Properties

Label 225.2.k.c.124.6
Level $225$
Weight $2$
Character 225.124
Analytic conductor $1.797$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 12x^{14} + 102x^{12} - 406x^{10} + 1167x^{8} - 1842x^{6} + 2023x^{4} - 441x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 124.6
Root \(1.27588 + 0.736627i\) of defining polynomial
Character \(\chi\) \(=\) 225.124
Dual form 225.2.k.c.49.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.27588 + 0.736627i) q^{2} +(0.350156 + 1.69629i) q^{3} +(0.0852394 + 0.147639i) q^{4} +(-0.802776 + 2.42219i) q^{6} +(3.34791 + 1.93291i) q^{7} -2.69535i q^{8} +(-2.75478 + 1.18793i) q^{9} +O(q^{10})\) \(q+(1.27588 + 0.736627i) q^{2} +(0.350156 + 1.69629i) q^{3} +(0.0852394 + 0.147639i) q^{4} +(-0.802776 + 2.42219i) q^{6} +(3.34791 + 1.93291i) q^{7} -2.69535i q^{8} +(-2.75478 + 1.18793i) q^{9} +(-0.130139 + 0.225407i) q^{11} +(-0.220591 + 0.196287i) q^{12} +(-3.53235 + 2.03940i) q^{13} +(2.84768 + 4.93232i) q^{14} +(2.15595 - 3.73421i) q^{16} -3.26028i q^{17} +(-4.38982 - 0.513594i) q^{18} -4.24928 q^{19} +(-2.10649 + 6.35583i) q^{21} +(-0.332082 + 0.191728i) q^{22} +(7.53039 - 4.34768i) q^{23} +(4.57209 - 0.943794i) q^{24} -6.00912 q^{26} +(-2.97968 - 4.25694i) q^{27} +0.659042i q^{28} +(2.11105 - 3.65644i) q^{29} +(-1.32643 - 2.29744i) q^{31} +(0.832959 - 0.480909i) q^{32} +(-0.427924 - 0.141825i) q^{33} +(2.40161 - 4.15971i) q^{34} +(-0.410201 - 0.305455i) q^{36} +2.27559i q^{37} +(-5.42156 - 3.13014i) q^{38} +(-4.69629 - 5.27777i) q^{39} +(-2.82093 - 4.88599i) q^{41} +(-7.36950 + 6.55756i) q^{42} +(7.85712 + 4.53631i) q^{43} -0.0443719 q^{44} +12.8105 q^{46} +(-1.23745 - 0.714441i) q^{47} +(7.08921 + 2.34955i) q^{48} +(3.97232 + 6.88026i) q^{49} +(5.53037 - 1.14161i) q^{51} +(-0.602191 - 0.347675i) q^{52} +11.3816i q^{53} +(-0.665919 - 7.62624i) q^{54} +(5.20988 - 9.02378i) q^{56} +(-1.48791 - 7.20801i) q^{57} +(5.38687 - 3.11011i) q^{58} +(-3.56212 - 6.16977i) q^{59} +(-1.26244 + 2.18660i) q^{61} -3.90833i q^{62} +(-11.5189 - 1.34768i) q^{63} -7.20679 q^{64} +(-0.441506 - 0.496172i) q^{66} +(-9.77361 + 5.64280i) q^{67} +(0.481344 - 0.277904i) q^{68} +(10.0117 + 11.2513i) q^{69} -8.38158 q^{71} +(3.20189 + 7.42510i) q^{72} +0.403568i q^{73} +(-1.67626 + 2.90337i) q^{74} +(-0.362207 - 0.627360i) q^{76} +(-0.871386 + 0.503095i) q^{77} +(-2.10413 - 10.1932i) q^{78} +(-1.52125 + 2.63488i) q^{79} +(6.17764 - 6.54498i) q^{81} -8.31189i q^{82} +(-3.96660 - 2.29012i) q^{83} +(-1.11792 + 0.230768i) q^{84} +(6.68314 + 11.5755i) q^{86} +(6.94157 + 2.30062i) q^{87} +(0.607551 + 0.350770i) q^{88} -7.17772 q^{89} -15.7680 q^{91} +(1.28377 + 0.741187i) q^{92} +(3.43266 - 3.05446i) q^{93} +(-1.05255 - 1.82308i) q^{94} +(1.10743 + 1.24454i) q^{96} +(2.69777 + 1.55756i) q^{97} +11.7045i q^{98} +(0.0907360 - 0.775544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 8 q^{4} + 16 q^{6} - 10 q^{9} + 2 q^{11} + 6 q^{14} - 8 q^{16} - 8 q^{19} - 30 q^{21} + 66 q^{24} - 40 q^{26} + 2 q^{29} + 8 q^{31} + 18 q^{34} - 28 q^{36} - 50 q^{39} + 10 q^{41} - 88 q^{44} - 6 q^{49} + 22 q^{51} - 52 q^{54} + 60 q^{56} + 34 q^{59} + 26 q^{61} - 76 q^{64} - 16 q^{66} + 54 q^{69} - 32 q^{71} + 80 q^{74} - 22 q^{76} - 14 q^{79} + 34 q^{81} - 54 q^{84} + 68 q^{86} + 36 q^{89} - 68 q^{91} + 6 q^{94} + 68 q^{96} + 34 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.27588 + 0.736627i 0.902180 + 0.520874i 0.877907 0.478831i \(-0.158939\pi\)
0.0242735 + 0.999705i \(0.492273\pi\)
\(3\) 0.350156 + 1.69629i 0.202163 + 0.979352i
\(4\) 0.0852394 + 0.147639i 0.0426197 + 0.0738195i
\(5\) 0 0
\(6\) −0.802776 + 2.42219i −0.327732 + 0.988854i
\(7\) 3.34791 + 1.93291i 1.26539 + 0.730573i 0.974112 0.226066i \(-0.0725864\pi\)
0.291278 + 0.956639i \(0.405920\pi\)
\(8\) 2.69535i 0.952950i
\(9\) −2.75478 + 1.18793i −0.918260 + 0.395977i
\(10\) 0 0
\(11\) −0.130139 + 0.225407i −0.0392384 + 0.0679628i −0.884978 0.465634i \(-0.845826\pi\)
0.845739 + 0.533596i \(0.179160\pi\)
\(12\) −0.220591 + 0.196287i −0.0636792 + 0.0566633i
\(13\) −3.53235 + 2.03940i −0.979697 + 0.565629i −0.902179 0.431362i \(-0.858033\pi\)
−0.0775187 + 0.996991i \(0.524700\pi\)
\(14\) 2.84768 + 4.93232i 0.761073 + 1.31822i
\(15\) 0 0
\(16\) 2.15595 3.73421i 0.538987 0.933553i
\(17\) 3.26028i 0.790734i −0.918523 0.395367i \(-0.870617\pi\)
0.918523 0.395367i \(-0.129383\pi\)
\(18\) −4.38982 0.513594i −1.03469 0.121055i
\(19\) −4.24928 −0.974853 −0.487426 0.873164i \(-0.662064\pi\)
−0.487426 + 0.873164i \(0.662064\pi\)
\(20\) 0 0
\(21\) −2.10649 + 6.35583i −0.459673 + 1.38696i
\(22\) −0.332082 + 0.191728i −0.0708002 + 0.0408765i
\(23\) 7.53039 4.34768i 1.57020 0.906553i 0.574052 0.818819i \(-0.305371\pi\)
0.996144 0.0877339i \(-0.0279625\pi\)
\(24\) 4.57209 0.943794i 0.933274 0.192651i
\(25\) 0 0
\(26\) −6.00912 −1.17849
\(27\) −2.97968 4.25694i −0.573439 0.819248i
\(28\) 0.659042i 0.124547i
\(29\) 2.11105 3.65644i 0.392012 0.678984i −0.600703 0.799472i \(-0.705113\pi\)
0.992715 + 0.120488i \(0.0384459\pi\)
\(30\) 0 0
\(31\) −1.32643 2.29744i −0.238233 0.412632i 0.721974 0.691920i \(-0.243235\pi\)
−0.960207 + 0.279288i \(0.909902\pi\)
\(32\) 0.832959 0.480909i 0.147248 0.0850135i
\(33\) −0.427924 0.141825i −0.0744921 0.0246886i
\(34\) 2.40161 4.15971i 0.411873 0.713384i
\(35\) 0 0
\(36\) −0.410201 0.305455i −0.0683668 0.0509091i
\(37\) 2.27559i 0.374104i 0.982350 + 0.187052i \(0.0598933\pi\)
−0.982350 + 0.187052i \(0.940107\pi\)
\(38\) −5.42156 3.13014i −0.879493 0.507776i
\(39\) −4.69629 5.27777i −0.752008 0.845120i
\(40\) 0 0
\(41\) −2.82093 4.88599i −0.440555 0.763064i 0.557176 0.830395i \(-0.311885\pi\)
−0.997731 + 0.0673308i \(0.978552\pi\)
\(42\) −7.36950 + 6.55756i −1.13714 + 1.01185i
\(43\) 7.85712 + 4.53631i 1.19820 + 0.691780i 0.960153 0.279474i \(-0.0901599\pi\)
0.238046 + 0.971254i \(0.423493\pi\)
\(44\) −0.0443719 −0.00668931
\(45\) 0 0
\(46\) 12.8105 1.88880
\(47\) −1.23745 0.714441i −0.180500 0.104212i 0.407027 0.913416i \(-0.366565\pi\)
−0.587528 + 0.809204i \(0.699899\pi\)
\(48\) 7.08921 + 2.34955i 1.02324 + 0.339128i
\(49\) 3.97232 + 6.88026i 0.567474 + 0.982894i
\(50\) 0 0
\(51\) 5.53037 1.14161i 0.774406 0.159857i
\(52\) −0.602191 0.347675i −0.0835089 0.0482139i
\(53\) 11.3816i 1.56338i 0.623667 + 0.781690i \(0.285642\pi\)
−0.623667 + 0.781690i \(0.714358\pi\)
\(54\) −0.665919 7.62624i −0.0906201 1.03780i
\(55\) 0 0
\(56\) 5.20988 9.02378i 0.696200 1.20585i
\(57\) −1.48791 7.20801i −0.197079 0.954724i
\(58\) 5.38687 3.11011i 0.707331 0.408378i
\(59\) −3.56212 6.16977i −0.463748 0.803235i 0.535396 0.844601i \(-0.320162\pi\)
−0.999144 + 0.0413660i \(0.986829\pi\)
\(60\) 0 0
\(61\) −1.26244 + 2.18660i −0.161638 + 0.279966i −0.935456 0.353442i \(-0.885011\pi\)
0.773818 + 0.633408i \(0.218344\pi\)
\(62\) 3.90833i 0.496358i
\(63\) −11.5189 1.34768i −1.45125 0.169791i
\(64\) −7.20679 −0.900848
\(65\) 0 0
\(66\) −0.441506 0.496172i −0.0543456 0.0610746i
\(67\) −9.77361 + 5.64280i −1.19404 + 0.689377i −0.959219 0.282662i \(-0.908782\pi\)
−0.234817 + 0.972040i \(0.575449\pi\)
\(68\) 0.481344 0.277904i 0.0583716 0.0337008i
\(69\) 10.0117 + 11.2513i 1.20527 + 1.35450i
\(70\) 0 0
\(71\) −8.38158 −0.994711 −0.497355 0.867547i \(-0.665695\pi\)
−0.497355 + 0.867547i \(0.665695\pi\)
\(72\) 3.20189 + 7.42510i 0.377346 + 0.875056i
\(73\) 0.403568i 0.0472340i 0.999721 + 0.0236170i \(0.00751823\pi\)
−0.999721 + 0.0236170i \(0.992482\pi\)
\(74\) −1.67626 + 2.90337i −0.194861 + 0.337509i
\(75\) 0 0
\(76\) −0.362207 0.627360i −0.0415480 0.0719632i
\(77\) −0.871386 + 0.503095i −0.0993036 + 0.0573330i
\(78\) −2.10413 10.1932i −0.238246 1.15415i
\(79\) −1.52125 + 2.63488i −0.171154 + 0.296447i −0.938824 0.344399i \(-0.888083\pi\)
0.767670 + 0.640846i \(0.221416\pi\)
\(80\) 0 0
\(81\) 6.17764 6.54498i 0.686404 0.727220i
\(82\) 8.31189i 0.917895i
\(83\) −3.96660 2.29012i −0.435391 0.251373i 0.266250 0.963904i \(-0.414215\pi\)
−0.701641 + 0.712531i \(0.747549\pi\)
\(84\) −1.11792 + 0.230768i −0.121976 + 0.0251788i
\(85\) 0 0
\(86\) 6.68314 + 11.5755i 0.720661 + 1.24822i
\(87\) 6.94157 + 2.30062i 0.744215 + 0.246652i
\(88\) 0.607551 + 0.350770i 0.0647652 + 0.0373922i
\(89\) −7.17772 −0.760837 −0.380419 0.924814i \(-0.624220\pi\)
−0.380419 + 0.924814i \(0.624220\pi\)
\(90\) 0 0
\(91\) −15.7680 −1.65293
\(92\) 1.28377 + 0.741187i 0.133843 + 0.0772741i
\(93\) 3.43266 3.05446i 0.355950 0.316733i
\(94\) −1.05255 1.82308i −0.108563 0.188036i
\(95\) 0 0
\(96\) 1.10743 + 1.24454i 0.113026 + 0.127021i
\(97\) 2.69777 + 1.55756i 0.273917 + 0.158146i 0.630666 0.776054i \(-0.282782\pi\)
−0.356749 + 0.934200i \(0.616115\pi\)
\(98\) 11.7045i 1.18233i
\(99\) 0.0907360 0.775544i 0.00911931 0.0779451i
\(100\) 0 0
\(101\) −1.92286 + 3.33049i −0.191332 + 0.331396i −0.945692 0.325065i \(-0.894614\pi\)
0.754360 + 0.656461i \(0.227947\pi\)
\(102\) 7.89700 + 2.61727i 0.781920 + 0.259149i
\(103\) −3.64318 + 2.10339i −0.358974 + 0.207254i −0.668630 0.743595i \(-0.733119\pi\)
0.309657 + 0.950848i \(0.399786\pi\)
\(104\) 5.49691 + 9.52092i 0.539016 + 0.933603i
\(105\) 0 0
\(106\) −8.38398 + 14.5215i −0.814324 + 1.41045i
\(107\) 1.62655i 0.157245i 0.996904 + 0.0786223i \(0.0250521\pi\)
−0.996904 + 0.0786223i \(0.974948\pi\)
\(108\) 0.374504 0.802776i 0.0360367 0.0772471i
\(109\) 12.9021 1.23580 0.617900 0.786256i \(-0.287984\pi\)
0.617900 + 0.786256i \(0.287984\pi\)
\(110\) 0 0
\(111\) −3.86005 + 0.796811i −0.366380 + 0.0756299i
\(112\) 14.4358 8.33452i 1.36406 0.787539i
\(113\) 1.15102 0.664539i 0.108278 0.0625146i −0.444883 0.895589i \(-0.646755\pi\)
0.553161 + 0.833074i \(0.313421\pi\)
\(114\) 3.41122 10.2926i 0.319490 0.963987i
\(115\) 0 0
\(116\) 0.719778 0.0668297
\(117\) 7.30818 9.81430i 0.675641 0.907332i
\(118\) 10.4958i 0.966217i
\(119\) 6.30184 10.9151i 0.577689 1.00059i
\(120\) 0 0
\(121\) 5.46613 + 9.46761i 0.496921 + 0.860692i
\(122\) −3.22142 + 1.85989i −0.291654 + 0.168386i
\(123\) 7.30028 6.49597i 0.658244 0.585722i
\(124\) 0.226128 0.391665i 0.0203069 0.0351725i
\(125\) 0 0
\(126\) −13.7040 10.2046i −1.22085 0.909099i
\(127\) 1.65285i 0.146667i 0.997307 + 0.0733335i \(0.0233637\pi\)
−0.997307 + 0.0733335i \(0.976636\pi\)
\(128\) −10.8609 6.27053i −0.959975 0.554242i
\(129\) −4.94366 + 14.9163i −0.435265 + 1.31331i
\(130\) 0 0
\(131\) 6.58886 + 11.4122i 0.575672 + 0.997092i 0.995968 + 0.0897057i \(0.0285926\pi\)
−0.420297 + 0.907387i \(0.638074\pi\)
\(132\) −0.0155371 0.0752675i −0.00135233 0.00655119i
\(133\) −14.2262 8.21350i −1.23357 0.712201i
\(134\) −16.6266 −1.43632
\(135\) 0 0
\(136\) −8.78759 −0.753530
\(137\) 17.5741 + 10.1464i 1.50146 + 0.866867i 0.999999 + 0.00168578i \(0.000536601\pi\)
0.501459 + 0.865181i \(0.332797\pi\)
\(138\) 4.48566 + 21.7302i 0.381845 + 1.84980i
\(139\) 1.53440 + 2.65766i 0.130146 + 0.225420i 0.923733 0.383038i \(-0.125122\pi\)
−0.793587 + 0.608457i \(0.791789\pi\)
\(140\) 0 0
\(141\) 0.778597 2.34923i 0.0655697 0.197841i
\(142\) −10.6939 6.17410i −0.897409 0.518119i
\(143\) 1.06162i 0.0887774i
\(144\) −1.50318 + 12.8480i −0.125265 + 1.07067i
\(145\) 0 0
\(146\) −0.297279 + 0.514902i −0.0246030 + 0.0426136i
\(147\) −10.2800 + 9.14736i −0.847877 + 0.754461i
\(148\) −0.335965 + 0.193970i −0.0276162 + 0.0159442i
\(149\) 2.03081 + 3.51747i 0.166371 + 0.288162i 0.937141 0.348951i \(-0.113462\pi\)
−0.770771 + 0.637113i \(0.780129\pi\)
\(150\) 0 0
\(151\) 6.80994 11.7952i 0.554185 0.959876i −0.443782 0.896135i \(-0.646363\pi\)
0.997966 0.0637412i \(-0.0203032\pi\)
\(152\) 11.4533i 0.928986i
\(153\) 3.87299 + 8.98135i 0.313112 + 0.726099i
\(154\) −1.48237 −0.119453
\(155\) 0 0
\(156\) 0.378896 1.14323i 0.0303360 0.0915316i
\(157\) −1.78627 + 1.03131i −0.142560 + 0.0823071i −0.569584 0.821933i \(-0.692896\pi\)
0.427023 + 0.904241i \(0.359562\pi\)
\(158\) −3.88185 + 2.24119i −0.308823 + 0.178299i
\(159\) −19.3064 + 3.98533i −1.53110 + 0.316057i
\(160\) 0 0
\(161\) 33.6147 2.64921
\(162\) 12.7031 3.79996i 0.998051 0.298553i
\(163\) 3.50525i 0.274552i −0.990533 0.137276i \(-0.956165\pi\)
0.990533 0.137276i \(-0.0438347\pi\)
\(164\) 0.480909 0.832959i 0.0375527 0.0650431i
\(165\) 0 0
\(166\) −3.37393 5.84381i −0.261868 0.453568i
\(167\) −17.7837 + 10.2674i −1.37615 + 0.794518i −0.991693 0.128626i \(-0.958943\pi\)
−0.384453 + 0.923145i \(0.625610\pi\)
\(168\) 17.1312 + 5.67772i 1.32170 + 0.438046i
\(169\) 1.81833 3.14944i 0.139871 0.242264i
\(170\) 0 0
\(171\) 11.7058 5.04786i 0.895169 0.386019i
\(172\) 1.54669i 0.117934i
\(173\) 6.71323 + 3.87589i 0.510397 + 0.294678i 0.732997 0.680232i \(-0.238121\pi\)
−0.222600 + 0.974910i \(0.571454\pi\)
\(174\) 7.16189 + 8.04865i 0.542941 + 0.610167i
\(175\) 0 0
\(176\) 0.561145 + 0.971932i 0.0422979 + 0.0732622i
\(177\) 9.21840 8.20275i 0.692897 0.616557i
\(178\) −9.15788 5.28731i −0.686412 0.396300i
\(179\) 10.7632 0.804477 0.402238 0.915535i \(-0.368232\pi\)
0.402238 + 0.915535i \(0.368232\pi\)
\(180\) 0 0
\(181\) −7.84572 −0.583168 −0.291584 0.956545i \(-0.594182\pi\)
−0.291584 + 0.956545i \(0.594182\pi\)
\(182\) −20.1180 11.6151i −1.49124 0.860970i
\(183\) −4.15116 1.37580i −0.306862 0.101702i
\(184\) −11.7185 20.2970i −0.863900 1.49632i
\(185\) 0 0
\(186\) 6.62965 1.36852i 0.486109 0.100345i
\(187\) 0.734890 + 0.424289i 0.0537405 + 0.0310271i
\(188\) 0.243594i 0.0177659i
\(189\) −1.74738 20.0113i −0.127103 1.45561i
\(190\) 0 0
\(191\) 2.86627 4.96453i 0.207396 0.359221i −0.743497 0.668739i \(-0.766834\pi\)
0.950894 + 0.309518i \(0.100168\pi\)
\(192\) −2.52350 12.2248i −0.182118 0.882248i
\(193\) −7.34595 + 4.24119i −0.528773 + 0.305287i −0.740517 0.672038i \(-0.765419\pi\)
0.211744 + 0.977325i \(0.432086\pi\)
\(194\) 2.29468 + 3.97450i 0.164748 + 0.285352i
\(195\) 0 0
\(196\) −0.677196 + 1.17294i −0.0483712 + 0.0837813i
\(197\) 10.6266i 0.757110i −0.925579 0.378555i \(-0.876421\pi\)
0.925579 0.378555i \(-0.123579\pi\)
\(198\) 0.687055 0.922659i 0.0488268 0.0655705i
\(199\) 18.5784 1.31699 0.658495 0.752585i \(-0.271193\pi\)
0.658495 + 0.752585i \(0.271193\pi\)
\(200\) 0 0
\(201\) −12.9941 14.6030i −0.916533 1.03002i
\(202\) −4.90666 + 2.83286i −0.345231 + 0.199319i
\(203\) 14.1352 8.16095i 0.992095 0.572786i
\(204\) 0.639951 + 0.719188i 0.0448055 + 0.0503533i
\(205\) 0 0
\(206\) −6.19767 −0.431812
\(207\) −15.5799 + 20.9225i −1.08287 + 1.45421i
\(208\) 17.5874i 1.21947i
\(209\) 0.552997 0.957820i 0.0382516 0.0662538i
\(210\) 0 0
\(211\) −5.22666 9.05283i −0.359818 0.623223i 0.628112 0.778123i \(-0.283828\pi\)
−0.987930 + 0.154900i \(0.950494\pi\)
\(212\) −1.68037 + 0.970160i −0.115408 + 0.0666308i
\(213\) −2.93486 14.2176i −0.201093 0.974172i
\(214\) −1.19816 + 2.07528i −0.0819046 + 0.141863i
\(215\) 0 0
\(216\) −11.4739 + 8.03127i −0.780703 + 0.546459i
\(217\) 10.2555i 0.696187i
\(218\) 16.4615 + 9.50407i 1.11492 + 0.643697i
\(219\) −0.684567 + 0.141312i −0.0462587 + 0.00954896i
\(220\) 0 0
\(221\) 6.64902 + 11.5164i 0.447261 + 0.774680i
\(222\) −5.51190 1.82679i −0.369934 0.122606i
\(223\) −3.40452 1.96560i −0.227983 0.131626i 0.381658 0.924304i \(-0.375353\pi\)
−0.609641 + 0.792677i \(0.708687\pi\)
\(224\) 3.71822 0.248434
\(225\) 0 0
\(226\) 1.95807 0.130249
\(227\) 4.18411 + 2.41570i 0.277709 + 0.160335i 0.632386 0.774654i \(-0.282076\pi\)
−0.354677 + 0.934989i \(0.615409\pi\)
\(228\) 0.937354 0.834081i 0.0620778 0.0552383i
\(229\) −9.42648 16.3271i −0.622919 1.07893i −0.988939 0.148321i \(-0.952613\pi\)
0.366020 0.930607i \(-0.380720\pi\)
\(230\) 0 0
\(231\) −1.15851 1.30196i −0.0762247 0.0856626i
\(232\) −9.85539 5.69001i −0.647038 0.373568i
\(233\) 11.9021i 0.779735i −0.920871 0.389867i \(-0.872521\pi\)
0.920871 0.389867i \(-0.127479\pi\)
\(234\) 16.5538 7.13842i 1.08216 0.466653i
\(235\) 0 0
\(236\) 0.607266 1.05181i 0.0395296 0.0684673i
\(237\) −5.00219 1.65786i −0.324927 0.107689i
\(238\) 16.0807 9.28421i 1.04236 0.601806i
\(239\) −10.8147 18.7317i −0.699547 1.21165i −0.968624 0.248533i \(-0.920052\pi\)
0.269076 0.963119i \(-0.413282\pi\)
\(240\) 0 0
\(241\) −1.94916 + 3.37604i −0.125556 + 0.217470i −0.921950 0.387308i \(-0.873405\pi\)
0.796394 + 0.604778i \(0.206738\pi\)
\(242\) 16.1060i 1.03533i
\(243\) 13.2653 + 8.18729i 0.850970 + 0.525215i
\(244\) −0.430437 −0.0275559
\(245\) 0 0
\(246\) 14.0994 2.91046i 0.898942 0.185564i
\(247\) 15.0100 8.66600i 0.955061 0.551405i
\(248\) −6.19240 + 3.57518i −0.393218 + 0.227024i
\(249\) 2.49577 7.53039i 0.158163 0.477219i
\(250\) 0 0
\(251\) −30.1033 −1.90010 −0.950052 0.312092i \(-0.898970\pi\)
−0.950052 + 0.312092i \(0.898970\pi\)
\(252\) −0.782897 1.81552i −0.0493179 0.114367i
\(253\) 2.26321i 0.142287i
\(254\) −1.21754 + 2.10883i −0.0763950 + 0.132320i
\(255\) 0 0
\(256\) −2.03131 3.51832i −0.126957 0.219895i
\(257\) 14.2151 8.20707i 0.886711 0.511943i 0.0138459 0.999904i \(-0.495593\pi\)
0.872865 + 0.487961i \(0.162259\pi\)
\(258\) −17.2953 + 15.3898i −1.07676 + 0.958125i
\(259\) −4.39851 + 7.61845i −0.273310 + 0.473388i
\(260\) 0 0
\(261\) −1.47187 + 12.5805i −0.0911067 + 0.778712i
\(262\) 19.4141i 1.19941i
\(263\) −22.3497 12.9036i −1.37814 0.795670i −0.386206 0.922413i \(-0.626214\pi\)
−0.991936 + 0.126743i \(0.959548\pi\)
\(264\) −0.382269 + 1.15341i −0.0235270 + 0.0709872i
\(265\) 0 0
\(266\) −12.1006 20.9588i −0.741934 1.28507i
\(267\) −2.51332 12.1755i −0.153813 0.745127i
\(268\) −1.66619 0.961978i −0.101779 0.0587621i
\(269\) 12.5206 0.763392 0.381696 0.924288i \(-0.375340\pi\)
0.381696 + 0.924288i \(0.375340\pi\)
\(270\) 0 0
\(271\) 19.6462 1.19342 0.596710 0.802457i \(-0.296474\pi\)
0.596710 + 0.802457i \(0.296474\pi\)
\(272\) −12.1746 7.02899i −0.738191 0.426195i
\(273\) −5.52125 26.7470i −0.334161 1.61880i
\(274\) 14.9483 + 25.8911i 0.903057 + 1.56414i
\(275\) 0 0
\(276\) −0.807745 + 2.43718i −0.0486205 + 0.146701i
\(277\) −18.0394 10.4150i −1.08388 0.625779i −0.151941 0.988390i \(-0.548552\pi\)
−0.931941 + 0.362610i \(0.881886\pi\)
\(278\) 4.52112i 0.271159i
\(279\) 6.38321 + 4.75324i 0.382153 + 0.284569i
\(280\) 0 0
\(281\) −2.36221 + 4.09146i −0.140917 + 0.244076i −0.927842 0.372973i \(-0.878339\pi\)
0.786925 + 0.617049i \(0.211672\pi\)
\(282\) 2.72390 2.42380i 0.162206 0.144335i
\(283\) 20.0506 11.5762i 1.19189 0.688136i 0.233152 0.972440i \(-0.425096\pi\)
0.958734 + 0.284304i \(0.0917626\pi\)
\(284\) −0.714441 1.23745i −0.0423943 0.0734291i
\(285\) 0 0
\(286\) 0.782020 1.35450i 0.0462418 0.0800932i
\(287\) 21.8105i 1.28743i
\(288\) −1.72333 + 2.31430i −0.101548 + 0.136371i
\(289\) 6.37059 0.374740
\(290\) 0 0
\(291\) −1.69742 + 5.12158i −0.0995048 + 0.300232i
\(292\) −0.0595824 + 0.0343999i −0.00348679 + 0.00201310i
\(293\) −14.6179 + 8.43963i −0.853985 + 0.493049i −0.861993 0.506919i \(-0.830784\pi\)
0.00800832 + 0.999968i \(0.497451\pi\)
\(294\) −19.8541 + 4.09839i −1.15792 + 0.239023i
\(295\) 0 0
\(296\) 6.13350 0.356503
\(297\) 1.34732 0.117647i 0.0781792 0.00682657i
\(298\) 5.98380i 0.346632i
\(299\) −17.7333 + 30.7150i −1.02554 + 1.77630i
\(300\) 0 0
\(301\) 17.5366 + 30.3743i 1.01079 + 1.75074i
\(302\) 17.3773 10.0328i 0.999949 0.577321i
\(303\) −6.32277 2.09553i −0.363233 0.120385i
\(304\) −9.16123 + 15.8677i −0.525433 + 0.910076i
\(305\) 0 0
\(306\) −1.67446 + 14.3120i −0.0957225 + 0.818165i
\(307\) 22.7177i 1.29657i 0.761398 + 0.648285i \(0.224513\pi\)
−0.761398 + 0.648285i \(0.775487\pi\)
\(308\) −0.148553 0.0857671i −0.00846459 0.00488703i
\(309\) −4.84364 5.44337i −0.275545 0.309663i
\(310\) 0 0
\(311\) −15.7968 27.3608i −0.895754 1.55149i −0.832869 0.553470i \(-0.813303\pi\)
−0.0628843 0.998021i \(-0.520030\pi\)
\(312\) −14.2254 + 12.6581i −0.805357 + 0.716626i
\(313\) 26.4134 + 15.2498i 1.49298 + 0.861970i 0.999968 0.00805392i \(-0.00256367\pi\)
0.493009 + 0.870024i \(0.335897\pi\)
\(314\) −3.03875 −0.171487
\(315\) 0 0
\(316\) −0.518682 −0.0291781
\(317\) 19.1296 + 11.0445i 1.07443 + 0.620320i 0.929387 0.369106i \(-0.120336\pi\)
0.145039 + 0.989426i \(0.453669\pi\)
\(318\) −27.5683 9.13686i −1.54595 0.512369i
\(319\) 0.549459 + 0.951691i 0.0307638 + 0.0532845i
\(320\) 0 0
\(321\) −2.75910 + 0.569547i −0.153998 + 0.0317890i
\(322\) 42.8882 + 24.7615i 2.39007 + 1.37991i
\(323\) 13.8538i 0.770849i
\(324\) 1.49287 + 0.354170i 0.0829374 + 0.0196761i
\(325\) 0 0
\(326\) 2.58206 4.47226i 0.143007 0.247696i
\(327\) 4.51776 + 21.8857i 0.249833 + 1.21028i
\(328\) −13.1695 + 7.60339i −0.727162 + 0.419827i
\(329\) −2.76191 4.78377i −0.152269 0.263738i
\(330\) 0 0
\(331\) 14.8024 25.6385i 0.813612 1.40922i −0.0967089 0.995313i \(-0.530832\pi\)
0.910321 0.413904i \(-0.135835\pi\)
\(332\) 0.780834i 0.0428538i
\(333\) −2.70324 6.26874i −0.148137 0.343525i
\(334\) −30.2531 −1.65538
\(335\) 0 0
\(336\) 19.1925 + 21.5689i 1.04704 + 1.17668i
\(337\) −10.8522 + 6.26553i −0.591158 + 0.341305i −0.765555 0.643370i \(-0.777536\pi\)
0.174397 + 0.984675i \(0.444202\pi\)
\(338\) 4.63992 2.67886i 0.252379 0.145711i
\(339\) 1.53028 + 1.71976i 0.0831136 + 0.0934045i
\(340\) 0 0
\(341\) 0.690479 0.0373915
\(342\) 18.6536 + 2.18241i 1.00867 + 0.118011i
\(343\) 3.65180i 0.197179i
\(344\) 12.2269 21.1777i 0.659232 1.14182i
\(345\) 0 0
\(346\) 5.71017 + 9.89030i 0.306980 + 0.531706i
\(347\) 14.8068 8.54872i 0.794872 0.458919i −0.0468031 0.998904i \(-0.514903\pi\)
0.841675 + 0.539985i \(0.181570\pi\)
\(348\) 0.252035 + 1.22095i 0.0135105 + 0.0654498i
\(349\) −9.20231 + 15.9389i −0.492588 + 0.853188i −0.999964 0.00853709i \(-0.997283\pi\)
0.507375 + 0.861725i \(0.330616\pi\)
\(350\) 0 0
\(351\) 19.2069 + 8.96024i 1.02519 + 0.478262i
\(352\) 0.250340i 0.0133432i
\(353\) 27.4693 + 15.8594i 1.46204 + 0.844110i 0.999106 0.0422810i \(-0.0134625\pi\)
0.462936 + 0.886391i \(0.346796\pi\)
\(354\) 17.8039 3.67517i 0.946267 0.195333i
\(355\) 0 0
\(356\) −0.611825 1.05971i −0.0324267 0.0561646i
\(357\) 20.7218 + 6.86774i 1.09671 + 0.363479i
\(358\) 13.7325 + 7.92844i 0.725783 + 0.419031i
\(359\) 11.4533 0.604483 0.302241 0.953231i \(-0.402265\pi\)
0.302241 + 0.953231i \(0.402265\pi\)
\(360\) 0 0
\(361\) −0.943580 −0.0496621
\(362\) −10.0102 5.77937i −0.526122 0.303757i
\(363\) −14.1458 + 12.5873i −0.742461 + 0.660660i
\(364\) −1.34405 2.32797i −0.0704475 0.122019i
\(365\) 0 0
\(366\) −4.28291 4.81321i −0.223871 0.251590i
\(367\) 2.15846 + 1.24619i 0.112671 + 0.0650506i 0.555276 0.831666i \(-0.312612\pi\)
−0.442606 + 0.896716i \(0.645946\pi\)
\(368\) 37.4934i 1.95448i
\(369\) 13.5753 + 10.1088i 0.706700 + 0.526242i
\(370\) 0 0
\(371\) −21.9996 + 38.1045i −1.14216 + 1.97829i
\(372\) 0.743556 + 0.246434i 0.0385516 + 0.0127770i
\(373\) −13.0227 + 7.51868i −0.674292 + 0.389303i −0.797701 0.603053i \(-0.793951\pi\)
0.123409 + 0.992356i \(0.460617\pi\)
\(374\) 0.625086 + 1.08268i 0.0323224 + 0.0559841i
\(375\) 0 0
\(376\) −1.92567 + 3.33536i −0.0993088 + 0.172008i
\(377\) 17.2211i 0.886932i
\(378\) 12.5114 26.8191i 0.643518 1.37943i
\(379\) −6.27273 −0.322208 −0.161104 0.986937i \(-0.551505\pi\)
−0.161104 + 0.986937i \(0.551505\pi\)
\(380\) 0 0
\(381\) −2.80371 + 0.578757i −0.143639 + 0.0296506i
\(382\) 7.31402 4.22275i 0.374218 0.216055i
\(383\) −19.2161 + 11.0944i −0.981894 + 0.566897i −0.902842 0.429973i \(-0.858523\pi\)
−0.0790528 + 0.996870i \(0.525190\pi\)
\(384\) 6.83362 20.6188i 0.348727 1.05220i
\(385\) 0 0
\(386\) −12.4967 −0.636065
\(387\) −27.0335 3.16282i −1.37419 0.160775i
\(388\) 0.531061i 0.0269605i
\(389\) −15.0461 + 26.0606i −0.762869 + 1.32133i 0.178498 + 0.983940i \(0.442876\pi\)
−0.941366 + 0.337387i \(0.890457\pi\)
\(390\) 0 0
\(391\) −14.1746 24.5512i −0.716842 1.24161i
\(392\) 18.5447 10.7068i 0.936649 0.540774i
\(393\) −17.0513 + 15.1727i −0.860125 + 0.765360i
\(394\) 7.82781 13.5582i 0.394359 0.683050i
\(395\) 0 0
\(396\) 0.122235 0.0527107i 0.00614253 0.00264881i
\(397\) 29.2313i 1.46708i −0.679648 0.733538i \(-0.737868\pi\)
0.679648 0.733538i \(-0.262132\pi\)
\(398\) 23.7038 + 13.6854i 1.18816 + 0.685986i
\(399\) 8.95107 27.0077i 0.448114 1.35208i
\(400\) 0 0
\(401\) −12.1171 20.9874i −0.605098 1.04806i −0.992036 0.125954i \(-0.959801\pi\)
0.386938 0.922106i \(-0.373533\pi\)
\(402\) −5.82189 28.2034i −0.290369 1.40666i
\(403\) 9.37080 + 5.41024i 0.466793 + 0.269503i
\(404\) −0.655614 −0.0326180
\(405\) 0 0
\(406\) 24.0463 1.19340
\(407\) −0.512934 0.296142i −0.0254252 0.0146792i
\(408\) −3.07703 14.9063i −0.152336 0.737971i
\(409\) 1.16995 + 2.02642i 0.0578504 + 0.100200i 0.893500 0.449063i \(-0.148242\pi\)
−0.835650 + 0.549263i \(0.814909\pi\)
\(410\) 0 0
\(411\) −11.0576 + 33.3636i −0.545429 + 1.64570i
\(412\) −0.621086 0.358584i −0.0305987 0.0176662i
\(413\) 27.5411i 1.35521i
\(414\) −35.2900 + 15.2179i −1.73441 + 0.747921i
\(415\) 0 0
\(416\) −1.96153 + 3.39748i −0.0961721 + 0.166575i
\(417\) −3.97087 + 3.53338i −0.194454 + 0.173030i
\(418\) 1.41111 0.814706i 0.0690197 0.0398486i
\(419\) 11.4212 + 19.7821i 0.557964 + 0.966421i 0.997666 + 0.0682778i \(0.0217504\pi\)
−0.439703 + 0.898143i \(0.644916\pi\)
\(420\) 0 0
\(421\) −5.93792 + 10.2848i −0.289396 + 0.501249i −0.973666 0.227980i \(-0.926788\pi\)
0.684269 + 0.729229i \(0.260121\pi\)
\(422\) 15.4004i 0.749679i
\(423\) 4.25761 + 0.498126i 0.207012 + 0.0242197i
\(424\) 30.6773 1.48982
\(425\) 0 0
\(426\) 6.72853 20.3018i 0.325998 0.983623i
\(427\) −8.45303 + 4.88036i −0.409071 + 0.236177i
\(428\) −0.240142 + 0.138646i −0.0116077 + 0.00670172i
\(429\) 1.80082 0.371734i 0.0869443 0.0179475i
\(430\) 0 0
\(431\) 8.86916 0.427212 0.213606 0.976920i \(-0.431479\pi\)
0.213606 + 0.976920i \(0.431479\pi\)
\(432\) −22.3203 + 1.94900i −1.07389 + 0.0937713i
\(433\) 9.37059i 0.450322i 0.974322 + 0.225161i \(0.0722908\pi\)
−0.974322 + 0.225161i \(0.927709\pi\)
\(434\) 7.55446 13.0847i 0.362626 0.628086i
\(435\) 0 0
\(436\) 1.09977 + 1.90486i 0.0526695 + 0.0912262i
\(437\) −31.9988 + 18.4745i −1.53071 + 0.883756i
\(438\) −0.977517 0.323974i −0.0467075 0.0154801i
\(439\) 9.71155 16.8209i 0.463507 0.802817i −0.535626 0.844455i \(-0.679924\pi\)
0.999133 + 0.0416380i \(0.0132576\pi\)
\(440\) 0 0
\(441\) −19.1161 14.2348i −0.910292 0.677846i
\(442\) 19.5914i 0.931868i
\(443\) −9.42172 5.43963i −0.447639 0.258445i 0.259193 0.965825i \(-0.416543\pi\)
−0.706833 + 0.707381i \(0.749877\pi\)
\(444\) −0.446669 0.501974i −0.0211980 0.0238226i
\(445\) 0 0
\(446\) −2.89583 5.01572i −0.137121 0.237501i
\(447\) −5.25554 + 4.67650i −0.248578 + 0.221191i
\(448\) −24.1276 13.9301i −1.13992 0.658136i
\(449\) −1.34014 −0.0632451 −0.0316225 0.999500i \(-0.510067\pi\)
−0.0316225 + 0.999500i \(0.510067\pi\)
\(450\) 0 0
\(451\) 1.46845 0.0691467
\(452\) 0.196224 + 0.113290i 0.00922959 + 0.00532871i
\(453\) 22.3925 + 7.42146i 1.05209 + 0.348691i
\(454\) 3.55894 + 6.16426i 0.167029 + 0.289303i
\(455\) 0 0
\(456\) −19.4281 + 4.01045i −0.909804 + 0.187806i
\(457\) 17.4169 + 10.0556i 0.814728 + 0.470383i 0.848595 0.529043i \(-0.177449\pi\)
−0.0338671 + 0.999426i \(0.510782\pi\)
\(458\) 27.7752i 1.29785i
\(459\) −13.8788 + 9.71457i −0.647807 + 0.453437i
\(460\) 0 0
\(461\) 16.8766 29.2312i 0.786024 1.36143i −0.142362 0.989815i \(-0.545470\pi\)
0.928386 0.371618i \(-0.121197\pi\)
\(462\) −0.519062 2.51453i −0.0241490 0.116987i
\(463\) −4.54262 + 2.62268i −0.211114 + 0.121886i −0.601829 0.798625i \(-0.705561\pi\)
0.390715 + 0.920512i \(0.372228\pi\)
\(464\) −9.10262 15.7662i −0.422578 0.731927i
\(465\) 0 0
\(466\) 8.76744 15.1856i 0.406144 0.703462i
\(467\) 14.2120i 0.657652i −0.944390 0.328826i \(-0.893347\pi\)
0.944390 0.328826i \(-0.106653\pi\)
\(468\) 2.07192 + 0.242408i 0.0957745 + 0.0112053i
\(469\) −43.6282 −2.01456
\(470\) 0 0
\(471\) −2.37486 2.66891i −0.109428 0.122977i
\(472\) −16.6297 + 9.60115i −0.765443 + 0.441929i
\(473\) −2.04503 + 1.18070i −0.0940307 + 0.0542887i
\(474\) −5.16095 5.79997i −0.237050 0.266401i
\(475\) 0 0
\(476\) 2.14866 0.0984837
\(477\) −13.5205 31.3538i −0.619063 1.43559i
\(478\) 31.8657i 1.45750i
\(479\) 10.2417 17.7391i 0.467954 0.810519i −0.531376 0.847136i \(-0.678325\pi\)
0.999329 + 0.0366168i \(0.0116581\pi\)
\(480\) 0 0
\(481\) −4.64084 8.03817i −0.211604 0.366509i
\(482\) −4.97377 + 2.87161i −0.226549 + 0.130798i
\(483\) 11.7704 + 57.0203i 0.535572 + 2.59451i
\(484\) −0.931859 + 1.61403i −0.0423572 + 0.0733649i
\(485\) 0 0
\(486\) 10.8939 + 20.2175i 0.494158 + 0.917087i
\(487\) 31.3554i 1.42085i −0.703772 0.710425i \(-0.748503\pi\)
0.703772 0.710425i \(-0.251497\pi\)
\(488\) 5.89366 + 3.40271i 0.266793 + 0.154033i
\(489\) 5.94591 1.22738i 0.268883 0.0555042i
\(490\) 0 0
\(491\) 5.19604 + 8.99980i 0.234494 + 0.406155i 0.959125 0.282981i \(-0.0913234\pi\)
−0.724632 + 0.689136i \(0.757990\pi\)
\(492\) 1.58133 + 0.524094i 0.0712919 + 0.0236280i
\(493\) −11.9210 6.88260i −0.536896 0.309977i
\(494\) 25.5345 1.14885
\(495\) 0 0
\(496\) −11.4388 −0.513618
\(497\) −28.0607 16.2009i −1.25870 0.726709i
\(498\) 8.73138 7.76940i 0.391263 0.348155i
\(499\) −1.91285 3.31316i −0.0856310 0.148317i 0.820029 0.572322i \(-0.193957\pi\)
−0.905660 + 0.424005i \(0.860624\pi\)
\(500\) 0 0
\(501\) −23.6436 26.5711i −1.05632 1.18711i
\(502\) −38.4081 22.1749i −1.71424 0.989715i
\(503\) 1.00236i 0.0446931i 0.999750 + 0.0223466i \(0.00711372\pi\)
−0.999750 + 0.0223466i \(0.992886\pi\)
\(504\) −3.63246 + 31.0475i −0.161802 + 1.38297i
\(505\) 0 0
\(506\) −1.66714 + 2.88757i −0.0741134 + 0.128368i
\(507\) 5.97905 + 1.98161i 0.265539 + 0.0880065i
\(508\) −0.244026 + 0.140888i −0.0108269 + 0.00625090i
\(509\) 2.28161 + 3.95187i 0.101131 + 0.175163i 0.912151 0.409855i \(-0.134421\pi\)
−0.811020 + 0.585018i \(0.801087\pi\)
\(510\) 0 0
\(511\) −0.780062 + 1.35111i −0.0345079 + 0.0597695i
\(512\) 19.0969i 0.843971i
\(513\) 12.6615 + 18.0889i 0.559019 + 0.798646i
\(514\) 24.1822 1.06663
\(515\) 0 0
\(516\) −2.62363 + 0.541583i −0.115499 + 0.0238419i
\(517\) 0.322080 0.185953i 0.0141651 0.00817822i
\(518\) −11.2239 + 6.48013i −0.493151 + 0.284721i
\(519\) −4.22394 + 12.7447i −0.185410 + 0.559432i
\(520\) 0 0
\(521\) 39.3708 1.72486 0.862432 0.506173i \(-0.168940\pi\)
0.862432 + 0.506173i \(0.168940\pi\)
\(522\) −11.1451 + 14.9669i −0.487806 + 0.655084i
\(523\) 10.3998i 0.454749i −0.973807 0.227375i \(-0.926986\pi\)
0.973807 0.227375i \(-0.0730142\pi\)
\(524\) −1.12326 + 1.94555i −0.0490699 + 0.0849916i
\(525\) 0 0
\(526\) −19.0103 32.9268i −0.828888 1.43568i
\(527\) −7.49029 + 4.32452i −0.326282 + 0.188379i
\(528\) −1.45219 + 1.29219i −0.0631984 + 0.0562354i
\(529\) 26.3046 45.5608i 1.14368 1.98091i
\(530\) 0 0
\(531\) 17.1421 + 12.7648i 0.743904 + 0.553946i
\(532\) 2.80046i 0.121415i
\(533\) 19.9290 + 11.5060i 0.863222 + 0.498381i
\(534\) 5.76210 17.3858i 0.249351 0.752357i
\(535\) 0 0
\(536\) 15.2093 + 26.3433i 0.656942 + 1.13786i
\(537\) 3.76879 + 18.2574i 0.162635 + 0.787866i
\(538\) 15.9747 + 9.22298i 0.688717 + 0.397631i
\(539\) −2.06781 −0.0890670
\(540\) 0 0
\(541\) 13.7093 0.589408 0.294704 0.955589i \(-0.404779\pi\)
0.294704 + 0.955589i \(0.404779\pi\)
\(542\) 25.0661 + 14.4719i 1.07668 + 0.621622i
\(543\) −2.74723 13.3086i −0.117895 0.571126i
\(544\) −1.56790 2.71568i −0.0672230 0.116434i
\(545\) 0 0
\(546\) 12.6581 38.1930i 0.541718 1.63451i
\(547\) 19.7322 + 11.3924i 0.843686 + 0.487102i 0.858515 0.512788i \(-0.171387\pi\)
−0.0148294 + 0.999890i \(0.504721\pi\)
\(548\) 3.45950i 0.147783i
\(549\) 0.880201 7.52330i 0.0375661 0.321087i
\(550\) 0 0
\(551\) −8.97044 + 15.5373i −0.382154 + 0.661910i
\(552\) 30.3263 26.9851i 1.29077 1.14856i
\(553\) −10.1860 + 5.88089i −0.433153 + 0.250081i
\(554\) −15.3440 26.5766i −0.651905 1.12913i
\(555\) 0 0
\(556\) −0.261583 + 0.453075i −0.0110936 + 0.0192146i
\(557\) 18.2341i 0.772605i 0.922372 + 0.386303i \(0.126248\pi\)
−0.922372 + 0.386303i \(0.873752\pi\)
\(558\) 4.64282 + 10.7666i 0.196546 + 0.455786i
\(559\) −37.0054 −1.56516
\(560\) 0 0
\(561\) −0.462390 + 1.39515i −0.0195221 + 0.0589034i
\(562\) −6.02776 + 3.48013i −0.254266 + 0.146800i
\(563\) 20.8809 12.0556i 0.880025 0.508083i 0.00935862 0.999956i \(-0.497021\pi\)
0.870667 + 0.491873i \(0.163688\pi\)
\(564\) 0.413206 0.0852961i 0.0173991 0.00359161i
\(565\) 0 0
\(566\) 34.1095 1.43373
\(567\) 33.3330 9.97113i 1.39986 0.418748i
\(568\) 22.5913i 0.947910i
\(569\) −16.0024 + 27.7170i −0.670857 + 1.16196i 0.306804 + 0.951773i \(0.400740\pi\)
−0.977661 + 0.210186i \(0.932593\pi\)
\(570\) 0 0
\(571\) 9.89042 + 17.1307i 0.413901 + 0.716898i 0.995312 0.0967121i \(-0.0308326\pi\)
−0.581411 + 0.813610i \(0.697499\pi\)
\(572\) 0.156737 0.0904921i 0.00655350 0.00378367i
\(573\) 9.42491 + 3.12366i 0.393731 + 0.130493i
\(574\) 16.0662 27.8274i 0.670589 1.16150i
\(575\) 0 0
\(576\) 19.8531 8.56117i 0.827213 0.356715i
\(577\) 35.4119i 1.47422i 0.675775 + 0.737108i \(0.263809\pi\)
−0.675775 + 0.737108i \(0.736191\pi\)
\(578\) 8.12808 + 4.69275i 0.338084 + 0.195193i
\(579\) −9.76650 10.9758i −0.405882 0.456137i
\(580\) 0 0
\(581\) −8.85321 15.3342i −0.367293 0.636170i
\(582\) −5.93840 + 5.28413i −0.246154 + 0.219034i
\(583\) −2.56549 1.48119i −0.106252 0.0613445i
\(584\) 1.08776 0.0450117
\(585\) 0 0
\(586\) −24.8675 −1.02726
\(587\) −28.0463 16.1925i −1.15759 0.668338i −0.206868 0.978369i \(-0.566327\pi\)
−0.950726 + 0.310031i \(0.899661\pi\)
\(588\) −2.22676 0.738008i −0.0918302 0.0304349i
\(589\) 5.63636 + 9.76247i 0.232242 + 0.402255i
\(590\) 0 0
\(591\) 18.0257 3.72095i 0.741478 0.153060i
\(592\) 8.49752 + 4.90605i 0.349246 + 0.201637i
\(593\) 29.2504i 1.20117i 0.799561 + 0.600585i \(0.205066\pi\)
−0.799561 + 0.600585i \(0.794934\pi\)
\(594\) 1.80567 + 0.842367i 0.0740876 + 0.0345627i
\(595\) 0 0
\(596\) −0.346210 + 0.599654i −0.0141813 + 0.0245628i
\(597\) 6.50535 + 31.5144i 0.266246 + 1.28980i
\(598\) −45.2510 + 26.1257i −1.85045 + 1.06836i
\(599\) 2.03081 + 3.51747i 0.0829767 + 0.143720i 0.904527 0.426416i \(-0.140224\pi\)
−0.821551 + 0.570136i \(0.806891\pi\)
\(600\) 0 0
\(601\) −23.4538 + 40.6232i −0.956700 + 1.65705i −0.226271 + 0.974064i \(0.572653\pi\)
−0.730429 + 0.682989i \(0.760680\pi\)
\(602\) 51.6717i 2.10598i
\(603\) 20.2209 27.1550i 0.823459 1.10584i
\(604\) 2.32190 0.0944768
\(605\) 0 0
\(606\) −6.52344 7.33116i −0.264997 0.297808i
\(607\) 35.4608 20.4733i 1.43931 0.830987i 0.441509 0.897257i \(-0.354443\pi\)
0.997802 + 0.0662702i \(0.0211099\pi\)
\(608\) −3.53948 + 2.04352i −0.143545 + 0.0828756i
\(609\) 18.7928 + 21.1197i 0.761524 + 0.855814i
\(610\) 0 0
\(611\) 5.82813 0.235781
\(612\) −0.995867 + 1.33737i −0.0402555 + 0.0540599i
\(613\) 33.3827i 1.34831i −0.738588 0.674157i \(-0.764507\pi\)
0.738588 0.674157i \(-0.235493\pi\)
\(614\) −16.7345 + 28.9850i −0.675350 + 1.16974i
\(615\) 0 0
\(616\) 1.35602 + 2.34869i 0.0546355 + 0.0946314i
\(617\) −1.94752 + 1.12440i −0.0784040 + 0.0452666i −0.538689 0.842504i \(-0.681080\pi\)
0.460285 + 0.887771i \(0.347747\pi\)
\(618\) −2.17015 10.5130i −0.0872963 0.422896i
\(619\) −17.1467 + 29.6990i −0.689184 + 1.19370i 0.282918 + 0.959144i \(0.408698\pi\)
−0.972102 + 0.234558i \(0.924636\pi\)
\(620\) 0 0
\(621\) −40.9459 19.1018i −1.64310 0.766527i
\(622\) 46.5454i 1.86630i
\(623\) −24.0303 13.8739i −0.962756 0.555847i
\(624\) −29.8333 + 6.15833i −1.19429 + 0.246531i
\(625\) 0 0
\(626\) 22.4669 + 38.9137i 0.897956 + 1.55531i
\(627\) 1.81837 + 0.602656i 0.0726188 + 0.0240678i
\(628\) −0.304522 0.175816i −0.0121517 0.00701581i
\(629\) 7.41904 0.295817
\(630\) 0 0
\(631\) −18.7552 −0.746633 −0.373316 0.927704i \(-0.621779\pi\)
−0.373316 + 0.927704i \(0.621779\pi\)
\(632\) 7.10193 + 4.10030i 0.282499 + 0.163101i
\(633\) 13.5261 12.0358i 0.537613 0.478381i
\(634\) 16.2713 + 28.1828i 0.646218 + 1.11928i
\(635\) 0 0
\(636\) −2.23406 2.51068i −0.0885862 0.0995548i
\(637\) −28.0632 16.2023i −1.11191 0.641959i
\(638\) 1.61899i 0.0640963i
\(639\) 23.0894 9.95674i 0.913403 0.393883i
\(640\) 0 0
\(641\) −10.3175 + 17.8704i −0.407517 + 0.705840i −0.994611 0.103679i \(-0.966939\pi\)
0.587094 + 0.809519i \(0.300272\pi\)
\(642\) −3.93981 1.30576i −0.155492 0.0515340i
\(643\) 23.5506 13.5970i 0.928746 0.536212i 0.0423312 0.999104i \(-0.486522\pi\)
0.886415 + 0.462892i \(0.153188\pi\)
\(644\) 2.86530 + 4.96285i 0.112909 + 0.195564i
\(645\) 0 0
\(646\) −10.2051 + 17.6758i −0.401515 + 0.695445i
\(647\) 16.7316i 0.657787i −0.944367 0.328893i \(-0.893324\pi\)
0.944367 0.328893i \(-0.106676\pi\)
\(648\) −17.6410 16.6509i −0.693004 0.654109i
\(649\) 1.85428 0.0727869
\(650\) 0 0
\(651\) 17.3962 3.59102i 0.681812 0.140743i
\(652\) 0.517511 0.298785i 0.0202673 0.0117013i
\(653\) −39.6060 + 22.8666i −1.54990 + 0.894837i −0.551756 + 0.834006i \(0.686042\pi\)
−0.998148 + 0.0608319i \(0.980625\pi\)
\(654\) −10.3575 + 31.2514i −0.405011 + 1.22203i
\(655\) 0 0
\(656\) −24.3271 −0.949814
\(657\) −0.479411 1.11174i −0.0187036 0.0433731i
\(658\) 8.13799i 0.317252i
\(659\) 9.30543 16.1175i 0.362488 0.627848i −0.625882 0.779918i \(-0.715261\pi\)
0.988370 + 0.152070i \(0.0485941\pi\)
\(660\) 0 0
\(661\) −8.39799 14.5457i −0.326644 0.565764i 0.655200 0.755456i \(-0.272584\pi\)
−0.981844 + 0.189692i \(0.939251\pi\)
\(662\) 37.7720 21.8077i 1.46805 0.847579i
\(663\) −17.2070 + 15.3112i −0.668264 + 0.594638i
\(664\) −6.17267 + 10.6914i −0.239546 + 0.414906i
\(665\) 0 0
\(666\) 1.16873 9.98942i 0.0452873 0.387082i
\(667\) 36.7126i 1.42152i
\(668\) −3.03175 1.75038i −0.117302 0.0677243i
\(669\) 2.14211 6.46331i 0.0828187 0.249886i
\(670\) 0 0
\(671\) −0.328584 0.569124i −0.0126848 0.0219708i
\(672\) 1.30196 + 6.30718i 0.0502242 + 0.243305i
\(673\) −43.2562 24.9740i −1.66740 0.962676i −0.969030 0.246944i \(-0.920574\pi\)
−0.698374 0.715733i \(-0.746093\pi\)
\(674\) −18.4614 −0.711108
\(675\) 0 0
\(676\) 0.619973 0.0238451
\(677\) 9.37998 + 5.41553i 0.360502 + 0.208136i 0.669301 0.742991i \(-0.266594\pi\)
−0.308799 + 0.951127i \(0.599927\pi\)
\(678\) 0.685630 + 3.32145i 0.0263315 + 0.127559i
\(679\) 6.02125 + 10.4291i 0.231074 + 0.400232i
\(680\) 0 0
\(681\) −2.63262 + 7.94333i −0.100882 + 0.304389i
\(682\) 0.880965 + 0.508625i 0.0337339 + 0.0194763i
\(683\) 0.429870i 0.0164485i 0.999966 + 0.00822426i \(0.00261789\pi\)
−0.999966 + 0.00822426i \(0.997382\pi\)
\(684\) 1.74306 + 1.29796i 0.0666476 + 0.0496289i
\(685\) 0 0
\(686\) −2.69001 + 4.65924i −0.102705 + 0.177891i
\(687\) 24.3948 21.7071i 0.930719 0.828176i
\(688\) 33.8791 19.5601i 1.29163 0.745721i
\(689\) −23.2116 40.2037i −0.884293 1.53164i
\(690\) 0 0
\(691\) −17.3518 + 30.0542i −0.660093 + 1.14331i 0.320498 + 0.947249i \(0.396150\pi\)
−0.980591 + 0.196065i \(0.937184\pi\)
\(692\) 1.32151i 0.0502364i
\(693\) 1.80284 2.42106i 0.0684841 0.0919686i
\(694\) 25.1889 0.956157
\(695\) 0 0
\(696\) 6.20097 18.7100i 0.235047 0.709200i
\(697\) −15.9297 + 9.19701i −0.603380 + 0.348362i
\(698\) −23.4820 + 13.5573i −0.888807 + 0.513153i
\(699\) 20.1894 4.16761i 0.763635 0.157633i
\(700\) 0 0
\(701\) 1.84808 0.0698010 0.0349005 0.999391i \(-0.488889\pi\)
0.0349005 + 0.999391i \(0.488889\pi\)
\(702\) 17.9052 + 25.5805i 0.675789 + 0.965472i
\(703\) 9.66962i 0.364696i
\(704\) 0.937884 1.62446i 0.0353478 0.0612242i
\(705\) 0 0
\(706\) 23.3649 + 40.4692i 0.879351 + 1.52308i
\(707\) −12.8751 + 7.43344i −0.484218 + 0.279563i
\(708\) 1.99682 + 0.661797i 0.0750450 + 0.0248719i
\(709\) −3.15338 + 5.46181i −0.118428 + 0.205123i −0.919145 0.393920i \(-0.871119\pi\)
0.800717 + 0.599043i \(0.204452\pi\)
\(710\) 0 0
\(711\) 1.06065 9.06566i 0.0397775 0.339989i
\(712\) 19.3465i 0.725040i
\(713\) −19.9770 11.5337i −0.748145 0.431942i
\(714\) 21.3795 + 24.0266i 0.800106 + 0.899173i
\(715\) 0 0
\(716\) 0.917446 + 1.58906i 0.0342866 + 0.0593861i
\(717\) 27.9875 24.9039i 1.04521 0.930054i
\(718\) 14.6130 + 8.43682i 0.545352 + 0.314859i
\(719\) −18.0129 −0.671770 −0.335885 0.941903i \(-0.609035\pi\)
−0.335885 + 0.941903i \(0.609035\pi\)
\(720\) 0 0
\(721\) −16.2627 −0.605655
\(722\) −1.20389 0.695067i −0.0448042 0.0258677i
\(723\) −6.40925 2.12419i −0.238363 0.0789996i
\(724\) −0.668765 1.15833i −0.0248544 0.0430491i
\(725\) 0 0
\(726\) −27.3204 + 5.63961i −1.01395 + 0.209306i
\(727\) 22.7612 + 13.1412i 0.844165 + 0.487379i 0.858678 0.512516i \(-0.171286\pi\)
−0.0145126 + 0.999895i \(0.504620\pi\)
\(728\) 42.5002i 1.57516i
\(729\) −9.24306 + 25.3686i −0.342336 + 0.939578i
\(730\) 0 0
\(731\) 14.7896 25.6164i 0.547014 0.947456i
\(732\) −0.150720 0.730145i −0.00557078 0.0269869i
\(733\) 41.2777 23.8317i 1.52462 0.880243i 0.525050 0.851071i \(-0.324046\pi\)
0.999574 0.0291714i \(-0.00928687\pi\)
\(734\) 1.83595 + 3.17997i 0.0677663 + 0.117375i
\(735\) 0 0
\(736\) 4.18167 7.24287i 0.154138 0.266976i
\(737\) 2.93739i 0.108200i
\(738\) 9.87396 + 22.8975i 0.363465 + 0.842867i
\(739\) 10.0273 0.368859 0.184429 0.982846i \(-0.440956\pi\)
0.184429 + 0.982846i \(0.440956\pi\)
\(740\) 0 0
\(741\) 19.9559 + 22.4267i 0.733097 + 0.823867i
\(742\) −56.1376 + 32.4110i −2.06088 + 1.18985i
\(743\) 7.16433 4.13633i 0.262834 0.151747i −0.362793 0.931870i \(-0.618177\pi\)
0.625627 + 0.780123i \(0.284843\pi\)
\(744\) −8.23285 9.25222i −0.301831 0.339203i
\(745\) 0 0
\(746\) −22.1539 −0.811111
\(747\) 13.6476 + 1.59673i 0.499340 + 0.0584212i
\(748\) 0.144665i 0.00528946i
\(749\) −3.14398 + 5.44554i −0.114879 + 0.198976i
\(750\) 0 0
\(751\) 2.89880 + 5.02087i 0.105779 + 0.183214i 0.914056 0.405588i \(-0.132933\pi\)
−0.808277 + 0.588802i \(0.799600\pi\)
\(752\) −5.33575 + 3.08060i −0.194575 + 0.112338i
\(753\) −10.5409 51.0638i −0.384130 1.86087i
\(754\) −12.6855 + 21.9720i −0.461980 + 0.800173i
\(755\) 0 0
\(756\) 2.80550 1.96373i 0.102035 0.0714203i
\(757\) 25.2804i 0.918830i 0.888222 + 0.459415i \(0.151941\pi\)
−0.888222 + 0.459415i \(0.848059\pi\)
\(758\) −8.00322 4.62066i −0.290690 0.167830i
\(759\) −3.83905 + 0.792476i −0.139349 + 0.0287651i
\(760\) 0 0
\(761\) −9.73190 16.8561i −0.352781 0.611035i 0.633954 0.773370i \(-0.281431\pi\)
−0.986736 + 0.162335i \(0.948097\pi\)
\(762\) −4.00352 1.32687i −0.145032 0.0480674i
\(763\) 43.1951 + 24.9387i 1.56377 + 0.902843i
\(764\) 0.977278 0.0353567
\(765\) 0 0
\(766\) −32.6897 −1.18113
\(767\) 25.1653 + 14.5292i 0.908666 + 0.524618i
\(768\) 5.25681 4.67764i 0.189689 0.168790i
\(769\) −24.6715 42.7324i −0.889678 1.54097i −0.840256 0.542190i \(-0.817595\pi\)
−0.0494224 0.998778i \(-0.515738\pi\)
\(770\) 0 0
\(771\) 18.8990 + 21.2391i 0.680632 + 0.764907i
\(772\) −1.25233 0.723033i −0.0450723 0.0260225i
\(773\) 20.8502i 0.749930i 0.927039 + 0.374965i \(0.122345\pi\)
−0.927039 + 0.374965i \(0.877655\pi\)
\(774\) −32.1615 23.9490i −1.15602 0.860827i
\(775\) 0 0
\(776\) 4.19816 7.27143i 0.150705 0.261029i
\(777\) −14.4632 4.79350i −0.518866 0.171966i
\(778\) −38.3940 + 22.1668i −1.37649 + 0.794717i
\(779\) 11.9869 + 20.7620i 0.429476 + 0.743875i
\(780\) 0 0
\(781\) 1.09077 1.88927i 0.0390308 0.0676034i
\(782\) 41.7657i 1.49354i
\(783\) −21.8555 + 1.90841i −0.781052 + 0.0682010i
\(784\) 34.2564 1.22344
\(785\) 0 0
\(786\) −32.9320 + 6.79798i −1.17464 + 0.242476i
\(787\) 38.2682 22.0941i 1.36411 0.787571i 0.373945 0.927451i \(-0.378005\pi\)
0.990169 + 0.139880i \(0.0446715\pi\)
\(788\) 1.56889 0.905801i 0.0558895 0.0322678i
\(789\) 14.0623 42.4298i 0.500632 1.51054i
\(790\) 0 0
\(791\) 5.13799 0.182686
\(792\) −2.09036 0.244565i −0.0742778 0.00869025i
\(793\) 10.2985i 0.365709i
\(794\) 21.5326 37.2955i 0.764162 1.32357i
\(795\) 0 0
\(796\) 1.58362 + 2.74290i 0.0561297 + 0.0972196i
\(797\) −26.8792 + 15.5187i −0.952110 + 0.549701i −0.893736 0.448594i \(-0.851925\pi\)
−0.0583744 + 0.998295i \(0.518592\pi\)
\(798\) 31.3151 27.8649i 1.10854 0.986408i
\(799\) −2.32928 + 4.03443i −0.0824039 + 0.142728i
\(800\) 0 0
\(801\) 19.7731 8.52664i 0.698647 0.301274i
\(802\) 35.7031i 1.26072i
\(803\) −0.0909671 0.0525199i −0.00321016 0.00185339i
\(804\) 1.04836 3.16319i 0.0369729 0.111557i
\(805\) 0 0
\(806\) 7.97065 + 13.8056i 0.280754 + 0.486281i
\(807\) 4.38415 + 21.2385i 0.154329 + 0.747629i
\(808\) 8.97683 + 5.18278i 0.315804 + 0.182329i
\(809\) −14.6229 −0.514114 −0.257057 0.966396i \(-0.582753\pi\)
−0.257057 + 0.966396i \(0.582753\pi\)
\(810\) 0 0
\(811\) 26.7177 0.938187 0.469093 0.883149i \(-0.344581\pi\)
0.469093 + 0.883149i \(0.344581\pi\)
\(812\) 2.40975 + 1.39127i 0.0845656 + 0.0488240i
\(813\) 6.87923 + 33.3256i 0.241265 + 1.16878i
\(814\) −0.436293 0.755682i −0.0152921 0.0264866i
\(815\) 0 0
\(816\) 7.66018 23.1128i 0.268160 0.809110i
\(817\) −33.3871 19.2761i −1.16807 0.674384i
\(818\) 3.44727i 0.120531i
\(819\) 43.4373 18.7313i 1.51782 0.654523i
\(820\) 0 0
\(821\) 9.29903 16.1064i 0.324538 0.562117i −0.656881 0.753995i \(-0.728124\pi\)
0.981419 + 0.191878i \(0.0614577\pi\)
\(822\) −38.6846 + 34.4225i −1.34928 + 1.20062i
\(823\) −2.65181 + 1.53102i −0.0924362 + 0.0533680i −0.545506 0.838107i \(-0.683662\pi\)
0.453069 + 0.891475i \(0.350329\pi\)
\(824\) 5.66938 + 9.81966i 0.197502 + 0.342084i
\(825\) 0 0
\(826\) 20.2875 35.1390i 0.705892 1.22264i
\(827\) 7.27526i 0.252985i −0.991968 0.126493i \(-0.959628\pi\)
0.991968 0.126493i \(-0.0403720\pi\)
\(828\) −4.41699 0.516773i −0.153501 0.0179591i
\(829\) −10.5211 −0.365411 −0.182706 0.983168i \(-0.558486\pi\)
−0.182706 + 0.983168i \(0.558486\pi\)
\(830\) 0 0
\(831\) 11.3503 34.2469i 0.393738 1.18801i
\(832\) 25.4569 14.6975i 0.882559 0.509546i
\(833\) 22.4315 12.9509i 0.777207 0.448721i
\(834\) −7.66912 + 1.58310i −0.265560 + 0.0548182i
\(835\) 0 0
\(836\) 0.188549 0.00652109
\(837\) −5.82773 + 12.4921i −0.201436 + 0.431791i
\(838\) 33.6528i 1.16252i
\(839\) 7.59033 13.1468i 0.262047 0.453879i −0.704739 0.709467i \(-0.748936\pi\)
0.966786 + 0.255588i \(0.0822691\pi\)
\(840\) 0 0
\(841\) 5.58695 + 9.67689i 0.192654 + 0.333686i
\(842\) −15.1521 + 8.74806i −0.522176 + 0.301478i
\(843\) −7.76744 2.57433i −0.267525 0.0886646i
\(844\) 0.891034 1.54332i 0.0306707 0.0531232i
\(845\) 0 0
\(846\) 5.06525 + 3.77182i 0.174147 + 0.129678i
\(847\) 42.2622i 1.45215i
\(848\) 42.5012 + 24.5381i 1.45950 + 0.842641i
\(849\) 26.6575 + 29.9581i 0.914882 + 1.02816i
\(850\) 0 0
\(851\) 9.89351 + 17.1361i 0.339145 + 0.587417i
\(852\) 1.84890 1.64520i 0.0633424 0.0563636i
\(853\) −9.08131 5.24309i −0.310938 0.179520i 0.336408 0.941716i \(-0.390788\pi\)
−0.647346 + 0.762196i \(0.724121\pi\)
\(854\) −14.3800 −0.492074
\(855\) 0 0
\(856\) 4.38412 0.149846
\(857\) −7.65631 4.42038i −0.261535 0.150997i 0.363500 0.931594i \(-0.381582\pi\)
−0.625034 + 0.780597i \(0.714915\pi\)
\(858\) 2.57145 + 0.852245i 0.0877878 + 0.0290952i
\(859\) −1.03416 1.79121i −0.0352849 0.0611153i 0.847844 0.530246i \(-0.177901\pi\)
−0.883129 + 0.469131i \(0.844567\pi\)
\(860\) 0 0
\(861\) 36.9968 7.63707i 1.26085 0.260271i
\(862\) 11.3159 + 6.53326i 0.385423 + 0.222524i
\(863\) 22.4434i 0.763984i −0.924166 0.381992i \(-0.875238\pi\)
0.924166 0.381992i \(-0.124762\pi\)
\(864\) −4.52915 2.11290i −0.154085 0.0718824i
\(865\) 0 0
\(866\) −6.90263 + 11.9557i −0.234561 + 0.406271i
\(867\) 2.23070 + 10.8063i 0.0757586 + 0.367003i
\(868\) 1.51411 0.874171i 0.0513922 0.0296713i
\(869\) −0.395947 0.685801i −0.0134316 0.0232642i
\(870\) 0 0
\(871\) 23.0159 39.8647i 0.779863 1.35076i
\(872\) 34.7758i 1.17766i
\(873\) −9.28203 1.08597i −0.314149 0.0367544i
\(874\) −54.4353 −1.84130
\(875\) 0 0
\(876\) −0.0792152 0.0890235i −0.00267643 0.00300782i
\(877\) −24.1562 + 13.9466i −0.815697 + 0.470943i −0.848930 0.528505i \(-0.822753\pi\)
0.0332332 + 0.999448i \(0.489420\pi\)
\(878\) 24.7815 14.3076i 0.836334 0.482857i
\(879\) −19.4346 21.8409i −0.655512 0.736676i
\(880\) 0 0
\(881\) −9.22153 −0.310681 −0.155341 0.987861i \(-0.549647\pi\)
−0.155341 + 0.987861i \(0.549647\pi\)
\(882\) −13.9041 32.2433i −0.468175 1.08569i
\(883\) 49.2436i 1.65718i 0.559858 + 0.828589i \(0.310856\pi\)
−0.559858 + 0.828589i \(0.689144\pi\)
\(884\) −1.13352 + 1.96331i −0.0381243 + 0.0660333i
\(885\) 0 0
\(886\) −8.01396 13.8806i −0.269234 0.466328i
\(887\) −9.32542 + 5.38403i −0.313117 + 0.180778i −0.648320 0.761368i \(-0.724528\pi\)
0.335203 + 0.942146i \(0.391195\pi\)
\(888\) 2.14768 + 10.4042i 0.0720716 + 0.349142i
\(889\) −3.19482 + 5.53360i −0.107151 + 0.185591i
\(890\) 0 0
\(891\) 0.671335 + 2.24424i 0.0224906 + 0.0751849i
\(892\) 0.670187i 0.0224395i
\(893\) 5.25827 + 3.03586i 0.175961 + 0.101591i
\(894\) −10.1503 + 2.09527i −0.339475 + 0.0700762i
\(895\) 0 0
\(896\) −24.2408 41.9863i −0.809829 1.40266i
\(897\) −58.3109 19.3258i −1.94695 0.645268i
\(898\) −1.70985 0.987183i −0.0570585 0.0329427i
\(899\) −11.2006 −0.373561
\(900\) 0 0
\(901\) 37.1071 1.23622
\(902\) 1.87356 + 1.08170i 0.0623828 + 0.0360167i
\(903\) −45.3829 + 40.3828i −1.51025 + 1.34386i
\(904\) −1.79116 3.10239i −0.0595733 0.103184i
\(905\) 0 0
\(906\) 23.1032 + 25.9638i 0.767553 + 0.862590i
\(907\) −27.6871 15.9852i −0.919336 0.530779i −0.0359130 0.999355i \(-0.511434\pi\)
−0.883423 + 0.468576i \(0.844767\pi\)
\(908\) 0.823651i 0.0273338i
\(909\) 1.34066 11.4590i 0.0444670 0.380071i
\(910\) 0 0
\(911\) 5.04010 8.72970i 0.166986 0.289228i −0.770373 0.637594i \(-0.779930\pi\)
0.937359 + 0.348366i \(0.113263\pi\)
\(912\) −30.1241 9.98390i −0.997508 0.330600i
\(913\) 1.03242 0.596067i 0.0341681 0.0197269i
\(914\) 14.8145 + 25.6595i 0.490021 + 0.848741i
\(915\) 0 0
\(916\) 1.60702 2.78343i 0.0530973 0.0919672i
\(917\) 50.9428i 1.68228i
\(918\) −24.8636 + 2.17108i −0.820623 + 0.0716564i
\(919\) 29.7976 0.982932 0.491466 0.870897i \(-0.336461\pi\)
0.491466 + 0.870897i \(0.336461\pi\)
\(920\) 0 0
\(921\) −38.5358 + 7.95476i −1.26980 + 0.262118i
\(922\) 43.0650 24.8636i 1.41827 0.818839i
\(923\) 29.6067 17.0934i 0.974516 0.562637i
\(924\) 0.0934688 0.282020i 0.00307490 0.00927779i
\(925\) 0 0
\(926\) −7.72776 −0.253950
\(927\) 7.53749 10.1222i 0.247564 0.332458i
\(928\) 4.06089i 0.133305i
\(929\) −6.19275 + 10.7262i −0.203178 + 0.351914i −0.949551 0.313614i \(-0.898460\pi\)
0.746373 + 0.665528i \(0.231794\pi\)
\(930\) 0 0
\(931\) −16.8795 29.2362i −0.553204 0.958177i
\(932\) 1.75722 1.01453i 0.0575597 0.0332321i
\(933\) 40.8805 36.3765i 1.33837 1.19091i
\(934\) 10.4689 18.1327i 0.342554 0.593321i
\(935\) 0 0
\(936\) −26.4530 19.6981i −0.864642 0.643853i
\(937\) 44.4280i 1.45140i 0.688012 + 0.725699i \(0.258484\pi\)
−0.688012 + 0.725699i \(0.741516\pi\)
\(938\) −55.6641 32.1377i −1.81750 1.04933i
\(939\) −16.6192 + 50.1446i −0.542348 + 1.63641i
\(940\) 0 0
\(941\) −7.66617 13.2782i −0.249910 0.432857i 0.713591 0.700563i \(-0.247068\pi\)
−0.963501 + 0.267706i \(0.913734\pi\)
\(942\) −1.06404 5.15459i −0.0346682 0.167946i
\(943\) −42.4854 24.5290i −1.38352 0.798773i
\(944\) −30.7189 −0.999816
\(945\) 0 0
\(946\) −3.47894 −0.113110
\(947\) −18.7925 10.8498i −0.610673 0.352572i 0.162556 0.986699i \(-0.448026\pi\)
−0.773229 + 0.634127i \(0.781360\pi\)
\(948\) −0.181620 0.879833i −0.00589873 0.0285756i
\(949\) −0.823037 1.42554i −0.0267169 0.0462751i
\(950\) 0 0
\(951\) −12.0363 + 36.3166i −0.390303 + 1.17765i
\(952\) −29.4200 16.9857i −0.953509 0.550508i
\(953\) 36.9099i 1.19563i −0.801634 0.597815i \(-0.796036\pi\)
0.801634 0.597815i \(-0.203964\pi\)
\(954\) 5.84552 49.9631i 0.189256 1.61762i
\(955\) 0 0
\(956\) 1.84368 3.19336i 0.0596290 0.103281i
\(957\) −1.42194 + 1.26528i −0.0459649 + 0.0409007i
\(958\) 26.1342 15.0886i 0.844357 0.487490i
\(959\) 39.2243 + 67.9385i 1.26662 + 2.19385i
\(960\) 0 0
\(961\) 11.9812 20.7520i 0.386490 0.669420i
\(962\) 13.6743i 0.440876i
\(963\) −1.93223 4.48079i −0.0622652 0.144391i
\(964\) −0.664581 −0.0214047
\(965\) 0 0
\(966\) −26.9851 + 81.4212i −0.868231 + 2.61968i
\(967\) −18.4794 + 10.6691i −0.594258 + 0.343095i −0.766779 0.641911i \(-0.778142\pi\)
0.172521 + 0.985006i \(0.444809\pi\)
\(968\) 25.5185 14.7331i 0.820197 0.473541i
\(969\) −23.5001 + 4.85101i −0.754932 + 0.155837i
\(970\) 0 0
\(971\) −42.5851 −1.36662 −0.683311 0.730128i \(-0.739460\pi\)
−0.683311 + 0.730128i \(0.739460\pi\)
\(972\) −0.0780359 + 2.65636i −0.00250300 + 0.0852027i
\(973\) 11.8635i 0.380325i
\(974\) 23.0973 40.0057i 0.740085 1.28186i
\(975\) 0 0
\(976\) 5.44349 + 9.42840i 0.174242 + 0.301796i
\(977\) 42.3826 24.4696i 1.35594 0.782852i 0.366865 0.930274i \(-0.380431\pi\)
0.989074 + 0.147423i \(0.0470977\pi\)
\(978\) 8.49036 + 2.81393i 0.271492 + 0.0899795i
\(979\) 0.934101 1.61791i 0.0298540 0.0517087i
\(980\) 0 0
\(981\) −35.5426 + 15.3268i −1.13479 + 0.489349i
\(982\) 15.3102i 0.488567i
\(983\) −31.2712 18.0545i −0.997398 0.575848i −0.0899205 0.995949i \(-0.528661\pi\)
−0.907477 + 0.420101i \(0.861995\pi\)
\(984\) −17.5089 19.6768i −0.558164 0.627274i
\(985\) 0 0
\(986\) −10.1398 17.5627i −0.322918 0.559310i
\(987\) 7.14754 6.36005i 0.227509 0.202443i
\(988\) 2.55888 + 1.47737i 0.0814088 + 0.0470014i
\(989\) 78.8896 2.50854
\(990\) 0 0
\(991\) 32.0054 1.01669 0.508343 0.861155i \(-0.330258\pi\)
0.508343 + 0.861155i \(0.330258\pi\)
\(992\) −2.20972 1.27578i −0.0701586 0.0405061i
\(993\) 48.6733 + 16.1316i 1.54460 + 0.511921i
\(994\) −23.8680 41.3406i −0.757048 1.31125i
\(995\) 0 0
\(996\) 1.32452 0.273414i 0.0419690 0.00866345i
\(997\) 44.8324 + 25.8840i 1.41986 + 0.819754i 0.996286 0.0861095i \(-0.0274435\pi\)
0.423570 + 0.905863i \(0.360777\pi\)
\(998\) 5.63624i 0.178412i
\(999\) 9.68703 6.78051i 0.306484 0.214526i
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.k.c.124.6 16
3.2 odd 2 675.2.k.c.424.3 16
5.2 odd 4 225.2.e.c.151.2 yes 8
5.3 odd 4 225.2.e.e.151.3 yes 8
5.4 even 2 inner 225.2.k.c.124.3 16
9.2 odd 6 2025.2.b.o.649.6 8
9.4 even 3 inner 225.2.k.c.49.3 16
9.5 odd 6 675.2.k.c.199.6 16
9.7 even 3 2025.2.b.n.649.3 8
15.2 even 4 675.2.e.e.451.3 8
15.8 even 4 675.2.e.c.451.2 8
15.14 odd 2 675.2.k.c.424.6 16
45.2 even 12 2025.2.a.p.1.2 4
45.4 even 6 inner 225.2.k.c.49.6 16
45.7 odd 12 2025.2.a.y.1.3 4
45.13 odd 12 225.2.e.e.76.3 yes 8
45.14 odd 6 675.2.k.c.199.3 16
45.22 odd 12 225.2.e.c.76.2 8
45.23 even 12 675.2.e.c.226.2 8
45.29 odd 6 2025.2.b.o.649.3 8
45.32 even 12 675.2.e.e.226.3 8
45.34 even 6 2025.2.b.n.649.6 8
45.38 even 12 2025.2.a.z.1.3 4
45.43 odd 12 2025.2.a.q.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
225.2.e.c.76.2 8 45.22 odd 12
225.2.e.c.151.2 yes 8 5.2 odd 4
225.2.e.e.76.3 yes 8 45.13 odd 12
225.2.e.e.151.3 yes 8 5.3 odd 4
225.2.k.c.49.3 16 9.4 even 3 inner
225.2.k.c.49.6 16 45.4 even 6 inner
225.2.k.c.124.3 16 5.4 even 2 inner
225.2.k.c.124.6 16 1.1 even 1 trivial
675.2.e.c.226.2 8 45.23 even 12
675.2.e.c.451.2 8 15.8 even 4
675.2.e.e.226.3 8 45.32 even 12
675.2.e.e.451.3 8 15.2 even 4
675.2.k.c.199.3 16 45.14 odd 6
675.2.k.c.199.6 16 9.5 odd 6
675.2.k.c.424.3 16 3.2 odd 2
675.2.k.c.424.6 16 15.14 odd 2
2025.2.a.p.1.2 4 45.2 even 12
2025.2.a.q.1.2 4 45.43 odd 12
2025.2.a.y.1.3 4 45.7 odd 12
2025.2.a.z.1.3 4 45.38 even 12
2025.2.b.n.649.3 8 9.7 even 3
2025.2.b.n.649.6 8 45.34 even 6
2025.2.b.o.649.3 8 45.29 odd 6
2025.2.b.o.649.6 8 9.2 odd 6