(390\) 0 0
\(391\) 6.89440 + 19.7358i 0.348665 + 0.998085i
\(392\) −1.62218 −0.0819324
\(393\) 1.85692 + 12.9152i 0.0936692 + 0.651484i
\(394\) −0.00961727 + 0.0210589i −0.000484511 + 0.00106093i
\(395\) 0 0
\(396\) 5.30841 6.12623i 0.266757 0.307855i
\(397\) 11.8219 + 3.47123i 0.593325 + 0.174216i 0.564590 0.825371i \(-0.309034\pi\)
0.0287344 + 0.999587i \(0.490852\pi\)
\(398\) 0.320841 0.206192i 0.0160823 0.0103355i
\(399\) 4.76890 + 10.4424i 0.238744 + 0.522776i
\(400\) 0 0
\(401\) −28.3895 18.2448i −1.41770 0.911102i −0.999997 0.00251937i \(-0.999198\pi\)
−0.417705 0.908583i \(-0.637166\pi\)
\(402\) 0.0246493 0.171440i 0.00122940 0.00855063i
\(403\) −0.275970 + 1.91941i −0.0137470 + 0.0956126i
\(404\) −7.53797 4.84436i −0.375028 0.241016i
\(405\) 0 0
\(406\) −0.253827 0.555804i −0.0125972 0.0275841i
\(407\) −18.9890 + 12.2035i −0.941249 + 0.604904i
\(408\) 1.47199 + 0.432214i 0.0728741 + 0.0213978i
\(409\) −10.6316 + 12.2695i −0.525698 + 0.606688i −0.955048 0.296450i \(-0.904197\pi\)
0.429350 + 0.903138i \(0.358743\pi\)
\(410\) 0 0
\(411\) −8.94256 + 19.5815i −0.441104 + 0.965883i
\(412\) −2.75950 19.1927i −0.135951 0.945558i
\(413\) 12.4018 0.610254
\(414\) −0.841961 0.0779495i −0.0413801 0.00383101i
\(415\) 0 0
\(416\) −0.320594 2.22978i −0.0157184 0.109324i
\(417\) −6.80112 + 14.8924i −0.333052 + 0.729282i
\(418\) −1.27764 + 0.375150i −0.0624916 + 0.0183492i
\(419\) 8.76692 10.1176i 0.428292 0.494275i −0.500053 0.865995i \(-0.666686\pi\)
0.928345 + 0.371719i \(0.121232\pi\)
\(420\) 0 0
\(421\) −10.9478 + 7.03572i −0.533563 + 0.342900i −0.779517 0.626382i \(-0.784535\pi\)
0.245954 + 0.969282i \(0.420899\pi\)
\(422\) 0.240510 + 0.526644i 0.0117079 + 0.0256366i
\(423\) 3.57325 + 4.12375i 0.173737 + 0.200504i
\(424\) 0.0812036 + 0.0521864i 0.00394360 + 0.00253439i
\(425\) 0 0
\(426\) −0.139903 + 0.973048i −0.00677833 + 0.0471443i
\(427\) −4.18698 2.69081i −0.202622 0.130217i
\(428\) 9.65005 + 11.1367i 0.466453 + 0.538315i
\(429\) 1.80906 + 3.96130i 0.0873424 + 0.191253i
\(430\) 0 0
\(431\) −8.97982 2.63671i −0.432543 0.127006i 0.0582112 0.998304i \(-0.481460\pi\)
−0.490754 + 0.871298i \(0.663279\pi\)
\(432\) 12.9447 14.9390i 0.622804 0.718754i
\(433\) −32.5898 + 9.56922i −1.56616 + 0.459867i −0.945882 0.324511i \(-0.894800\pi\)
−0.620283 + 0.784378i \(0.712982\pi\)
\(434\) 0.0512961 0.112323i 0.00246229 0.00539167i
\(435\) 0 0
\(436\) −20.7432 −0.993419
\(437\) −28.0522 21.9300i −1.34192 1.04905i
\(438\) −0.914218 −0.0436830
\(439\) −4.53831 31.5646i −0.216602 1.50650i −0.750456 0.660921i \(-0.770166\pi\)
0.533854 0.845577i \(-0.320743\pi\)
\(440\) 0 0
\(441\) −8.84511 + 2.59716i −0.421196 + 0.123674i
\(442\) 0.538668 0.621656i 0.0256218 0.0295691i
\(443\) 29.3691 + 8.62354i 1.39537 + 0.409717i 0.891091 0.453825i \(-0.149941\pi\)
0.504277 + 0.863542i \(0.331759\pi\)
\(444\) −18.5950 + 11.9502i −0.882477 + 0.567134i
\(445\) 0 0
\(446\) 0.531535 + 0.613424i 0.0251689 + 0.0290465i
\(447\) 16.2542 + 10.4459i 0.768797 + 0.494076i
\(448\) 1.71947 11.9592i 0.0812373 0.565018i
\(449\) 2.39840 16.6812i 0.113187 0.787236i −0.851597 0.524196i \(-0.824366\pi\)
0.964785 0.263040i \(-0.0847251\pi\)
\(450\) 0 0
\(451\) −8.05133 9.29173i −0.379122 0.437530i
\(452\) 16.2145 + 35.5048i 0.762666 + 1.67001i
\(453\) 16.8366 10.8202i 0.791054 0.508380i
\(454\) 0.750400 + 0.220337i 0.0352180 + 0.0103409i
\(455\) 0 0
\(456\) −2.50714 + 0.736163i −0.117408 + 0.0344740i
\(457\) 1.12972 2.47375i 0.0528463 0.115717i −0.881367 0.472432i \(-0.843376\pi\)
0.934213 + 0.356715i \(0.116103\pi\)
\(458\) −0.105195 0.731650i −0.00491546 0.0341877i
\(459\) 21.7954 1.01732
\(460\) 0 0
\(461\) −35.7457 −1.66484 −0.832421 0.554143i \(-0.813046\pi\)
−0.832421 + 0.554143i \(0.813046\pi\)
\(462\) −0.0394651 0.274486i −0.00183608 0.0127702i
\(463\) 17.3020 37.8860i 0.804091 1.76071i 0.173130 0.984899i \(-0.444612\pi\)
0.630961 0.775814i \(-0.282661\pi\)
\(464\) −17.0041 + 4.99286i −0.789397 + 0.231788i
\(465\) 0 0
\(466\) 2.03119 + 0.596411i 0.0940931 + 0.0276282i
\(467\) −14.8682 + 9.55519i −0.688017 + 0.442161i −0.837380 0.546621i \(-0.815914\pi\)
0.149364 + 0.988782i \(0.452278\pi\)
\(468\) −3.54305 7.75819i −0.163777 0.358623i
\(469\) −1.98938 2.29587i −0.0918610 0.106013i
\(470\) 0 0
\(471\) 0.821781 5.71561i 0.0378657 0.263361i
\(472\) −0.401733 + 2.79411i −0.0184913 + 0.128609i
\(473\) 9.23343 + 5.93396i 0.424553 + 0.272844i
\(474\) 0.185866 + 0.214501i 0.00853712 + 0.00985237i
\(475\) 0 0
\(476\) 11.2961 7.25953i 0.517754 0.332740i
\(477\) 0.526324 + 0.154543i 0.0240987 + 0.00707602i
\(478\) −0.648752 + 0.748699i −0.0296732 + 0.0342447i
\(479\) 11.4723 3.36858i 0.524184 0.153914i −0.00892633 0.999960i \(-0.502841\pi\)
0.533110 + 0.846046i \(0.321023\pi\)
\(480\) 0 0
\(481\) 3.37991 + 23.5078i 0.154111 + 1.07186i
\(482\) 2.47780 0.112861
\(483\) 5.35195 5.13260i 0.243522 0.233541i
\(484\) 13.6687 0.621306
\(485\) 0 0
\(486\) −0.585941 + 1.28303i −0.0265788 + 0.0581995i
\(487\) −18.1024 + 5.31536i −0.820300 + 0.240862i −0.664845 0.746981i \(-0.731503\pi\)
−0.155455 + 0.987843i \(0.549684\pi\)
\(488\) 0.741863 0.856156i 0.0335826 0.0387563i
\(489\) 8.44701 + 2.48026i 0.381987 + 0.112161i
\(490\) 0 0
\(491\) 9.10363 + 19.9342i 0.410841 + 0.899616i 0.996055 + 0.0887373i \(0.0282832\pi\)
−0.585214 + 0.810879i \(0.698990\pi\)
\(492\) −7.88425 9.09891i −0.355450 0.410211i
\(493\) −16.4384 10.5643i −0.740349 0.475794i
\(494\) −0.199387 + 1.38677i −0.00897086 + 0.0623937i
\(495\) 0 0
\(496\) −3.01291 1.93628i −0.135284 0.0869416i
\(497\) 11.2912 + 13.0308i 0.506480 + 0.584509i
\(498\) −0.159693 0.349679i −0.00715602 0.0156695i
\(499\) 8.48768 5.45470i 0.379961 0.244186i −0.336694 0.941614i \(-0.609309\pi\)
0.716655 + 0.697428i \(0.245672\pi\)
\(500\) 0 0
\(501\) −12.7879 + 14.7581i −0.571323 + 0.659341i
\(502\) −2.32553 + 0.682837i −0.103793 + 0.0304765i
\(503\) −5.56885 + 12.1941i −0.248303 + 0.543707i −0.992210 0.124576i \(-0.960243\pi\)
0.743907 + 0.668283i \(0.232970\pi\)
\(504\) 0.154886 + 1.07726i 0.00689918 + 0.0479849i
\(505\) 0 0
\(506\) 0.500939 + 0.699196i 0.0222694 + 0.0310831i
\(507\) −8.41804 −0.373858
\(508\) 4.97451 + 34.5985i 0.220708 + 1.53506i
\(509\) 8.03460 17.5933i 0.356127 0.779810i −0.643766 0.765222i \(-0.722629\pi\)
0.999894 0.0145879i \(-0.00464363\pi\)
\(510\) 0 0
\(511\) −10.5006 + 12.1183i −0.464518 + 0.536082i
\(512\) 6.66205 + 1.95615i 0.294424 + 0.0864506i
\(513\) −31.2297 + 20.0701i −1.37882 + 0.886116i
\(514\) 0.650495 + 1.42439i 0.0286921 + 0.0628270i
\(515\) 0 0
\(516\) 9.04182 + 5.81083i 0.398044 + 0.255807i
\(517\) 0.789915 5.49398i 0.0347404 0.241625i
\(518\) 0.215227 1.49694i 0.00945652 0.0657716i
\(519\) −18.1562 11.6683i −0.796970 0.512182i
\(520\) 0 0
\(521\) −4.67119 10.2285i −0.204648 0.448117i 0.779281 0.626674i \(-0.215584\pi\)
−0.983930 + 0.178557i \(0.942857\pi\)
\(522\) 0.664885 0.427296i 0.0291012 0.0187022i
\(523\) −17.3487 5.09404i −0.758605 0.222747i −0.120519 0.992711i \(-0.538456\pi\)
−0.638087 + 0.769964i \(0.720274\pi\)
\(524\) −17.0228 + 19.6454i −0.743645 + 0.858212i
\(525\) 0 0
\(526\) −0.320098 + 0.700917i −0.0139569 + 0.0305614i
\(527\) −0.561992 3.90874i −0.0244808 0.170267i
\(528\) −8.04304 −0.350028
\(529\) −7.39715 + 21.7780i −0.321615 + 0.946870i
\(530\) 0 0
\(531\) 2.28297 + 15.8784i 0.0990725 + 0.689064i
\(532\) −9.50074 + 20.8037i −0.411909 + 0.901955i
\(533\) −12.4119 + 3.64448i −0.537621 + 0.157860i
\(534\) 0.0370854 0.0427988i 0.00160484 0.00185209i
\(535\) 0 0
\(536\) 0.581697 0.373834i 0.0251255 0.0161472i
\(537\) −6.37863 13.9672i −0.275258 0.602731i
\(538\) 0.169194 + 0.195260i 0.00729445 + 0.00841825i
\(539\) 7.88869 + 5.06975i 0.339790 + 0.218370i
\(540\) 0 0
\(541\) 1.97456 13.7333i 0.0848928 0.590442i −0.902324 0.431059i \(-0.858140\pi\)
0.987217 0.159384i \(-0.0509507\pi\)
\(542\) 0.486530 + 0.312674i 0.0208983 + 0.0134305i
\(543\) −0.536306 0.618931i −0.0230151 0.0265609i
\(544\) 1.90571 + 4.17292i 0.0817065 + 0.178912i
\(545\) 0 0
\(546\) −0.279953 0.0822015i −0.0119809 0.00351790i
\(547\) −19.7384 + 22.7793i −0.843952 + 0.973973i −0.999905 0.0137919i \(-0.995610\pi\)
0.155953 + 0.987764i \(0.450155\pi\)
\(548\) −41.1491 + 12.0825i −1.75780 + 0.516138i
\(549\) 2.67436 5.85603i 0.114139 0.249929i
\(550\) 0 0
\(551\) 33.2819 1.41786
\(552\) 0.983001 + 1.37204i 0.0418393 + 0.0583981i
\(553\) 4.97813 0.211692
\(554\) 0.285906 + 1.98852i 0.0121470 + 0.0844840i
\(555\) 0 0
\(556\) −31.2953 + 9.18913i −1.32722 + 0.389706i
\(557\) 14.1622 16.3440i 0.600071 0.692519i −0.371724 0.928343i \(-0.621233\pi\)
0.971796 + 0.235824i \(0.0757788\pi\)
\(558\) 0.153253 + 0.0449991i 0.00648771 + 0.00190496i
\(559\) 9.71499 6.24345i 0.410900 0.264070i
\(560\) 0 0
\(561\) −5.80751 6.70222i −0.245193 0.282968i
\(562\) 1.05631 + 0.678850i 0.0445578 + 0.0286356i
\(563\) 0.0407395 0.283349i 0.00171696 0.0119418i −0.988945 0.148283i \(-0.952625\pi\)
0.990662 + 0.136341i \(0.0435344\pi\)
\(564\) 0.773524 5.37998i 0.0325712 0.226538i
\(565\) 0 0
\(566\) −1.36864 1.57949i −0.0575281 0.0663910i
\(567\) 0.642315 + 1.40647i 0.0269747 + 0.0590663i
\(568\) −3.30156 + 2.12179i −0.138531 + 0.0890282i
\(569\) 1.66147 + 0.487852i 0.0696525 + 0.0204518i 0.316373 0.948635i \(-0.397535\pi\)
−0.246721 + 0.969087i \(0.579353\pi\)
\(570\) 0 0
\(571\) −19.8922 + 5.84086i −0.832461 + 0.244433i −0.670074 0.742295i \(-0.733738\pi\)
−0.162387 + 0.986727i \(0.551919\pi\)
\(572\) −3.60407 + 7.89181i −0.150694 + 0.329973i
\(573\) 0.607097 + 4.22245i 0.0253618 + 0.176395i
\(574\) 0.823739 0.0343822
\(575\) 0 0
\(576\) 15.6282 0.651174
\(577\) 3.43290 + 23.8763i 0.142913 + 0.993985i 0.927462 + 0.373917i \(0.121986\pi\)
−0.784549 + 0.620067i \(0.787105\pi\)
\(578\) −0.0733005 + 0.160506i −0.00304890 + 0.00667616i
\(579\) 4.63848 1.36198i 0.192769 0.0566020i
\(580\) 0 0
\(581\) −6.46934 1.89957i −0.268394 0.0788074i
\(582\) −0.410917 + 0.264080i −0.0170330 + 0.0109465i
\(583\) −0.231798 0.507567i −0.00960009 0.0210213i
\(584\) −2.39009 2.75831i −0.0989026 0.114140i
\(585\) 0 0
\(586\) 0.0536241 0.372964i 0.00221519 0.0154070i
\(587\) −4.77952 + 33.2423i −0.197272 + 1.37206i 0.614885 + 0.788617i \(0.289202\pi\)
−0.812157 + 0.583439i \(0.801707\pi\)
\(588\) 7.72499 + 4.96455i 0.318573 + 0.204734i
\(589\) 4.40458 + 5.08316i 0.181488 + 0.209448i
\(590\) 0 0
\(591\) 0.220925 0.141980i 0.00908764 0.00584027i
\(592\) −42.0867 12.3578i −1.72975 0.507901i
\(593\) 19.5470 22.5585i 0.802700 0.926365i −0.195827 0.980639i \(-0.562739\pi\)
0.998526 + 0.0542739i \(0.0172844\pi\)
\(594\) 0.860418 0.252641i 0.0353034 0.0103660i
\(595\) 0 0
\(596\) 5.47807 + 38.1008i 0.224391 + 1.56067i
\(597\) −4.32625 −0.177062
\(598\) 0.888133 0.173830i 0.0363185 0.00710843i
\(599\) 4.70186 0.192113 0.0960564 0.995376i \(-0.469377\pi\)
0.0960564 + 0.995376i \(0.469377\pi\)
\(600\) 0 0
\(601\) 8.89729 19.4823i 0.362928 0.794701i −0.636792 0.771036i \(-0.719739\pi\)
0.999720 0.0236658i \(-0.00753375\pi\)
\(602\) −0.705584 + 0.207178i −0.0287575 + 0.00844395i
\(603\) 2.57325 2.96969i 0.104791 0.120935i
\(604\) 38.2569 + 11.2332i 1.55665 + 0.457073i
\(605\) 0 0
\(606\) −0.164711 0.360666i −0.00669091 0.0146511i
\(607\) −25.2756 29.1696i −1.02591 1.18396i −0.982759 0.184891i \(-0.940807\pi\)
−0.0431477 0.999069i \(-0.513739\pi\)
\(608\) −6.57319 4.22433i −0.266578 0.171319i
\(609\) −0.986403 + 6.86058i −0.0399711 + 0.278005i
\(610\) 0 0
\(611\) −4.91289 3.15732i −0.198754 0.127732i
\(612\) 11.3740 + 13.1263i 0.459766 + 0.530599i
\(613\) −7.81638 17.1155i −0.315700 0.691288i 0.683554 0.729900i \(-0.260433\pi\)
−0.999254 + 0.0386125i \(0.987706\pi\)
\(614\) −0.663370 + 0.426322i −0.0267714 + 0.0172050i
\(615\) 0 0
\(616\) 0.724983 0.836675i 0.0292104 0.0337106i
\(617\) 15.2099 4.46602i 0.612326 0.179795i 0.0391580 0.999233i \(-0.487532\pi\)
0.573168 + 0.819438i \(0.305714\pi\)
\(618\) 0.356430 0.780473i 0.0143377 0.0313952i
\(619\) 4.22984 + 29.4192i 0.170012 + 1.18246i 0.878854 + 0.477091i \(0.158309\pi\)
−0.708842 + 0.705367i \(0.750782\pi\)
\(620\) 0 0
\(621\) 18.8915 + 14.7685i 0.758091 + 0.592641i
\(622\) 2.05794 0.0825158
\(623\) −0.141357 0.983162i −0.00566336 0.0393896i
\(624\) −3.51546 + 7.69778i −0.140731 + 0.308158i
\(625\) 0 0
\(626\) 1.29956 1.49977i 0.0519408 0.0599429i
\(627\) 14.4930 + 4.25553i 0.578794 + 0.169949i
\(628\) 9.67769 6.21947i 0.386182 0.248184i
\(629\) −20.0912 43.9936i −0.801089 1.75414i
\(630\) 0 0
\(631\) −14.0318 9.01768i −0.558597 0.358988i 0.230677 0.973030i \(-0.425906\pi\)
−0.789273 + 0.614042i \(0.789542\pi\)
\(632\) −0.161257 + 1.12156i −0.00641444 + 0.0446134i
\(633\) 0.934652 6.50065i 0.0371491 0.258378i
\(634\) 0.945584 + 0.607690i 0.0375539 + 0.0241345i
\(635\) 0 0
\(636\) −0.226988 0.497034i −0.00900066 0.0197087i
\(637\) 8.30012 5.33416i 0.328863 0.211347i
\(638\) −0.771397 0.226502i −0.0305399 0.00896732i
\(639\) −14.6051 + 16.8552i −0.577769 + 0.666781i
\(640\) 0 0
\(641\) −12.5542 + 27.4898i −0.495859 + 1.08578i 0.481934 + 0.876208i \(0.339935\pi\)
−0.977793 + 0.209573i \(0.932793\pi\)
\(642\) 0.0927990 + 0.645431i 0.00366248 + 0.0254731i
\(643\) 7.45857 0.294137 0.147069 0.989126i \(-0.453016\pi\)
0.147069 + 0.989126i \(0.453016\pi\)
\(644\) 14.7101 + 1.36187i 0.579659 + 0.0536653i
\(645\) 0 0
\(646\) −0.406038 2.82406i −0.0159754 0.111111i
\(647\) −3.17102 + 6.94356i −0.124666 + 0.272980i −0.961666 0.274222i \(-0.911580\pi\)
0.837001 + 0.547202i \(0.184307\pi\)
\(648\) −0.337683 + 0.0991526i −0.0132654 + 0.00389508i
\(649\) 10.6860 12.3323i 0.419462 0.484085i
\(650\) 0 0
\(651\) −1.17836 + 0.757286i −0.0461836 + 0.0296804i
\(652\) 7.28589 + 15.9539i 0.285337 + 0.624802i
\(653\) 25.4564 + 29.3782i 0.996185 + 1.14966i 0.988734 + 0.149686i \(0.0478264\pi\)
0.00745135 + 0.999972i \(0.497628\pi\)
\(654\) −0.772173 0.496246i −0.0301944 0.0194047i
\(655\) 0 0
\(656\) 3.40014 23.6485i 0.132753 0.923319i
\(657\) −17.4484 11.2134i −0.680726 0.437476i
\(658\) 0.243529 + 0.281047i 0.00949374 + 0.0109564i
\(659\) −5.38310 11.7873i −0.209696 0.459170i 0.775335 0.631551i \(-0.217581\pi\)
−0.985030 + 0.172381i \(0.944854\pi\)
\(660\) 0 0
\(661\) 28.9778 + 8.50866i 1.12711 + 0.330949i 0.791570 0.611078i \(-0.209264\pi\)
0.335537 + 0.942027i \(0.391082\pi\)
\(662\) −0.946639 + 1.09248i −0.0367922 + 0.0424604i
\(663\) −8.95287 + 2.62880i −0.347701 + 0.102094i
\(664\) 0.637531 1.39600i 0.0247410 0.0541753i
\(665\) 0 0
\(666\) 1.95619 0.0758007
\(667\) −7.08990 20.2955i −0.274522 0.785844i
\(668\) −38.9037 −1.50523
\(669\) −1.31033 9.11356i −0.0506604 0.352351i
\(670\) 0 0
\(671\) −6.28342 + 1.84498i −0.242569 + 0.0712246i
\(672\) 1.06560 1.22977i 0.0411064 0.0474393i
\(673\) −2.27218 0.667173i −0.0875862 0.0257176i 0.237646 0.971352i \(-0.423624\pi\)
−0.325232 + 0.945634i \(0.605442\pi\)
\(674\) 2.03488 1.30773i 0.0783805 0.0503721i
\(675\) 0 0
\(676\) −10.9824 12.6744i −0.422402 0.487478i
\(677\) 29.1912 + 18.7600i 1.12191 + 0.721006i 0.963856 0.266425i \(-0.0858423\pi\)
0.158052 + 0.987431i \(0.449479\pi\)
\(678\) −0.245801 + 1.70958i −0.00943993 + 0.0656562i
\(679\) −1.21925 + 8.48004i −0.0467904 + 0.325434i
\(680\) 0 0
\(681\) −5.80963 6.70467i −0.222626 0.256924i
\(682\) −0.0674940 0.147791i −0.00258448 0.00565922i
\(683\) 19.5711 12.5776i 0.748869 0.481269i −0.109702 0.993965i \(-0.534990\pi\)
0.858570 + 0.512696i \(0.171353\pi\)
\(684\) −28.3845 8.33444i −1.08531 0.318675i
\(685\) 0 0
\(686\) −1.51832 + 0.445819i −0.0579698 + 0.0170215i
\(687\) −3.48319 + 7.62712i −0.132892 + 0.290993i
\(688\) 3.03539 + 21.1116i 0.115723 + 0.804872i
\(689\) −0.587093 −0.0223665
\(690\) 0 0
\(691\) −45.0096 −1.71225 −0.856123 0.516772i \(-0.827133\pi\)
−0.856123 + 0.516772i \(0.827133\pi\)
\(692\) −6.11911 42.5593i −0.232614 1.61786i
\(693\) 2.61351 5.72279i 0.0992790 0.217391i
\(694\) −0.510520 + 0.149902i −0.0193791 + 0.00569020i
\(695\) 0 0
\(696\) −1.51372 0.444470i −0.0573776 0.0168476i
\(697\) 22.1612 14.2422i 0.839417 0.539461i
\(698\) −0.305688 0.669363i −0.0115705 0.0253358i
\(699\) −15.7256 18.1483i −0.594796 0.686431i
\(700\) 0 0
\(701\) −3.34738 + 23.2815i −0.126429 + 0.879332i 0.823600 + 0.567171i \(0.191962\pi\)
−0.950029 + 0.312161i \(0.898947\pi\)
\(702\) 0.134276 0.933908i 0.00506791 0.0352481i
\(703\) 69.2989 + 44.5357i 2.61366 + 1.67969i
\(704\) −10.4105 12.0144i −0.392362 0.452810i
\(705\) 0 0
\(706\) −1.93952 + 1.24645i −0.0729946 + 0.0469108i
\(707\) −6.67261 1.95925i −0.250949 0.0736854i
\(708\) 10.4643 12.0764i 0.393271 0.453859i
\(709\) 32.8793 9.65422i 1.23481 0.362572i 0.401745 0.915752i \(-0.368404\pi\)
0.833062 + 0.553180i \(0.186586\pi\)
\(710\) 0 0
\(711\) 0.916390 + 6.37363i 0.0343673 + 0.239030i
\(712\) 0.226084 0.00847285
\(713\) 2.16144 3.76877i 0.0809467 0.141142i
\(714\) 0.594172 0.0222363
\(715\) 0 0
\(716\) 12.7077 27.8260i 0.474909 1.03990i
\(717\) 10.7825 3.16603i 0.402680 0.118238i
\(718\) 0.326770 0.377112i 0.0121949 0.0140737i
\(719\) −22.3827 6.57217i −0.834735 0.245100i −0.163685 0.986513i \(-0.552338\pi\)
−0.671050 + 0.741412i \(0.734156\pi\)
\(720\) 0 0
\(721\) −6.25157 13.6890i −0.232821 0.509806i
\(722\) 2.08543 + 2.40672i 0.0776117 + 0.0895687i
\(723\) −23.6451 15.1958i −0.879371 0.565138i
\(724\) 0.232195 1.61495i 0.00862947 0.0600193i
\(725\) 0 0
\(726\) 0.508824 + 0.327001i 0.0188842 + 0.0121362i
\(727\) 26.3834 + 30.4481i 0.978507 + 1.12926i 0.991600 + 0.129343i \(0.0412867\pi\)
−0.0130932 + 0.999914i \(0.504168\pi\)
\(728\) −0.483883 1.05956i −0.0179339 0.0392698i
\(729\) 10.9363 7.02833i 0.405048 0.260309i
\(730\) 0 0
\(731\) −15.4005 + 17.7731i −0.569607 + 0.657361i
\(732\) −6.15303 + 1.80669i −0.227422 + 0.0667773i
\(733\) 9.43781 20.6659i 0.348594 0.763313i −0.651396 0.758738i \(-0.725816\pi\)
0.999990 0.00457542i \(-0.00145641\pi\)
\(734\) 0.154499 + 1.07456i 0.00570266 + 0.0396629i
\(735\) 0 0
\(736\) −1.17576 + 4.90825i −0.0433391 + 0.180921i
\(737\) −3.99714 −0.147236
\(738\) 0.151637 + 1.05466i 0.00558182 + 0.0388224i
\(739\) −7.47356 + 16.3648i −0.274919 + 0.601989i −0.995849 0.0910188i \(-0.970988\pi\)
0.720930 + 0.693008i \(0.243715\pi\)
\(740\) 0 0
\(741\) 10.4075 12.0109i 0.382328 0.441230i
\(742\) 0.0358708 + 0.0105326i 0.00131686 + 0.000386664i
\(743\) 4.89833 3.14797i 0.179702 0.115488i −0.447697 0.894185i \(-0.647756\pi\)
0.627399 + 0.778698i \(0.284119\pi\)
\(744\) −0.132445 0.290013i −0.00485566 0.0106324i
\(745\) 0 0
\(746\) 2.16002 + 1.38816i 0.0790840 + 0.0508242i
\(747\) 1.24117 8.63256i 0.0454122 0.315849i
\(748\) 2.51438 17.4879i 0.0919347 0.639420i
\(749\) 9.62131 + 6.18324i 0.351555 + 0.225931i
\(750\) 0 0
\(751\) 3.84740 + 8.42462i 0.140393 + 0.307419i 0.966748 0.255732i \(-0.0823164\pi\)
−0.826354 + 0.563151i \(0.809589\pi\)
\(752\) 9.07372 5.83133i 0.330885 0.212647i
\(753\) 26.3797 + 7.74578i 0.961330 + 0.282272i
\(754\) −0.553942 + 0.639283i −0.0201734 + 0.0232813i
\(755\) 0 0
\(756\) 6.39819 14.0101i 0.232700 0.509542i
\(757\) −1.15607 8.04064i −0.0420180 0.292242i −0.999986 0.00536536i \(-0.998292\pi\)
0.957968 0.286877i \(-0.0926169\pi\)
\(758\) 2.94048 0.106803
\(759\) −0.492336 9.74443i −0.0178707 0.353700i
\(760\) 0 0
\(761\) −4.15984 28.9323i −0.150794 1.04880i −0.914893 0.403697i \(-0.867725\pi\)
0.764099 0.645099i \(-0.223184\pi\)
\(762\) −0.642532 + 1.40695i −0.0232765 + 0.0509684i
\(763\) −15.4470 + 4.53565i −0.559219 + 0.164201i
\(764\) −5.56539 + 6.42281i −0.201349 + 0.232369i
\(765\) 0 0
\(766\) 2.30544 1.48162i 0.0832990 0.0535330i
\(767\) −7.13228 15.6175i −0.257532 0.563915i
\(768\) −10.0730 11.6249i −0.363478 0.419476i
\(769\) 12.2803 + 7.89208i 0.442840 + 0.284596i 0.742998 0.669294i \(-0.233403\pi\)
−0.300158 + 0.953889i \(0.597040\pi\)
\(770\) 0 0
\(771\) 2.52790 17.5820i 0.0910403 0.633199i
\(772\) 8.10215 + 5.20693i 0.291603 + 0.187402i
\(773\) −11.3054 13.0471i −0.406625 0.469271i 0.515091 0.857136i \(-0.327758\pi\)
−0.921716 + 0.387865i \(0.873213\pi\)
\(774\) −0.395142 0.865241i −0.0142031 0.0311004i
\(775\) 0 0
\(776\) −1.87104 0.549388i −0.0671666 0.0197219i
\(777\) −11.2342 + 12.9650i −0.403026 + 0.465117i
\(778\) −1.07306 + 0.315080i −0.0384712 + 0.0112962i
\(779\) −18.6391 + 40.8139i −0.667815 + 1.46231i
\(780\) 0 0
\(781\) 22.6867 0.811795
\(782\) −1.63563 + 0.849200i −0.0584899 + 0.0303673i
\(783\) −22.4134 −0.800991
\(784\) 2.59332 + 18.0369i 0.0926186 + 0.644176i
\(785\) 0 0
\(786\) −1.10366 + 0.324065i −0.0393663 + 0.0115590i
\(787\) 10.0471 11.5950i 0.358142 0.413318i −0.547875 0.836561i \(-0.684563\pi\)
0.906016 + 0.423243i \(0.139108\pi\)
\(788\) 0.501995 + 0.147399i 0.0178828 + 0.00525087i
\(789\) 7.35320 4.72561i 0.261781 0.168236i
\(790\) 0 0
\(791\) 19.8380 + 22.8942i 0.705356 + 0.814025i
\(792\) 1.20467 + 0.774198i 0.0428063 + 0.0275099i
\(793\) −0.980582 + 6.82010i −0.0348215 + 0.242189i
\(794\) −0.154578 + 1.07511i −0.00548577 + 0.0381544i
\(795\) 0 0
\(796\) −5.64417 6.51371i −0.200052 0.230872i
\(797\) −10.4360 22.8517i −0.369663 0.809448i −0.999465 0.0326932i \(-0.989592\pi\)
0.629803 0.776755i \(-0.283136\pi\)
\(798\) −0.851362 + 0.547137i −0.0301379 + 0.0193685i
\(799\) 11.4109 + 3.35055i 0.403690 + 0.118534i
\(800\) 0 0
\(801\) 1.23275 0.361967i 0.0435570 0.0127895i
\(802\) 1.23584 2.70612i 0.0436392 0.0955565i
\(803\) 3.00258 + 20.8834i 0.105959 + 0.736959i
\(804\) −3.91419 −0.138043
\(805\) 0 0
\(806\) −0.170947 −0.00602136
\(807\) −0.417094 2.90095i −0.0146824 0.102118i
\(808\) 0.657563 1.43986i 0.0231330 0.0506542i
\(809\) −21.8919 + 6.42804i −0.769678 + 0.225998i −0.642917 0.765935i \(-0.722276\pi\)
−0.126761 + 0.991933i \(0.540458\pi\)
\(810\) 0 0
\(811\) 41.7803 + 12.2678i 1.46711 + 0.430781i 0.915157 0.403097i \(-0.132066\pi\)
0.551949 + 0.833878i \(0.313884\pi\)
\(812\) −11.6164 + 7.46538i −0.407654 + 0.261984i
\(813\) −2.72530 5.96757i −0.0955803 0.209292i
\(814\) −1.30309 1.50385i −0.0456734 0.0527099i
\(815\) 0 0
\(816\) 2.45256 17.0579i 0.0858567 0.597147i
\(817\) 5.70046 39.6476i 0.199434 1.38709i
\(818\) −1.20400 0.773766i −0.0420970 0.0270541i
\(819\) −4.33481 5.00264i −0.151471 0.174806i
\(820\) 0 0
\(821\) 40.9122 26.2927i 1.42785 0.917621i 0.427942 0.903806i \(-0.359239\pi\)
0.999905 0.0138148i \(-0.00439753\pi\)
\(822\) −1.82085 0.534648i −0.0635093 0.0186480i
\(823\) 0.752583 0.868528i 0.0262334 0.0302750i −0.742481 0.669867i \(-0.766351\pi\)
0.768715 + 0.639592i \(0.220897\pi\)
\(824\) 3.28662 0.965039i 0.114495 0.0336187i
\(825\) 0 0
\(826\) 0.155592 + 1.08217i 0.00541374 + 0.0376534i
\(827\) 15.3873 0.535069 0.267534 0.963548i \(-0.413791\pi\)
0.267534 + 0.963548i \(0.413791\pi\)
\(828\) 0.964240 + 19.0844i 0.0335096 + 0.663230i
\(829\) −43.7168 −1.51835 −0.759174 0.650888i \(-0.774397\pi\)
−0.759174 + 0.650888i \(0.774397\pi\)
\(830\) 0 0
\(831\) 9.46680 20.7294i 0.328400 0.719095i
\(832\) −16.0489 + 4.71239i −0.556396 + 0.163373i
\(833\) −13.1576 + 15.1846i −0.455883 + 0.526117i
\(834\) −1.38481 0.406618i −0.0479522 0.0140800i
\(835\) 0 0
\(836\) 12.5008 + 27.3729i 0.432349 + 0.946712i
\(837\) −2.96623 3.42321i −0.102528 0.118323i
\(838\) 0.992833 + 0.638055i 0.0342969 + 0.0220413i
\(839\) 1.60650 11.1735i 0.0554627 0.385751i −0.943116 0.332462i \(-0.892121\pi\)
0.998579 0.0532888i \(-0.0169704\pi\)
\(840\) 0 0
\(841\) −7.49181 4.81469i −0.258338 0.166024i
\(842\) −0.751277 0.867020i −0.0258907 0.0298795i
\(843\) −5.91692 12.9563i −0.203790 0.446237i
\(844\) 11.0069 7.07372i 0.378874 0.243488i
\(845\) 0 0
\(846\) −0.315003 + 0.363533i −0.0108300 + 0.0124985i
\(847\) 10.1788 2.98877i 0.349748 0.102695i
\(848\) 0.450441 0.986328i 0.0154682 0.0338707i
\(849\) 3.37394 + 23.4663i 0.115793 + 0.805361i
\(850\) 0 0
\(851\) 12.3956 51.7460i 0.424917 1.77383i
\(852\) 22.2160 0.761106
\(853\) 2.37985 + 16.5522i 0.0814845 + 0.566737i 0.989135 + 0.147010i \(0.0469650\pi\)
−0.907651 + 0.419727i \(0.862126\pi\)
\(854\) 0.182267 0.399108i 0.00623704 0.0136572i
\(855\) 0 0
\(856\) −1.70474 + 1.96737i −0.0582667 + 0.0672433i
\(857\) 5.93618 + 1.74302i 0.202776 + 0.0595405i 0.381543 0.924351i \(-0.375393\pi\)
−0.178767 + 0.983891i \(0.557211\pi\)
\(858\) −0.322961 + 0.207554i −0.0110257 + 0.00708579i
\(859\) −3.60612 7.89631i −0.123039 0.269419i 0.838082 0.545544i \(-0.183677\pi\)
−0.961122 + 0.276125i \(0.910950\pi\)
\(860\) 0 0
\(861\) −7.86077 5.05181i −0.267894 0.172165i
\(862\) 0.117416 0.816646i 0.00399921 0.0278151i
\(863\) 1.61006 11.1982i 0.0548072 0.381192i −0.943894 0.330248i \(-0.892868\pi\)
0.998701 0.0509446i \(-0.0162232\pi\)
\(864\) 4.42666 + 2.84484i 0.150598 + 0.0967834i
\(865\) 0 0
\(866\) −1.24386 2.72368i −0.0422682 0.0925546i
\(867\) 1.68384 1.08214i 0.0571861 0.0367513i
\(868\) −2.67752 0.786189i −0.0908808 0.0266850i
\(869\) 4.28939 4.95022i 0.145508 0.167925i
\(870\) 0 0
\(871\) −1.74707 + 3.82555i −0.0591973 + 0.129624i
\(872\) −0.521499 3.62711i −0.0176602 0.122829i
\(873\) −11.0817 −0.375058
\(874\) 1.56164 2.72293i 0.0528232 0.0921045i
\(875\) 0 0
\(876\) 2.94027 + 20.4500i 0.0993426 + 0.690943i
\(877\) −10.2913 + 22.5349i −0.347514 + 0.760950i 0.652481 + 0.757805i \(0.273728\pi\)
−0.999995 + 0.00314460i \(0.998999\pi\)
\(878\) 2.69735 0.792013i 0.0910311 0.0267291i
\(879\) −2.79903 + 3.23025i −0.0944090 + 0.108954i
\(880\) 0 0
\(881\) 28.0492 18.0261i 0.945000 0.607315i 0.0251917 0.999683i \(-0.491980\pi\)
0.919808 + 0.392368i \(0.128344\pi\)
\(882\) −0.337594 0.739229i −0.0113674 0.0248911i
\(883\) −8.56278 9.88198i −0.288161 0.332555i 0.593150 0.805092i \(-0.297884\pi\)
−0.881311 + 0.472537i \(0.843338\pi\)
\(884\) −15.6382 10.0501i −0.525969 0.338020i
\(885\) 0 0
\(886\) −0.384017 + 2.67090i −0.0129013 + 0.0897305i
\(887\) −18.6668 11.9964i −0.626770 0.402800i 0.188343 0.982103i \(-0.439688\pi\)
−0.815112 + 0.579303i \(0.803325\pi\)
\(888\) −2.55708 2.95103i −0.0858101 0.0990301i
\(889\) 11.2696 + 24.6770i 0.377971 + 0.827641i
\(890\) 0 0
\(891\) 1.95204 + 0.573170i 0.0653957 + 0.0192019i
\(892\) 12.0121 13.8627i 0.402195 0.464158i
\(893\) −19.4355 + 5.70679i −0.650385 + 0.190970i
\(894\) −0.707574 + 1.54937i −0.0236648 + 0.0518187i
\(895\) 0 0
\(896\) 4.31954 0.144306
\(897\) −9.54133 3.78790i −0.318576 0.126474i
\(898\) 1.48567 0.0495775
\(899\) 0.577928 + 4.01958i 0.0192750 + 0.134060i
\(900\) 0 0
\(901\) 1.14714 0.336832i 0.0382169 0.0112215i
\(902\) 0.709772 0.819121i 0.0236328 0.0272737i
\(903\) 8.00382 + 2.35013i 0.266351 + 0.0782076i
\(904\) −5.80064 + 3.72784i −0.192926 + 0.123986i
\(905\) 0 0
\(906\) 1.15539 + 1.33339i 0.0383853 + 0.0442990i
\(907\) 18.0240 + 11.5834i 0.598479 + 0.384619i 0.804521 0.593924i \(-0.202422\pi\)
−0.206042 + 0.978543i \(0.566058\pi\)
\(908\) 2.51530 17.4943i 0.0834730 0.580568i
\(909\) 1.28017 8.90379i 0.0424606 0.295320i
\(910\) 0 0
\(911\) 25.5067 + 29.4363i 0.845076 + 0.975269i 0.999920 0.0126696i \(-0.00403297\pi\)
−0.154844 + 0.987939i \(0.549488\pi\)
\(912\) 12.1935 + 26.6999i 0.403766 + 0.884123i
\(913\) −7.46321 + 4.79631i −0.246996 + 0.158735i
\(914\) 0.230030 + 0.0675428i 0.00760870 + 0.00223412i
\(915\) 0 0
\(916\) −16.0279 + 4.70621i −0.529576 + 0.155497i
\(917\) −8.38091 + 18.3516i −0.276762 + 0.606024i
\(918\) 0.273443 + 1.90184i 0.00902496 + 0.0627700i
\(919\) 29.9408 0.987657 0.493829 0.869559i \(-0.335597\pi\)
0.493829 + 0.869559i \(0.335597\pi\)
\(920\) 0 0
\(921\) 8.94494 0.294746
\(922\) −0.448462 3.11912i −0.0147693 0.102723i
\(923\) 9.91594 21.7129i 0.326387 0.714688i
\(924\) −6.01302 + 1.76558i −0.197814 + 0.0580834i
\(925\) 0 0
\(926\) 3.52295 + 1.03443i 0.115771 + 0.0339935i
\(927\) 16.3756 10.5240i 0.537846 0.345653i
\(928\) −1.95974 4.29124i −0.0643318 0.140867i
\(929\) 8.14358 + 9.39819i 0.267182 + 0.308345i 0.873448 0.486917i \(-0.161879\pi\)
−0.606266 + 0.795262i \(0.707333\pi\)
\(930\) 0 0
\(931\) 4.87026 33.8734i 0.159616 1.11016i
\(932\) 6.80843 47.3537i 0.223017 1.55112i
\(933\) −19.6385 12.6209i −0.642934 0.413189i
\(934\) −1.02031 1.17750i −0.0333855 0.0385289i
\(935\) 0 0
\(936\) 1.26750 0.814576i 0.0414297 0.0266252i
\(937\) 9.15473 + 2.68807i 0.299072 + 0.0878155i 0.427826 0.903861i \(-0.359280\pi\)
−0.128754 + 0.991677i \(0.541098\pi\)
\(938\) 0.175376 0.202394i 0.00572621 0.00660840i
\(939\) −21.5992 + 6.34209i −0.704863 + 0.206966i
\(940\) 0 0
\(941\) 0.484266 + 3.36814i 0.0157866 + 0.109798i 0.996191 0.0871966i \(-0.0277908\pi\)
−0.980405 + 0.196995i \(0.936882\pi\)
\(942\) 0.509046 0.0165856
\(943\) 28.8591 + 2.67180i 0.939782 + 0.0870058i
\(944\) 31.7099 1.03207
\(945\) 0 0
\(946\) −0.401948 + 0.880143i −0.0130684 + 0.0286159i
\(947\) 11.9343 3.50424i 0.387814 0.113872i −0.0820124 0.996631i \(-0.526135\pi\)
0.469826 + 0.882759i \(0.344317\pi\)
\(948\) 4.20038 4.84750i 0.136422 0.157439i
\(949\) 21.2993 + 6.25405i 0.691405 + 0.203015i
\(950\) 0 0
\(951\) −5.29668 11.5981i −0.171757 0.376095i
\(952\) 1.55338 + 1.79269i 0.0503452 + 0.0581015i
\(953\) −11.2590 7.23572i −0.364715 0.234388i 0.345429 0.938445i \(-0.387734\pi\)
−0.710143 + 0.704057i \(0.751370\pi\)
\(954\) −0.00688198 + 0.0478652i −0.000222812 + 0.00154969i
\(955\) 0 0
\(956\) 18.8341 + 12.1039i 0.609137 + 0.391469i
\(957\) 5.97219 + 6.89227i 0.193053 + 0.222795i
\(958\) 0.437868 + 0.958797i 0.0141469 + 0.0309773i
\(959\) −28.0009 + 17.9951i −0.904197 + 0.581092i
\(960\) 0 0
\(961\) 19.7633 22.8080i 0.637524 0.735742i
\(962\) −2.00885 + 0.589852i −0.0647680 + 0.0190176i
\(963\) −6.14545 + 13.4567i −0.198034 + 0.433635i
\(964\) −7.96900 55.4256i −0.256664 1.78514i
\(965\) 0 0
\(966\) 0.515009 + 0.402610i 0.0165701 + 0.0129538i
\(967\) 24.7635 0.796341 0.398170 0.917311i \(-0.369645\pi\)
0.398170 + 0.917311i \(0.369645\pi\)
\(968\) 0.343642 + 2.39008i 0.0110451 + 0.0768202i
\(969\) −13.4446 + 29.4395i −0.431902 + 0.945734i
\(970\) 0 0
\(971\) −11.6629 + 13.4597i −0.374281 + 0.431944i −0.911374 0.411580i \(-0.864977\pi\)
0.537092 + 0.843523i \(0.319523\pi\)
\(972\) 30.5845 + 8.98041i 0.980997 + 0.288047i
\(973\) −21.2956 + 13.6859i −0.682707 + 0.438749i
\(974\) −0.690922 1.51291i −0.0221386 0.0484767i
\(975\) 0 0
\(976\) −10.7056 6.88004i −0.342676 0.220225i
\(977\) 1.03522 7.20015i 0.0331198 0.230353i −0.966538 0.256525i \(-0.917423\pi\)
0.999657 + 0.0261716i \(0.00833162\pi\)
\(978\) −0.110449 + 0.768191i −0.00353178 + 0.0245640i
\(979\) −1.09945 0.706574i −0.0351386 0.0225822i
\(980\) 0 0
\(981\) −8.65065 18.9423i −0.276194 0.604780i
\(982\) −1.62521 + 1.04446i −0.0518627 + 0.0333301i
\(983\) −30.9104 9.07613i −0.985890 0.289483i −0.251236 0.967926i \(-0.580837\pi\)
−0.734654 + 0.678442i \(0.762655\pi\)
\(984\) 1.39280 1.60738i 0.0444008 0.0512412i
\(985\) 0 0
\(986\) 0.715594 1.56693i 0.0227892 0.0499013i
\(987\) −0.600344 4.17548i −0.0191092 0.132907i
\(988\) 31.6618 1.00729
\(989\) −25.3916 + 4.96978i −0.807407 + 0.158030i
\(990\) 0 0
\(991\) −1.54572 10.7507i −0.0491013 0.341507i −0.999533 0.0305723i \(-0.990267\pi\)
0.950431 0.310935i \(-0.100642\pi\)
\(992\) 0.396047 0.867221i 0.0125745 0.0275343i
\(993\) 15.7335 4.61978i 0.499288 0.146604i
\(994\) −0.995387 + 1.14874i −0.0315718 + 0.0364358i
\(995\) 0 0
\(996\) −7.30834 + 4.69678i −0.231574 + 0.148823i
\(997\) 8.76152 + 19.1851i 0.277480 + 0.607597i 0.996141 0.0877636i \(-0.0279720\pi\)
−0.718661 + 0.695360i \(0.755245\pi\)
\(998\) 0.582455 + 0.672189i 0.0184373 + 0.0212778i
\(999\) −46.6687 29.9922i −1.47653 0.948910i
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 575.2.k.a.26.1 10
5.2 odd 4 575.2.p.a.49.1 20
5.3 odd 4 575.2.p.a.49.2 20
5.4 even 2 115.2.g.a.26.1 10
23.8 even 11 inner 575.2.k.a.376.1 10
115.8 odd 44 575.2.p.a.399.1 20
115.54 even 22 115.2.g.a.31.1 yes 10
115.59 even 22 2645.2.a.n.1.4 5
115.77 odd 44 575.2.p.a.399.2 20
115.79 odd 22 2645.2.a.o.1.4 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
115.2.g.a.26.1 10 5.4 even 2
115.2.g.a.31.1 yes 10 115.54 even 22
575.2.k.a.26.1 10 1.1 even 1 trivial
575.2.k.a.376.1 10 23.8 even 11 inner
575.2.p.a.49.1 20 5.2 odd 4
575.2.p.a.49.2 20 5.3 odd 4
575.2.p.a.399.1 20 115.8 odd 44
575.2.p.a.399.2 20 115.77 odd 44
2645.2.a.n.1.4 5 115.59 even 22
2645.2.a.o.1.4 5 115.79 odd 22