Properties

Label 400.2.j.d.307.7
Level $400$
Weight $2$
Character 400.307
Analytic conductor $3.194$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(43,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.43");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 400 = 2^{4} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 400.j (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.19401608085\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 307.7
Root \(-0.635486 - 1.26339i\) of defining polynomial
Character \(\chi\) \(=\) 400.307
Dual form 400.2.j.d.43.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.14628 - 0.828280i) q^{2} +0.692712i q^{3} +(0.627905 - 1.89888i) q^{4} +(0.573759 + 0.794040i) q^{6} +(0.343872 + 0.343872i) q^{7} +(-0.853049 - 2.69672i) q^{8} +2.52015 q^{9} +O(q^{10})\) \(q+(1.14628 - 0.828280i) q^{2} +0.692712i q^{3} +(0.627905 - 1.89888i) q^{4} +(0.573759 + 0.794040i) q^{6} +(0.343872 + 0.343872i) q^{7} +(-0.853049 - 2.69672i) q^{8} +2.52015 q^{9} +(0.843672 + 0.843672i) q^{11} +(1.31538 + 0.434957i) q^{12} +3.68390 q^{13} +(0.678995 + 0.109350i) q^{14} +(-3.21147 - 2.38463i) q^{16} +(-0.412137 - 0.412137i) q^{17} +(2.88879 - 2.08739i) q^{18} +(-5.37721 - 5.37721i) q^{19} +(-0.238204 + 0.238204i) q^{21} +(1.66588 + 0.268286i) q^{22} +(3.08788 - 3.08788i) q^{23} +(1.86805 - 0.590917i) q^{24} +(4.22278 - 3.05130i) q^{26} +3.82387i q^{27} +(0.868890 - 0.437052i) q^{28} +(-4.22969 + 4.22969i) q^{29} +8.75966i q^{31} +(-5.65638 - 0.0734474i) q^{32} +(-0.584422 + 0.584422i) q^{33} +(-0.813788 - 0.131059i) q^{34} +(1.58241 - 4.78546i) q^{36} +5.41752 q^{37} +(-10.6176 - 1.70994i) q^{38} +2.55188i q^{39} +2.54777i q^{41} +(-0.0757484 + 0.470348i) q^{42} -4.30732 q^{43} +(2.13178 - 1.07228i) q^{44} +(0.981939 - 6.09720i) q^{46} +(-4.56972 + 4.56972i) q^{47} +(1.65186 - 2.22462i) q^{48} -6.76350i q^{49} +(0.285492 - 0.285492i) q^{51} +(2.31314 - 6.99528i) q^{52} +6.07536i q^{53} +(3.16724 + 4.38322i) q^{54} +(0.633987 - 1.22067i) q^{56} +(3.72486 - 3.72486i) q^{57} +(-1.34503 + 8.35177i) q^{58} +(-7.33694 + 7.33694i) q^{59} +(-4.81576 - 4.81576i) q^{61} +(7.25545 + 10.0410i) q^{62} +(0.866609 + 0.866609i) q^{63} +(-6.54461 + 4.60087i) q^{64} +(-0.185845 + 1.15397i) q^{66} -14.3626 q^{67} +(-1.04138 + 0.523815i) q^{68} +(2.13901 + 2.13901i) q^{69} -2.97605 q^{71} +(-2.14981 - 6.79614i) q^{72} +(6.87152 + 6.87152i) q^{73} +(6.20998 - 4.48722i) q^{74} +(-13.5870 + 6.83429i) q^{76} +0.580231i q^{77} +(2.11367 + 2.92517i) q^{78} +10.1654 q^{79} +4.91161 q^{81} +(2.11027 + 2.92046i) q^{82} -7.15276i q^{83} +(0.302751 + 0.601890i) q^{84} +(-4.93739 + 3.56767i) q^{86} +(-2.92996 - 2.92996i) q^{87} +(1.55545 - 2.99484i) q^{88} +1.10953 q^{89} +(1.26679 + 1.26679i) q^{91} +(-3.92461 - 7.80240i) q^{92} -6.06792 q^{93} +(-1.45316 + 9.02318i) q^{94} +(0.0508779 - 3.91824i) q^{96} +(-7.15920 - 7.15920i) q^{97} +(-5.60207 - 7.75285i) q^{98} +(2.12618 + 2.12618i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 4 q^{2} - 4 q^{4} - 8 q^{6} - 2 q^{7} + 4 q^{8} - 10 q^{9} - 2 q^{11} - 4 q^{12} + 12 q^{14} + 6 q^{17} - 16 q^{18} + 2 q^{19} - 16 q^{21} - 4 q^{22} + 2 q^{23} + 4 q^{24} - 16 q^{26} + 4 q^{28} - 14 q^{29} + 4 q^{32} + 8 q^{33} - 28 q^{34} - 4 q^{36} - 8 q^{37} - 16 q^{38} - 28 q^{42} + 44 q^{43} + 44 q^{44} + 12 q^{46} + 38 q^{47} - 60 q^{48} + 8 q^{51} + 40 q^{52} - 4 q^{54} + 20 q^{56} - 24 q^{57} + 20 q^{58} - 10 q^{59} + 14 q^{61} - 6 q^{63} - 16 q^{64} + 4 q^{66} - 12 q^{67} - 36 q^{68} + 32 q^{69} + 24 q^{71} + 36 q^{72} - 14 q^{73} + 48 q^{74} - 16 q^{76} + 84 q^{78} + 16 q^{79} + 2 q^{81} + 28 q^{82} - 24 q^{84} - 36 q^{86} - 24 q^{87} + 96 q^{88} - 12 q^{89} - 52 q^{92} - 16 q^{93} + 28 q^{94} - 40 q^{96} - 18 q^{97} - 32 q^{98} - 22 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(177\) \(351\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.14628 0.828280i 0.810541 0.585682i
\(3\) 0.692712i 0.399937i 0.979802 + 0.199969i \(0.0640841\pi\)
−0.979802 + 0.199969i \(0.935916\pi\)
\(4\) 0.627905 1.89888i 0.313952 0.949439i
\(5\) 0 0
\(6\) 0.573759 + 0.794040i 0.234236 + 0.324166i
\(7\) 0.343872 + 0.343872i 0.129971 + 0.129971i 0.769100 0.639129i \(-0.220705\pi\)
−0.639129 + 0.769100i \(0.720705\pi\)
\(8\) −0.853049 2.69672i −0.301598 0.953435i
\(9\) 2.52015 0.840050
\(10\) 0 0
\(11\) 0.843672 + 0.843672i 0.254377 + 0.254377i 0.822762 0.568386i \(-0.192432\pi\)
−0.568386 + 0.822762i \(0.692432\pi\)
\(12\) 1.31538 + 0.434957i 0.379716 + 0.125561i
\(13\) 3.68390 1.02173 0.510865 0.859661i \(-0.329325\pi\)
0.510865 + 0.859661i \(0.329325\pi\)
\(14\) 0.678995 + 0.109350i 0.181469 + 0.0292251i
\(15\) 0 0
\(16\) −3.21147 2.38463i −0.802868 0.596157i
\(17\) −0.412137 0.412137i −0.0999579 0.0999579i 0.655359 0.755317i \(-0.272517\pi\)
−0.755317 + 0.655359i \(0.772517\pi\)
\(18\) 2.88879 2.08739i 0.680895 0.492003i
\(19\) −5.37721 5.37721i −1.23362 1.23362i −0.962565 0.271052i \(-0.912629\pi\)
−0.271052 0.962565i \(-0.587371\pi\)
\(20\) 0 0
\(21\) −0.238204 + 0.238204i −0.0519804 + 0.0519804i
\(22\) 1.66588 + 0.268286i 0.355167 + 0.0571987i
\(23\) 3.08788 3.08788i 0.643868 0.643868i −0.307636 0.951504i \(-0.599538\pi\)
0.951504 + 0.307636i \(0.0995380\pi\)
\(24\) 1.86805 0.590917i 0.381314 0.120621i
\(25\) 0 0
\(26\) 4.22278 3.05130i 0.828154 0.598410i
\(27\) 3.82387i 0.735905i
\(28\) 0.868890 0.437052i 0.164205 0.0825951i
\(29\) −4.22969 + 4.22969i −0.785434 + 0.785434i −0.980742 0.195308i \(-0.937429\pi\)
0.195308 + 0.980742i \(0.437429\pi\)
\(30\) 0 0
\(31\) 8.75966i 1.57328i 0.617411 + 0.786641i \(0.288182\pi\)
−0.617411 + 0.786641i \(0.711818\pi\)
\(32\) −5.65638 0.0734474i −0.999916 0.0129838i
\(33\) −0.584422 + 0.584422i −0.101735 + 0.101735i
\(34\) −0.813788 0.131059i −0.139564 0.0224764i
\(35\) 0 0
\(36\) 1.58241 4.78546i 0.263736 0.797576i
\(37\) 5.41752 0.890634 0.445317 0.895373i \(-0.353091\pi\)
0.445317 + 0.895373i \(0.353091\pi\)
\(38\) −10.6176 1.70994i −1.72240 0.277389i
\(39\) 2.55188i 0.408628i
\(40\) 0 0
\(41\) 2.54777i 0.397895i 0.980010 + 0.198948i \(0.0637524\pi\)
−0.980010 + 0.198948i \(0.936248\pi\)
\(42\) −0.0757484 + 0.470348i −0.0116882 + 0.0725763i
\(43\) −4.30732 −0.656861 −0.328430 0.944528i \(-0.606520\pi\)
−0.328430 + 0.944528i \(0.606520\pi\)
\(44\) 2.13178 1.07228i 0.321377 0.161653i
\(45\) 0 0
\(46\) 0.981939 6.09720i 0.144779 0.898983i
\(47\) −4.56972 + 4.56972i −0.666562 + 0.666562i −0.956919 0.290356i \(-0.906226\pi\)
0.290356 + 0.956919i \(0.406226\pi\)
\(48\) 1.65186 2.22462i 0.238425 0.321097i
\(49\) 6.76350i 0.966215i
\(50\) 0 0
\(51\) 0.285492 0.285492i 0.0399769 0.0399769i
\(52\) 2.31314 6.99528i 0.320775 0.970071i
\(53\) 6.07536i 0.834515i 0.908788 + 0.417257i \(0.137009\pi\)
−0.908788 + 0.417257i \(0.862991\pi\)
\(54\) 3.16724 + 4.38322i 0.431007 + 0.596481i
\(55\) 0 0
\(56\) 0.633987 1.22067i 0.0847201 0.163118i
\(57\) 3.72486 3.72486i 0.493369 0.493369i
\(58\) −1.34503 + 8.35177i −0.176611 + 1.09664i
\(59\) −7.33694 + 7.33694i −0.955189 + 0.955189i −0.999038 0.0438495i \(-0.986038\pi\)
0.0438495 + 0.999038i \(0.486038\pi\)
\(60\) 0 0
\(61\) −4.81576 4.81576i −0.616595 0.616595i 0.328062 0.944656i \(-0.393605\pi\)
−0.944656 + 0.328062i \(0.893605\pi\)
\(62\) 7.25545 + 10.0410i 0.921444 + 1.27521i
\(63\) 0.866609 + 0.866609i 0.109183 + 0.109183i
\(64\) −6.54461 + 4.60087i −0.818077 + 0.575109i
\(65\) 0 0
\(66\) −0.185845 + 1.15397i −0.0228759 + 0.142044i
\(67\) −14.3626 −1.75467 −0.877334 0.479880i \(-0.840680\pi\)
−0.877334 + 0.479880i \(0.840680\pi\)
\(68\) −1.04138 + 0.523815i −0.126286 + 0.0635219i
\(69\) 2.13901 + 2.13901i 0.257507 + 0.257507i
\(70\) 0 0
\(71\) −2.97605 −0.353193 −0.176596 0.984283i \(-0.556509\pi\)
−0.176596 + 0.984283i \(0.556509\pi\)
\(72\) −2.14981 6.79614i −0.253358 0.800933i
\(73\) 6.87152 + 6.87152i 0.804250 + 0.804250i 0.983757 0.179507i \(-0.0574501\pi\)
−0.179507 + 0.983757i \(0.557450\pi\)
\(74\) 6.20998 4.48722i 0.721895 0.521629i
\(75\) 0 0
\(76\) −13.5870 + 6.83429i −1.55854 + 0.783947i
\(77\) 0.580231i 0.0661234i
\(78\) 2.11367 + 2.92517i 0.239326 + 0.331210i
\(79\) 10.1654 1.14369 0.571847 0.820360i \(-0.306227\pi\)
0.571847 + 0.820360i \(0.306227\pi\)
\(80\) 0 0
\(81\) 4.91161 0.545734
\(82\) 2.11027 + 2.92046i 0.233040 + 0.322510i
\(83\) 7.15276i 0.785118i −0.919727 0.392559i \(-0.871590\pi\)
0.919727 0.392559i \(-0.128410\pi\)
\(84\) 0.302751 + 0.601890i 0.0330329 + 0.0656716i
\(85\) 0 0
\(86\) −4.93739 + 3.56767i −0.532412 + 0.384712i
\(87\) −2.92996 2.92996i −0.314124 0.314124i
\(88\) 1.55545 2.99484i 0.165812 0.319251i
\(89\) 1.10953 0.117610 0.0588050 0.998269i \(-0.481271\pi\)
0.0588050 + 0.998269i \(0.481271\pi\)
\(90\) 0 0
\(91\) 1.26679 + 1.26679i 0.132796 + 0.132796i
\(92\) −3.92461 7.80240i −0.409169 0.813457i
\(93\) −6.06792 −0.629214
\(94\) −1.45316 + 9.02318i −0.149882 + 0.930670i
\(95\) 0 0
\(96\) 0.0508779 3.91824i 0.00519270 0.399904i
\(97\) −7.15920 7.15920i −0.726906 0.726906i 0.243096 0.970002i \(-0.421837\pi\)
−0.970002 + 0.243096i \(0.921837\pi\)
\(98\) −5.60207 7.75285i −0.565895 0.783156i
\(99\) 2.12618 + 2.12618i 0.213689 + 0.213689i
\(100\) 0 0
\(101\) 0.953394 0.953394i 0.0948663 0.0948663i −0.658081 0.752947i \(-0.728632\pi\)
0.752947 + 0.658081i \(0.228632\pi\)
\(102\) 0.0907858 0.563721i 0.00898914 0.0558167i
\(103\) −9.59425 + 9.59425i −0.945350 + 0.945350i −0.998582 0.0532322i \(-0.983048\pi\)
0.0532322 + 0.998582i \(0.483048\pi\)
\(104\) −3.14255 9.93446i −0.308152 0.974154i
\(105\) 0 0
\(106\) 5.03210 + 6.96405i 0.488761 + 0.676408i
\(107\) 5.28201i 0.510631i 0.966858 + 0.255316i \(0.0821794\pi\)
−0.966858 + 0.255316i \(0.917821\pi\)
\(108\) 7.26107 + 2.40103i 0.698697 + 0.231039i
\(109\) 1.53980 1.53980i 0.147486 0.147486i −0.629508 0.776994i \(-0.716744\pi\)
0.776994 + 0.629508i \(0.216744\pi\)
\(110\) 0 0
\(111\) 3.75278i 0.356198i
\(112\) −0.284329 1.92434i −0.0268665 0.181833i
\(113\) 2.99656 2.99656i 0.281893 0.281893i −0.551971 0.833863i \(-0.686124\pi\)
0.833863 + 0.551971i \(0.186124\pi\)
\(114\) 1.18450 7.35494i 0.110938 0.688854i
\(115\) 0 0
\(116\) 5.37582 + 10.6875i 0.499133 + 0.992310i
\(117\) 9.28399 0.858305
\(118\) −2.33313 + 14.4872i −0.214782 + 1.33366i
\(119\) 0.283445i 0.0259833i
\(120\) 0 0
\(121\) 9.57643i 0.870585i
\(122\) −9.50899 1.53140i −0.860904 0.138646i
\(123\) −1.76487 −0.159133
\(124\) 16.6335 + 5.50023i 1.49373 + 0.493935i
\(125\) 0 0
\(126\) 1.71117 + 0.275580i 0.152443 + 0.0245506i
\(127\) 10.5522 10.5522i 0.936360 0.936360i −0.0617330 0.998093i \(-0.519663\pi\)
0.998093 + 0.0617330i \(0.0196627\pi\)
\(128\) −3.69113 + 10.6947i −0.326253 + 0.945282i
\(129\) 2.98373i 0.262703i
\(130\) 0 0
\(131\) −0.850513 + 0.850513i −0.0743096 + 0.0743096i −0.743285 0.668975i \(-0.766733\pi\)
0.668975 + 0.743285i \(0.266733\pi\)
\(132\) 0.742784 + 1.47671i 0.0646511 + 0.128531i
\(133\) 3.69814i 0.320670i
\(134\) −16.4635 + 11.8962i −1.42223 + 1.02768i
\(135\) 0 0
\(136\) −0.759845 + 1.46299i −0.0651562 + 0.125451i
\(137\) 5.50145 5.50145i 0.470021 0.470021i −0.431901 0.901921i \(-0.642157\pi\)
0.901921 + 0.431901i \(0.142157\pi\)
\(138\) 4.22360 + 0.680201i 0.359537 + 0.0579025i
\(139\) 3.03517 3.03517i 0.257440 0.257440i −0.566572 0.824012i \(-0.691731\pi\)
0.824012 + 0.566572i \(0.191731\pi\)
\(140\) 0 0
\(141\) −3.16550 3.16550i −0.266583 0.266583i
\(142\) −3.41138 + 2.46501i −0.286277 + 0.206859i
\(143\) 3.10801 + 3.10801i 0.259905 + 0.259905i
\(144\) −8.09339 6.00962i −0.674449 0.500802i
\(145\) 0 0
\(146\) 13.5682 + 2.18513i 1.12291 + 0.180842i
\(147\) 4.68516 0.386425
\(148\) 3.40168 10.2872i 0.279617 0.845603i
\(149\) 11.1571 + 11.1571i 0.914023 + 0.914023i 0.996586 0.0825625i \(-0.0263104\pi\)
−0.0825625 + 0.996586i \(0.526310\pi\)
\(150\) 0 0
\(151\) 3.18265 0.259000 0.129500 0.991579i \(-0.458663\pi\)
0.129500 + 0.991579i \(0.458663\pi\)
\(152\) −9.91381 + 19.0879i −0.804116 + 1.54823i
\(153\) −1.03865 1.03865i −0.0839696 0.0839696i
\(154\) 0.480593 + 0.665105i 0.0387273 + 0.0535957i
\(155\) 0 0
\(156\) 4.84571 + 1.60234i 0.387968 + 0.128290i
\(157\) 7.05454i 0.563014i 0.959559 + 0.281507i \(0.0908342\pi\)
−0.959559 + 0.281507i \(0.909166\pi\)
\(158\) 11.6523 8.41978i 0.927011 0.669842i
\(159\) −4.20847 −0.333754
\(160\) 0 0
\(161\) 2.12367 0.167369
\(162\) 5.63007 4.06819i 0.442340 0.319627i
\(163\) 16.0208i 1.25484i −0.778680 0.627422i \(-0.784110\pi\)
0.778680 0.627422i \(-0.215890\pi\)
\(164\) 4.83791 + 1.59976i 0.377777 + 0.124920i
\(165\) 0 0
\(166\) −5.92449 8.19905i −0.459830 0.636370i
\(167\) 16.6023 + 16.6023i 1.28473 + 1.28473i 0.937946 + 0.346780i \(0.112725\pi\)
0.346780 + 0.937946i \(0.387275\pi\)
\(168\) 0.845571 + 0.439171i 0.0652372 + 0.0338827i
\(169\) 0.571141 0.0439339
\(170\) 0 0
\(171\) −13.5514 13.5514i −1.03630 1.03630i
\(172\) −2.70459 + 8.17908i −0.206223 + 0.623649i
\(173\) −14.9958 −1.14011 −0.570054 0.821607i \(-0.693078\pi\)
−0.570054 + 0.821607i \(0.693078\pi\)
\(174\) −5.78537 0.931719i −0.438588 0.0706335i
\(175\) 0 0
\(176\) −0.697585 4.72127i −0.0525825 0.355879i
\(177\) −5.08239 5.08239i −0.382016 0.382016i
\(178\) 1.27183 0.919002i 0.0953277 0.0688821i
\(179\) −9.91310 9.91310i −0.740940 0.740940i 0.231819 0.972759i \(-0.425532\pi\)
−0.972759 + 0.231819i \(0.925532\pi\)
\(180\) 0 0
\(181\) 1.04015 1.04015i 0.0773139 0.0773139i −0.667392 0.744706i \(-0.732590\pi\)
0.744706 + 0.667392i \(0.232590\pi\)
\(182\) 2.50135 + 0.402837i 0.185413 + 0.0298602i
\(183\) 3.33593 3.33593i 0.246599 0.246599i
\(184\) −10.9613 5.69304i −0.808075 0.419696i
\(185\) 0 0
\(186\) −6.95552 + 5.02594i −0.510004 + 0.368520i
\(187\) 0.695417i 0.0508539i
\(188\) 5.80799 + 11.5467i 0.423591 + 0.842129i
\(189\) −1.31492 + 1.31492i −0.0956466 + 0.0956466i
\(190\) 0 0
\(191\) 3.08419i 0.223164i −0.993755 0.111582i \(-0.964408\pi\)
0.993755 0.111582i \(-0.0355918\pi\)
\(192\) −3.18708 4.53353i −0.230008 0.327179i
\(193\) 12.0915 12.0915i 0.870368 0.870368i −0.122144 0.992512i \(-0.538977\pi\)
0.992512 + 0.122144i \(0.0389770\pi\)
\(194\) −14.1362 2.27661i −1.01492 0.163451i
\(195\) 0 0
\(196\) −12.8431 4.24683i −0.917362 0.303345i
\(197\) −13.0186 −0.927540 −0.463770 0.885956i \(-0.653504\pi\)
−0.463770 + 0.885956i \(0.653504\pi\)
\(198\) 4.19827 + 0.676120i 0.298358 + 0.0480498i
\(199\) 10.6279i 0.753395i −0.926336 0.376697i \(-0.877060\pi\)
0.926336 0.376697i \(-0.122940\pi\)
\(200\) 0 0
\(201\) 9.94913i 0.701758i
\(202\) 0.303177 1.88253i 0.0213315 0.132455i
\(203\) −2.90894 −0.204168
\(204\) −0.362853 0.721377i −0.0254048 0.0505065i
\(205\) 0 0
\(206\) −3.05095 + 18.9444i −0.212570 + 1.31992i
\(207\) 7.78192 7.78192i 0.540881 0.540881i
\(208\) −11.8308 8.78474i −0.820315 0.609112i
\(209\) 9.07320i 0.627607i
\(210\) 0 0
\(211\) 11.4801 11.4801i 0.790321 0.790321i −0.191225 0.981546i \(-0.561246\pi\)
0.981546 + 0.191225i \(0.0612460\pi\)
\(212\) 11.5364 + 3.81475i 0.792321 + 0.261998i
\(213\) 2.06155i 0.141255i
\(214\) 4.37499 + 6.05465i 0.299068 + 0.413888i
\(215\) 0 0
\(216\) 10.3119 3.26195i 0.701638 0.221948i
\(217\) −3.01220 + 3.01220i −0.204482 + 0.204482i
\(218\) 0.489652 3.04042i 0.0331634 0.205923i
\(219\) −4.75998 + 4.75998i −0.321650 + 0.321650i
\(220\) 0 0
\(221\) −1.51827 1.51827i −0.102130 0.102130i
\(222\) 3.10835 + 4.30173i 0.208619 + 0.288713i
\(223\) −2.17863 2.17863i −0.145892 0.145892i 0.630388 0.776280i \(-0.282896\pi\)
−0.776280 + 0.630388i \(0.782896\pi\)
\(224\) −1.91981 1.97033i −0.128273 0.131648i
\(225\) 0 0
\(226\) 0.952898 5.91688i 0.0633859 0.393585i
\(227\) −9.32318 −0.618801 −0.309401 0.950932i \(-0.600128\pi\)
−0.309401 + 0.950932i \(0.600128\pi\)
\(228\) −4.73419 9.41190i −0.313530 0.623318i
\(229\) −2.72259 2.72259i −0.179914 0.179914i 0.611404 0.791318i \(-0.290605\pi\)
−0.791318 + 0.611404i \(0.790605\pi\)
\(230\) 0 0
\(231\) −0.401933 −0.0264452
\(232\) 15.0144 + 7.79816i 0.985746 + 0.511974i
\(233\) −12.3897 12.3897i −0.811679 0.811679i 0.173206 0.984886i \(-0.444587\pi\)
−0.984886 + 0.173206i \(0.944587\pi\)
\(234\) 10.6420 7.68974i 0.695691 0.502694i
\(235\) 0 0
\(236\) 9.32506 + 18.5389i 0.607010 + 1.20678i
\(237\) 7.04168i 0.457406i
\(238\) −0.234772 0.324906i −0.0152180 0.0210606i
\(239\) 25.2180 1.63122 0.815609 0.578604i \(-0.196402\pi\)
0.815609 + 0.578604i \(0.196402\pi\)
\(240\) 0 0
\(241\) 12.0218 0.774391 0.387195 0.921998i \(-0.373444\pi\)
0.387195 + 0.921998i \(0.373444\pi\)
\(242\) −7.93197 10.9773i −0.509886 0.705645i
\(243\) 14.8740i 0.954164i
\(244\) −12.1684 + 6.12070i −0.779000 + 0.391838i
\(245\) 0 0
\(246\) −2.02303 + 1.46181i −0.128984 + 0.0932015i
\(247\) −19.8091 19.8091i −1.26042 1.26042i
\(248\) 23.6224 7.47242i 1.50002 0.474499i
\(249\) 4.95480 0.313998
\(250\) 0 0
\(251\) 7.48911 + 7.48911i 0.472709 + 0.472709i 0.902790 0.430081i \(-0.141515\pi\)
−0.430081 + 0.902790i \(0.641515\pi\)
\(252\) 2.18973 1.10144i 0.137940 0.0693840i
\(253\) 5.21032 0.327570
\(254\) 3.35559 20.8360i 0.210548 1.30737i
\(255\) 0 0
\(256\) 4.62710 + 15.3163i 0.289194 + 0.957271i
\(257\) 10.0809 + 10.0809i 0.628832 + 0.628832i 0.947774 0.318942i \(-0.103328\pi\)
−0.318942 + 0.947774i \(0.603328\pi\)
\(258\) −2.47137 3.42019i −0.153861 0.212932i
\(259\) 1.86293 + 1.86293i 0.115757 + 0.115757i
\(260\) 0 0
\(261\) −10.6595 + 10.6595i −0.659804 + 0.659804i
\(262\) −0.270461 + 1.67939i −0.0167091 + 0.103753i
\(263\) 3.83599 3.83599i 0.236537 0.236537i −0.578877 0.815415i \(-0.696509\pi\)
0.815415 + 0.578877i \(0.196509\pi\)
\(264\) 2.07456 + 1.07748i 0.127681 + 0.0663144i
\(265\) 0 0
\(266\) −3.06310 4.23910i −0.187811 0.259916i
\(267\) 0.768585i 0.0470367i
\(268\) −9.01833 + 27.2728i −0.550882 + 1.66595i
\(269\) −13.4250 + 13.4250i −0.818539 + 0.818539i −0.985896 0.167357i \(-0.946477\pi\)
0.167357 + 0.985896i \(0.446477\pi\)
\(270\) 0 0
\(271\) 12.3519i 0.750326i −0.926959 0.375163i \(-0.877587\pi\)
0.926959 0.375163i \(-0.122413\pi\)
\(272\) 0.340773 + 2.30636i 0.0206624 + 0.139844i
\(273\) −0.877522 + 0.877522i −0.0531100 + 0.0531100i
\(274\) 1.74945 10.8629i 0.105688 0.656253i
\(275\) 0 0
\(276\) 5.40482 2.71863i 0.325332 0.163642i
\(277\) 6.78804 0.407854 0.203927 0.978986i \(-0.434630\pi\)
0.203927 + 0.978986i \(0.434630\pi\)
\(278\) 0.965177 5.99312i 0.0578875 0.359443i
\(279\) 22.0757i 1.32164i
\(280\) 0 0
\(281\) 21.5509i 1.28562i 0.766026 + 0.642810i \(0.222232\pi\)
−0.766026 + 0.642810i \(0.777768\pi\)
\(282\) −6.25046 1.00662i −0.372210 0.0599434i
\(283\) 9.86809 0.586597 0.293299 0.956021i \(-0.405247\pi\)
0.293299 + 0.956021i \(0.405247\pi\)
\(284\) −1.86868 + 5.65116i −0.110886 + 0.335335i
\(285\) 0 0
\(286\) 6.13694 + 0.988339i 0.362885 + 0.0584417i
\(287\) −0.876108 + 0.876108i −0.0517150 + 0.0517150i
\(288\) −14.2549 0.185099i −0.839979 0.0109070i
\(289\) 16.6603i 0.980017i
\(290\) 0 0
\(291\) 4.95926 4.95926i 0.290717 0.290717i
\(292\) 17.3628 8.73351i 1.01608 0.511090i
\(293\) 14.1972i 0.829410i 0.909956 + 0.414705i \(0.136115\pi\)
−0.909956 + 0.414705i \(0.863885\pi\)
\(294\) 5.37049 3.88062i 0.313214 0.226323i
\(295\) 0 0
\(296\) −4.62141 14.6095i −0.268614 0.849162i
\(297\) −3.22610 + 3.22610i −0.187197 + 0.187197i
\(298\) 22.0303 + 3.54792i 1.27618 + 0.205526i
\(299\) 11.3755 11.3755i 0.657859 0.657859i
\(300\) 0 0
\(301\) −1.48117 1.48117i −0.0853731 0.0853731i
\(302\) 3.64820 2.63612i 0.209930 0.151692i
\(303\) 0.660428 + 0.660428i 0.0379406 + 0.0379406i
\(304\) 4.44611 + 30.0914i 0.255002 + 1.72586i
\(305\) 0 0
\(306\) −2.05087 0.330287i −0.117240 0.0188813i
\(307\) 20.4161 1.16521 0.582604 0.812756i \(-0.302034\pi\)
0.582604 + 0.812756i \(0.302034\pi\)
\(308\) 1.10179 + 0.364329i 0.0627801 + 0.0207596i
\(309\) −6.64605 6.64605i −0.378081 0.378081i
\(310\) 0 0
\(311\) −6.81074 −0.386202 −0.193101 0.981179i \(-0.561854\pi\)
−0.193101 + 0.981179i \(0.561854\pi\)
\(312\) 6.88172 2.17688i 0.389601 0.123242i
\(313\) 1.20933 + 1.20933i 0.0683555 + 0.0683555i 0.740458 0.672103i \(-0.234609\pi\)
−0.672103 + 0.740458i \(0.734609\pi\)
\(314\) 5.84314 + 8.08646i 0.329747 + 0.456345i
\(315\) 0 0
\(316\) 6.38289 19.3028i 0.359065 1.08587i
\(317\) 3.44178i 0.193310i 0.995318 + 0.0966548i \(0.0308143\pi\)
−0.995318 + 0.0966548i \(0.969186\pi\)
\(318\) −4.82408 + 3.48580i −0.270521 + 0.195474i
\(319\) −7.13694 −0.399592
\(320\) 0 0
\(321\) −3.65891 −0.204221
\(322\) 2.43432 1.75899i 0.135659 0.0980249i
\(323\) 4.43229i 0.246619i
\(324\) 3.08402 9.32654i 0.171334 0.518141i
\(325\) 0 0
\(326\) −13.2697 18.3643i −0.734940 1.01710i
\(327\) 1.06664 + 1.06664i 0.0589852 + 0.0589852i
\(328\) 6.87063 2.17338i 0.379367 0.120005i
\(329\) −3.14280 −0.173268
\(330\) 0 0
\(331\) −1.48462 1.48462i −0.0816019 0.0816019i 0.665128 0.746730i \(-0.268377\pi\)
−0.746730 + 0.665128i \(0.768377\pi\)
\(332\) −13.5822 4.49125i −0.745421 0.246489i
\(333\) 13.6530 0.748177
\(334\) 32.7822 + 5.27950i 1.79376 + 0.288881i
\(335\) 0 0
\(336\) 1.33301 0.196958i 0.0727219 0.0107449i
\(337\) −6.21211 6.21211i −0.338395 0.338395i 0.517368 0.855763i \(-0.326912\pi\)
−0.855763 + 0.517368i \(0.826912\pi\)
\(338\) 0.654686 0.473065i 0.0356102 0.0257313i
\(339\) 2.07575 + 2.07575i 0.112739 + 0.112739i
\(340\) 0 0
\(341\) −7.39028 + 7.39028i −0.400206 + 0.400206i
\(342\) −26.7580 4.30930i −1.44691 0.233020i
\(343\) 4.73288 4.73288i 0.255552 0.255552i
\(344\) 3.67436 + 11.6156i 0.198108 + 0.626274i
\(345\) 0 0
\(346\) −17.1893 + 12.4207i −0.924104 + 0.667741i
\(347\) 10.1502i 0.544889i −0.962171 0.272445i \(-0.912168\pi\)
0.962171 0.272445i \(-0.0878321\pi\)
\(348\) −7.40336 + 3.72390i −0.396862 + 0.199622i
\(349\) −3.99595 + 3.99595i −0.213898 + 0.213898i −0.805921 0.592023i \(-0.798329\pi\)
0.592023 + 0.805921i \(0.298329\pi\)
\(350\) 0 0
\(351\) 14.0868i 0.751897i
\(352\) −4.71016 4.83409i −0.251053 0.257658i
\(353\) −22.6637 + 22.6637i −1.20627 + 1.20627i −0.234043 + 0.972226i \(0.575196\pi\)
−0.972226 + 0.234043i \(0.924804\pi\)
\(354\) −10.0355 1.61619i −0.533379 0.0858994i
\(355\) 0 0
\(356\) 0.696680 2.10686i 0.0369239 0.111664i
\(357\) 0.196346 0.0103917
\(358\) −19.5740 3.15234i −1.03452 0.166606i
\(359\) 4.31874i 0.227934i 0.993485 + 0.113967i \(0.0363559\pi\)
−0.993485 + 0.113967i \(0.963644\pi\)
\(360\) 0 0
\(361\) 38.8288i 2.04362i
\(362\) 0.330766 2.05384i 0.0173847 0.107947i
\(363\) 6.63371 0.348180
\(364\) 3.20091 1.61006i 0.167773 0.0843899i
\(365\) 0 0
\(366\) 1.06082 6.58699i 0.0554499 0.344308i
\(367\) 6.46940 6.46940i 0.337700 0.337700i −0.517801 0.855501i \(-0.673249\pi\)
0.855501 + 0.517801i \(0.173249\pi\)
\(368\) −17.2801 + 2.55320i −0.900787 + 0.133095i
\(369\) 6.42077i 0.334252i
\(370\) 0 0
\(371\) −2.08915 + 2.08915i −0.108463 + 0.108463i
\(372\) −3.81008 + 11.5222i −0.197543 + 0.597400i
\(373\) 16.7831i 0.868995i −0.900673 0.434497i \(-0.856926\pi\)
0.900673 0.434497i \(-0.143074\pi\)
\(374\) −0.576000 0.797141i −0.0297842 0.0412192i
\(375\) 0 0
\(376\) 16.2215 + 8.42507i 0.836558 + 0.434490i
\(377\) −15.5818 + 15.5818i −0.802502 + 0.802502i
\(378\) −0.418142 + 2.59639i −0.0215069 + 0.133544i
\(379\) −7.31046 + 7.31046i −0.375513 + 0.375513i −0.869480 0.493967i \(-0.835546\pi\)
0.493967 + 0.869480i \(0.335546\pi\)
\(380\) 0 0
\(381\) 7.30966 + 7.30966i 0.374485 + 0.374485i
\(382\) −2.55457 3.53533i −0.130703 0.180883i
\(383\) 5.31492 + 5.31492i 0.271580 + 0.271580i 0.829736 0.558156i \(-0.188491\pi\)
−0.558156 + 0.829736i \(0.688491\pi\)
\(384\) −7.40831 2.55689i −0.378054 0.130481i
\(385\) 0 0
\(386\) 3.84508 23.8754i 0.195710 1.21523i
\(387\) −10.8551 −0.551796
\(388\) −18.0897 + 9.09915i −0.918367 + 0.461939i
\(389\) −1.28845 1.28845i −0.0653271 0.0653271i 0.673688 0.739016i \(-0.264709\pi\)
−0.739016 + 0.673688i \(0.764709\pi\)
\(390\) 0 0
\(391\) −2.54526 −0.128719
\(392\) −18.2393 + 5.76960i −0.921223 + 0.291409i
\(393\) −0.589160 0.589160i −0.0297192 0.0297192i
\(394\) −14.9230 + 10.7831i −0.751809 + 0.543244i
\(395\) 0 0
\(396\) 5.37239 2.70232i 0.269973 0.135797i
\(397\) 9.53832i 0.478715i −0.970932 0.239357i \(-0.923063\pi\)
0.970932 0.239357i \(-0.0769367\pi\)
\(398\) −8.80291 12.1826i −0.441250 0.610657i
\(399\) 2.56175 0.128248
\(400\) 0 0
\(401\) −24.6103 −1.22898 −0.614491 0.788924i \(-0.710638\pi\)
−0.614491 + 0.788924i \(0.710638\pi\)
\(402\) −8.24067 11.4045i −0.411007 0.568803i
\(403\) 32.2697i 1.60747i
\(404\) −1.21174 2.40902i −0.0602862 0.119853i
\(405\) 0 0
\(406\) −3.33446 + 2.40942i −0.165486 + 0.119578i
\(407\) 4.57061 + 4.57061i 0.226557 + 0.226557i
\(408\) −1.01343 0.526354i −0.0501724 0.0260584i
\(409\) −16.9457 −0.837911 −0.418955 0.908007i \(-0.637604\pi\)
−0.418955 + 0.908007i \(0.637604\pi\)
\(410\) 0 0
\(411\) 3.81092 + 3.81092i 0.187979 + 0.187979i
\(412\) 12.1940 + 24.2426i 0.600757 + 1.19435i
\(413\) −5.04594 −0.248294
\(414\) 2.47463 15.3659i 0.121622 0.755190i
\(415\) 0 0
\(416\) −20.8375 0.270573i −1.02164 0.0132659i
\(417\) 2.10250 + 2.10250i 0.102960 + 0.102960i
\(418\) −7.51515 10.4004i −0.367578 0.508701i
\(419\) −6.56956 6.56956i −0.320944 0.320944i 0.528185 0.849129i \(-0.322873\pi\)
−0.849129 + 0.528185i \(0.822873\pi\)
\(420\) 0 0
\(421\) 13.8805 13.8805i 0.676493 0.676493i −0.282712 0.959205i \(-0.591234\pi\)
0.959205 + 0.282712i \(0.0912341\pi\)
\(422\) 3.65064 22.6681i 0.177710 1.10346i
\(423\) −11.5164 + 11.5164i −0.559946 + 0.559946i
\(424\) 16.3836 5.18258i 0.795656 0.251688i
\(425\) 0 0
\(426\) −1.70754 2.36311i −0.0827305 0.114493i
\(427\) 3.31201i 0.160279i
\(428\) 10.0299 + 3.31660i 0.484813 + 0.160314i
\(429\) −2.15295 + 2.15295i −0.103946 + 0.103946i
\(430\) 0 0
\(431\) 12.3740i 0.596035i −0.954560 0.298017i \(-0.903675\pi\)
0.954560 0.298017i \(-0.0963254\pi\)
\(432\) 9.11852 12.2803i 0.438715 0.590834i
\(433\) 0.145326 0.145326i 0.00698392 0.00698392i −0.703606 0.710590i \(-0.748428\pi\)
0.710590 + 0.703606i \(0.248428\pi\)
\(434\) −0.957873 + 5.94777i −0.0459794 + 0.285502i
\(435\) 0 0
\(436\) −1.95704 3.89074i −0.0937253 0.186332i
\(437\) −33.2084 −1.58857
\(438\) −1.51366 + 9.39886i −0.0723256 + 0.449095i
\(439\) 3.65842i 0.174607i −0.996182 0.0873035i \(-0.972175\pi\)
0.996182 0.0873035i \(-0.0278250\pi\)
\(440\) 0 0
\(441\) 17.0450i 0.811669i
\(442\) −2.99792 0.482807i −0.142596 0.0229648i
\(443\) −3.94027 −0.187208 −0.0936039 0.995610i \(-0.529839\pi\)
−0.0936039 + 0.995610i \(0.529839\pi\)
\(444\) 7.12607 + 2.35639i 0.338188 + 0.111829i
\(445\) 0 0
\(446\) −4.30184 0.692800i −0.203698 0.0328050i
\(447\) −7.72864 + 7.72864i −0.365552 + 0.365552i
\(448\) −3.83262 0.668398i −0.181074 0.0315788i
\(449\) 38.0014i 1.79340i 0.442642 + 0.896698i \(0.354041\pi\)
−0.442642 + 0.896698i \(0.645959\pi\)
\(450\) 0 0
\(451\) −2.14949 + 2.14949i −0.101215 + 0.101215i
\(452\) −3.80855 7.57165i −0.179139 0.356140i
\(453\) 2.20466i 0.103584i
\(454\) −10.6870 + 7.72221i −0.501564 + 0.362421i
\(455\) 0 0
\(456\) −13.2224 6.86742i −0.619195 0.321596i
\(457\) −18.1142 + 18.1142i −0.847348 + 0.847348i −0.989801 0.142454i \(-0.954501\pi\)
0.142454 + 0.989801i \(0.454501\pi\)
\(458\) −5.37592 0.865778i −0.251200 0.0404551i
\(459\) 1.57596 1.57596i 0.0735595 0.0735595i
\(460\) 0 0
\(461\) 12.4144 + 12.4144i 0.578197 + 0.578197i 0.934406 0.356209i \(-0.115931\pi\)
−0.356209 + 0.934406i \(0.615931\pi\)
\(462\) −0.460726 + 0.332913i −0.0214349 + 0.0154885i
\(463\) 8.56578 + 8.56578i 0.398085 + 0.398085i 0.877557 0.479472i \(-0.159172\pi\)
−0.479472 + 0.877557i \(0.659172\pi\)
\(464\) 23.6698 3.49729i 1.09884 0.162358i
\(465\) 0 0
\(466\) −24.4643 3.93991i −1.13329 0.182513i
\(467\) 34.3465 1.58937 0.794684 0.607023i \(-0.207636\pi\)
0.794684 + 0.607023i \(0.207636\pi\)
\(468\) 5.82946 17.6292i 0.269467 0.814908i
\(469\) −4.93889 4.93889i −0.228057 0.228057i
\(470\) 0 0
\(471\) −4.88677 −0.225170
\(472\) 26.0445 + 13.5269i 1.19879 + 0.622627i
\(473\) −3.63397 3.63397i −0.167090 0.167090i
\(474\) 5.83248 + 8.07172i 0.267895 + 0.370746i
\(475\) 0 0
\(476\) −0.538227 0.177976i −0.0246696 0.00815753i
\(477\) 15.3108i 0.701034i
\(478\) 28.9068 20.8876i 1.32217 0.955375i
\(479\) −23.4504 −1.07148 −0.535738 0.844384i \(-0.679966\pi\)
−0.535738 + 0.844384i \(0.679966\pi\)
\(480\) 0 0
\(481\) 19.9576 0.909988
\(482\) 13.7803 9.95740i 0.627675 0.453547i
\(483\) 1.47109i 0.0669370i
\(484\) −18.1845 6.01309i −0.826567 0.273322i
\(485\) 0 0
\(486\) 12.3198 + 17.0497i 0.558837 + 0.773389i
\(487\) 5.31215 + 5.31215i 0.240716 + 0.240716i 0.817146 0.576430i \(-0.195555\pi\)
−0.576430 + 0.817146i \(0.695555\pi\)
\(488\) −8.87868 + 17.0948i −0.401919 + 0.773847i
\(489\) 11.0978 0.501859
\(490\) 0 0
\(491\) −3.71980 3.71980i −0.167872 0.167872i 0.618171 0.786044i \(-0.287874\pi\)
−0.786044 + 0.618171i \(0.787874\pi\)
\(492\) −1.10817 + 3.35128i −0.0499602 + 0.151087i
\(493\) 3.48642 0.157021
\(494\) −39.1142 6.29925i −1.75983 0.283417i
\(495\) 0 0
\(496\) 20.8885 28.1314i 0.937923 1.26314i
\(497\) −1.02338 1.02338i −0.0459050 0.0459050i
\(498\) 5.67958 4.10396i 0.254508 0.183903i
\(499\) 13.6065 + 13.6065i 0.609111 + 0.609111i 0.942714 0.333603i \(-0.108264\pi\)
−0.333603 + 0.942714i \(0.608264\pi\)
\(500\) 0 0
\(501\) −11.5006 + 11.5006i −0.513810 + 0.513810i
\(502\) 14.7877 + 2.38152i 0.660007 + 0.106292i
\(503\) 9.31208 9.31208i 0.415205 0.415205i −0.468342 0.883547i \(-0.655148\pi\)
0.883547 + 0.468342i \(0.155148\pi\)
\(504\) 1.59774 3.07626i 0.0711691 0.137028i
\(505\) 0 0
\(506\) 5.97247 4.31560i 0.265509 0.191852i
\(507\) 0.395636i 0.0175708i
\(508\) −13.4116 26.6632i −0.595044 1.18299i
\(509\) 7.94836 7.94836i 0.352305 0.352305i −0.508662 0.860966i \(-0.669860\pi\)
0.860966 + 0.508662i \(0.169860\pi\)
\(510\) 0 0
\(511\) 4.72585i 0.209059i
\(512\) 17.9902 + 13.7242i 0.795060 + 0.606531i
\(513\) 20.5618 20.5618i 0.907824 0.907824i
\(514\) 19.9054 + 3.20571i 0.877989 + 0.141398i
\(515\) 0 0
\(516\) −5.66575 1.87350i −0.249421 0.0824762i
\(517\) −7.71069 −0.339116
\(518\) 3.67847 + 0.592408i 0.161623 + 0.0260289i
\(519\) 10.3878i 0.455972i
\(520\) 0 0
\(521\) 29.3979i 1.28795i −0.765048 0.643974i \(-0.777285\pi\)
0.765048 0.643974i \(-0.222715\pi\)
\(522\) −3.38968 + 21.0477i −0.148362 + 0.921233i
\(523\) 19.5121 0.853205 0.426602 0.904439i \(-0.359710\pi\)
0.426602 + 0.904439i \(0.359710\pi\)
\(524\) 1.08098 + 2.14906i 0.0472228 + 0.0938821i
\(525\) 0 0
\(526\) 1.21984 7.57438i 0.0531874 0.330259i
\(527\) 3.61018 3.61018i 0.157262 0.157262i
\(528\) 3.27048 0.483226i 0.142329 0.0210297i
\(529\) 3.92999i 0.170869i
\(530\) 0 0
\(531\) −18.4902 + 18.4902i −0.802406 + 0.802406i
\(532\) −7.02232 2.32208i −0.304456 0.100675i
\(533\) 9.38575i 0.406542i
\(534\) 0.636604 + 0.881012i 0.0275485 + 0.0381251i
\(535\) 0 0
\(536\) 12.2520 + 38.7319i 0.529205 + 1.67296i
\(537\) 6.86692 6.86692i 0.296329 0.296329i
\(538\) −4.26913 + 26.5085i −0.184055 + 1.14286i
\(539\) 5.70618 5.70618i 0.245783 0.245783i
\(540\) 0 0
\(541\) 8.47183 + 8.47183i 0.364232 + 0.364232i 0.865369 0.501136i \(-0.167084\pi\)
−0.501136 + 0.865369i \(0.667084\pi\)
\(542\) −10.2309 14.1587i −0.439453 0.608170i
\(543\) 0.720526 + 0.720526i 0.0309207 + 0.0309207i
\(544\) 2.30093 + 2.36147i 0.0986516 + 0.101247i
\(545\) 0 0
\(546\) −0.279050 + 1.73272i −0.0119422 + 0.0741534i
\(547\) −9.97988 −0.426709 −0.213355 0.976975i \(-0.568439\pi\)
−0.213355 + 0.976975i \(0.568439\pi\)
\(548\) −6.99219 13.9010i −0.298692 0.593820i
\(549\) −12.1364 12.1364i −0.517971 0.517971i
\(550\) 0 0
\(551\) 45.4879 1.93785
\(552\) 3.94364 7.59300i 0.167852 0.323180i
\(553\) 3.49559 + 3.49559i 0.148648 + 0.148648i
\(554\) 7.78098 5.62240i 0.330582 0.238873i
\(555\) 0 0
\(556\) −3.85762 7.66922i −0.163600 0.325247i
\(557\) 13.4866i 0.571445i −0.958312 0.285722i \(-0.907766\pi\)
0.958312 0.285722i \(-0.0922335\pi\)
\(558\) 18.2848 + 25.3048i 0.774059 + 1.07124i
\(559\) −15.8678 −0.671135
\(560\) 0 0
\(561\) 0.481724 0.0203384
\(562\) 17.8502 + 24.7033i 0.752965 + 1.04205i
\(563\) 20.3451i 0.857445i −0.903436 0.428723i \(-0.858964\pi\)
0.903436 0.428723i \(-0.141036\pi\)
\(564\) −7.99853 + 4.02327i −0.336799 + 0.169410i
\(565\) 0 0
\(566\) 11.3116 8.17354i 0.475461 0.343560i
\(567\) 1.68896 + 1.68896i 0.0709298 + 0.0709298i
\(568\) 2.53872 + 8.02559i 0.106522 + 0.336746i
\(569\) −17.1460 −0.718797 −0.359399 0.933184i \(-0.617018\pi\)
−0.359399 + 0.933184i \(0.617018\pi\)
\(570\) 0 0
\(571\) 6.24329 + 6.24329i 0.261274 + 0.261274i 0.825571 0.564298i \(-0.190853\pi\)
−0.564298 + 0.825571i \(0.690853\pi\)
\(572\) 7.85325 3.95019i 0.328361 0.165166i
\(573\) 2.13645 0.0892516
\(574\) −0.278600 + 1.72993i −0.0116285 + 0.0722057i
\(575\) 0 0
\(576\) −16.4934 + 11.5949i −0.687225 + 0.483120i
\(577\) 10.0373 + 10.0373i 0.417859 + 0.417859i 0.884465 0.466606i \(-0.154523\pi\)
−0.466606 + 0.884465i \(0.654523\pi\)
\(578\) −13.7994 19.0973i −0.573979 0.794343i
\(579\) 8.37596 + 8.37596i 0.348093 + 0.348093i
\(580\) 0 0
\(581\) 2.45963 2.45963i 0.102043 0.102043i
\(582\) 1.57703 9.79235i 0.0653701 0.405906i
\(583\) −5.12561 + 5.12561i −0.212281 + 0.212281i
\(584\) 12.6688 24.3923i 0.524240 1.00936i
\(585\) 0 0
\(586\) 11.7593 + 16.2739i 0.485771 + 0.672270i
\(587\) 30.6857i 1.26654i −0.773933 0.633268i \(-0.781713\pi\)
0.773933 0.633268i \(-0.218287\pi\)
\(588\) 2.94183 8.89655i 0.121319 0.366887i
\(589\) 47.1025 47.1025i 1.94083 1.94083i
\(590\) 0 0
\(591\) 9.01817i 0.370958i
\(592\) −17.3982 12.9188i −0.715062 0.530958i
\(593\) 2.10671 2.10671i 0.0865123 0.0865123i −0.662526 0.749039i \(-0.730516\pi\)
0.749039 + 0.662526i \(0.230516\pi\)
\(594\) −1.02589 + 6.37011i −0.0420928 + 0.261369i
\(595\) 0 0
\(596\) 28.1915 14.1803i 1.15477 0.580850i
\(597\) 7.36210 0.301311
\(598\) 3.61737 22.4615i 0.147925 0.918518i
\(599\) 32.1322i 1.31289i −0.754375 0.656444i \(-0.772060\pi\)
0.754375 0.656444i \(-0.227940\pi\)
\(600\) 0 0
\(601\) 14.9811i 0.611091i 0.952177 + 0.305546i \(0.0988388\pi\)
−0.952177 + 0.305546i \(0.901161\pi\)
\(602\) −2.92465 0.471008i −0.119200 0.0191968i
\(603\) −36.1959 −1.47401
\(604\) 1.99840 6.04345i 0.0813136 0.245905i
\(605\) 0 0
\(606\) 1.30405 + 0.210014i 0.0529735 + 0.00853125i
\(607\) −27.3357 + 27.3357i −1.10952 + 1.10952i −0.116310 + 0.993213i \(0.537107\pi\)
−0.993213 + 0.116310i \(0.962893\pi\)
\(608\) 30.0206 + 30.8105i 1.21750 + 1.24953i
\(609\) 2.01506i 0.0816544i
\(610\) 0 0
\(611\) −16.8344 + 16.8344i −0.681047 + 0.681047i
\(612\) −2.62443 + 1.32009i −0.106086 + 0.0533616i
\(613\) 48.3829i 1.95417i −0.212859 0.977083i \(-0.568277\pi\)
0.212859 0.977083i \(-0.431723\pi\)
\(614\) 23.4025 16.9103i 0.944449 0.682442i
\(615\) 0 0
\(616\) 1.56472 0.494965i 0.0630444 0.0199427i
\(617\) 31.1565 31.1565i 1.25432 1.25432i 0.300549 0.953766i \(-0.402830\pi\)
0.953766 0.300549i \(-0.0971699\pi\)
\(618\) −13.1230 2.11343i −0.527885 0.0850146i
\(619\) 0.198272 0.198272i 0.00796922 0.00796922i −0.703111 0.711080i \(-0.748206\pi\)
0.711080 + 0.703111i \(0.248206\pi\)
\(620\) 0 0
\(621\) 11.8077 + 11.8077i 0.473825 + 0.473825i
\(622\) −7.80700 + 5.64120i −0.313032 + 0.226191i
\(623\) 0.381537 + 0.381537i 0.0152859 + 0.0152859i
\(624\) 6.08529 8.19530i 0.243607 0.328075i
\(625\) 0 0
\(626\) 2.38790 + 0.384565i 0.0954395 + 0.0153703i
\(627\) 6.28512 0.251003
\(628\) 13.3957 + 4.42958i 0.534547 + 0.176759i
\(629\) −2.23276 2.23276i −0.0890259 0.0890259i
\(630\) 0 0
\(631\) −32.3314 −1.28709 −0.643547 0.765407i \(-0.722538\pi\)
−0.643547 + 0.765407i \(0.722538\pi\)
\(632\) −8.67157 27.4132i −0.344936 1.09044i
\(633\) 7.95239 + 7.95239i 0.316079 + 0.316079i
\(634\) 2.85076 + 3.94523i 0.113218 + 0.156685i
\(635\) 0 0
\(636\) −2.64252 + 7.99138i −0.104783 + 0.316879i
\(637\) 24.9161i 0.987212i
\(638\) −8.18092 + 5.91139i −0.323886 + 0.234034i
\(639\) −7.50010 −0.296700
\(640\) 0 0
\(641\) −46.5662 −1.83926 −0.919628 0.392790i \(-0.871510\pi\)
−0.919628 + 0.392790i \(0.871510\pi\)
\(642\) −4.19413 + 3.03060i −0.165529 + 0.119608i
\(643\) 40.2247i 1.58631i −0.609021 0.793154i \(-0.708437\pi\)
0.609021 0.793154i \(-0.291563\pi\)
\(644\) 1.33346 4.03259i 0.0525458 0.158906i
\(645\) 0 0
\(646\) 3.67118 + 5.08064i 0.144441 + 0.199895i
\(647\) 10.7938 + 10.7938i 0.424349 + 0.424349i 0.886698 0.462349i \(-0.152993\pi\)
−0.462349 + 0.886698i \(0.652993\pi\)
\(648\) −4.18984 13.2452i −0.164593 0.520322i
\(649\) −12.3799 −0.485956
\(650\) 0 0
\(651\) −2.08659 2.08659i −0.0817799 0.0817799i
\(652\) −30.4215 10.0595i −1.19140 0.393961i
\(653\) 3.92443 0.153575 0.0767875 0.997047i \(-0.475534\pi\)
0.0767875 + 0.997047i \(0.475534\pi\)
\(654\) 2.10614 + 0.339188i 0.0823564 + 0.0132633i
\(655\) 0 0
\(656\) 6.07549 8.18210i 0.237208 0.319457i
\(657\) 17.3173 + 17.3173i 0.675610 + 0.675610i
\(658\) −3.60252 + 2.60312i −0.140441 + 0.101480i
\(659\) 34.6142 + 34.6142i 1.34838 + 1.34838i 0.887425 + 0.460952i \(0.152492\pi\)
0.460952 + 0.887425i \(0.347508\pi\)
\(660\) 0 0
\(661\) 21.7641 21.7641i 0.846525 0.846525i −0.143173 0.989698i \(-0.545730\pi\)
0.989698 + 0.143173i \(0.0457304\pi\)
\(662\) −2.93146 0.472104i −0.113934 0.0183489i
\(663\) 1.05173 1.05173i 0.0408456 0.0408456i
\(664\) −19.2890 + 6.10166i −0.748559 + 0.236790i
\(665\) 0 0
\(666\) 15.6501 11.3085i 0.606428 0.438194i
\(667\) 26.1216i 1.01143i
\(668\) 41.9505 21.1011i 1.62311 0.816426i
\(669\) 1.50917 1.50917i 0.0583477 0.0583477i
\(670\) 0 0
\(671\) 8.12584i 0.313695i
\(672\) 1.36487 1.32988i 0.0526510 0.0513012i
\(673\) −29.4450 + 29.4450i −1.13502 + 1.13502i −0.145691 + 0.989330i \(0.546541\pi\)
−0.989330 + 0.145691i \(0.953459\pi\)
\(674\) −12.2662 1.97544i −0.472475 0.0760910i
\(675\) 0 0
\(676\) 0.358622 1.08453i 0.0137932 0.0417126i
\(677\) 34.7351 1.33498 0.667490 0.744619i \(-0.267369\pi\)
0.667490 + 0.744619i \(0.267369\pi\)
\(678\) 4.09869 + 0.660084i 0.157409 + 0.0253504i
\(679\) 4.92370i 0.188954i
\(680\) 0 0
\(681\) 6.45828i 0.247482i
\(682\) −2.35009 + 14.5925i −0.0899897 + 0.558777i
\(683\) 22.2693 0.852110 0.426055 0.904697i \(-0.359903\pi\)
0.426055 + 0.904697i \(0.359903\pi\)
\(684\) −34.2414 + 17.2234i −1.30925 + 0.658554i
\(685\) 0 0
\(686\) 1.50505 9.34535i 0.0574629 0.356807i
\(687\) 1.88597 1.88597i 0.0719543 0.0719543i
\(688\) 13.8328 + 10.2714i 0.527372 + 0.391592i
\(689\) 22.3810i 0.852650i
\(690\) 0 0
\(691\) 15.7043 15.7043i 0.597420 0.597420i −0.342205 0.939625i \(-0.611174\pi\)
0.939625 + 0.342205i \(0.111174\pi\)
\(692\) −9.41591 + 28.4751i −0.357939 + 1.08246i
\(693\) 1.46227i 0.0555470i
\(694\) −8.40717 11.6349i −0.319132 0.441655i
\(695\) 0 0
\(696\) −5.40188 + 10.4007i −0.204758 + 0.394237i
\(697\) 1.05003 1.05003i 0.0397728 0.0397728i
\(698\) −1.27070 + 7.89023i −0.0480968 + 0.298650i
\(699\) 8.58253 8.58253i 0.324621 0.324621i
\(700\) 0 0
\(701\) −21.5588 21.5588i −0.814266 0.814266i 0.171004 0.985270i \(-0.445299\pi\)
−0.985270 + 0.171004i \(0.945299\pi\)
\(702\) 11.6678 + 16.1474i 0.440373 + 0.609443i
\(703\) −29.1311 29.1311i −1.09870 1.09870i
\(704\) −9.40314 1.63988i −0.354394 0.0618053i
\(705\) 0 0
\(706\) −7.20702 + 44.7509i −0.271240 + 1.68422i
\(707\) 0.655691 0.0246598
\(708\) −12.8421 + 6.45958i −0.482635 + 0.242766i
\(709\) −2.96687 2.96687i −0.111423 0.111423i 0.649197 0.760620i \(-0.275105\pi\)
−0.760620 + 0.649197i \(0.775105\pi\)
\(710\) 0 0
\(711\) 25.6183 0.960760
\(712\) −0.946485 2.99210i −0.0354710 0.112134i
\(713\) 27.0488 + 27.0488i 1.01299 + 1.01299i
\(714\) 0.225067 0.162629i 0.00842290 0.00608624i
\(715\) 0 0
\(716\) −25.0482 + 12.5993i −0.936096 + 0.470857i
\(717\) 17.4688i 0.652385i
\(718\) 3.57712 + 4.95047i 0.133497 + 0.184750i
\(719\) −25.8357 −0.963509 −0.481755 0.876306i \(-0.660000\pi\)
−0.481755 + 0.876306i \(0.660000\pi\)
\(720\) 0 0
\(721\) −6.59839 −0.245737
\(722\) 32.1611 + 44.5085i 1.19691 + 1.65644i
\(723\) 8.32763i 0.309708i
\(724\) −1.32201 2.62824i −0.0491320 0.0976777i
\(725\) 0 0
\(726\) 7.60407 5.49457i 0.282214 0.203923i
\(727\) −28.9620 28.9620i −1.07414 1.07414i −0.997022 0.0771198i \(-0.975428\pi\)
−0.0771198 0.997022i \(-0.524572\pi\)
\(728\) 2.33555 4.49682i 0.0865612 0.166663i
\(729\) 4.43146 0.164128
\(730\) 0 0
\(731\) 1.77521 + 1.77521i 0.0656584 + 0.0656584i
\(732\) −4.23988 8.42918i −0.156711 0.311551i
\(733\) −21.1673 −0.781832 −0.390916 0.920426i \(-0.627842\pi\)
−0.390916 + 0.920426i \(0.627842\pi\)
\(734\) 2.05725 12.7742i 0.0759346 0.471504i
\(735\) 0 0
\(736\) −17.6930 + 17.2394i −0.652173 + 0.635453i
\(737\) −12.1173 12.1173i −0.446347 0.446347i
\(738\) 5.31820 + 7.35999i 0.195765 + 0.270925i
\(739\) 2.23302 + 2.23302i 0.0821431 + 0.0821431i 0.746985 0.664841i \(-0.231501\pi\)
−0.664841 + 0.746985i \(0.731501\pi\)
\(740\) 0 0
\(741\) 13.7220 13.7220i 0.504091 0.504091i
\(742\) −0.664344 + 4.12514i −0.0243888 + 0.151439i
\(743\) 18.4514 18.4514i 0.676915 0.676915i −0.282386 0.959301i \(-0.591126\pi\)
0.959301 + 0.282386i \(0.0911258\pi\)
\(744\) 5.17624 + 16.3635i 0.189770 + 0.599915i
\(745\) 0 0
\(746\) −13.9011 19.2381i −0.508955 0.704356i
\(747\) 18.0260i 0.659538i
\(748\) −1.32051 0.436655i −0.0482827 0.0159657i
\(749\) −1.81634 + 1.81634i −0.0663675 + 0.0663675i
\(750\) 0 0
\(751\) 42.4243i 1.54808i −0.633134 0.774042i \(-0.718232\pi\)
0.633134 0.774042i \(-0.281768\pi\)
\(752\) 25.5726 3.77845i 0.932537 0.137786i
\(753\) −5.18780 + 5.18780i −0.189054 + 0.189054i
\(754\) −4.95496 + 30.7671i −0.180449 + 1.12047i
\(755\) 0 0
\(756\) 1.67123 + 3.32253i 0.0607821 + 0.120839i
\(757\) 19.7595 0.718170 0.359085 0.933305i \(-0.383089\pi\)
0.359085 + 0.933305i \(0.383089\pi\)
\(758\) −2.32471 + 14.4349i −0.0844372 + 0.524300i
\(759\) 3.60925i 0.131007i
\(760\) 0 0
\(761\) 48.0351i 1.74127i −0.491928 0.870636i \(-0.663708\pi\)
0.491928 0.870636i \(-0.336292\pi\)
\(762\) 14.4333 + 2.32445i 0.522865 + 0.0842061i
\(763\) 1.05899 0.0383379
\(764\) −5.85649 1.93657i −0.211880 0.0700628i
\(765\) 0 0
\(766\) 10.4946 + 1.69013i 0.379186 + 0.0610669i
\(767\) −27.0286 + 27.0286i −0.975946 + 0.975946i
\(768\) −10.6098 + 3.20525i −0.382848 + 0.115659i
\(769\) 24.0184i 0.866127i 0.901363 + 0.433064i \(0.142567\pi\)
−0.901363 + 0.433064i \(0.857433\pi\)
\(770\) 0 0
\(771\) −6.98319 + 6.98319i −0.251493 + 0.251493i
\(772\) −15.3680 30.5527i −0.553107 1.09962i
\(773\) 22.4630i 0.807937i 0.914773 + 0.403969i \(0.132370\pi\)
−0.914773 + 0.403969i \(0.867630\pi\)
\(774\) −12.4430 + 8.99106i −0.447253 + 0.323177i
\(775\) 0 0
\(776\) −13.1992 + 25.4135i −0.473824 + 0.912292i
\(777\) −1.29048 + 1.29048i −0.0462956 + 0.0462956i
\(778\) −2.54412 0.409725i −0.0912113 0.0146893i
\(779\) 13.6999 13.6999i 0.490850 0.490850i
\(780\) 0 0
\(781\) −2.51081 2.51081i −0.0898440 0.0898440i
\(782\) −2.91757 + 2.10819i −0.104332 + 0.0753886i
\(783\) −16.1738 16.1738i −0.578005 0.578005i
\(784\) −16.1284 + 21.7208i −0.576016 + 0.775743i
\(785\) 0 0
\(786\) −1.16333 0.187352i −0.0414946 0.00668261i
\(787\) −26.1054 −0.930556 −0.465278 0.885165i \(-0.654046\pi\)
−0.465278 + 0.885165i \(0.654046\pi\)
\(788\) −8.17446 + 24.7208i −0.291203 + 0.880642i
\(789\) 2.65724 + 2.65724i 0.0946001 + 0.0946001i
\(790\) 0 0
\(791\) 2.06087 0.0732759
\(792\) 3.91998 7.54745i 0.139290 0.268187i
\(793\) −17.7408 17.7408i −0.629994 0.629994i
\(794\) −7.90040 10.9336i −0.280375 0.388018i
\(795\) 0 0
\(796\) −20.1812 6.67333i −0.715302 0.236530i
\(797\) 43.4888i 1.54045i −0.637770 0.770227i \(-0.720143\pi\)
0.637770 0.770227i \(-0.279857\pi\)
\(798\) 2.93647 2.12185i 0.103950 0.0751125i
\(799\) 3.76670 0.133256
\(800\) 0 0
\(801\) 2.79618 0.0987983
\(802\) −28.2103 + 20.3842i −0.996139 + 0.719793i
\(803\) 11.5946i 0.409165i
\(804\) −18.8922 6.24710i −0.666276 0.220318i
\(805\) 0 0
\(806\) 26.7284 + 36.9901i 0.941467 + 1.30292i
\(807\) −9.29969 9.29969i −0.327364 0.327364i
\(808\) −3.38433 1.75775i −0.119060 0.0618373i
\(809\) 36.6271 1.28774 0.643870 0.765135i \(-0.277328\pi\)
0.643870 + 0.765135i \(0.277328\pi\)
\(810\) 0 0
\(811\) 18.7904 + 18.7904i 0.659821 + 0.659821i 0.955338 0.295516i \(-0.0954917\pi\)
−0.295516 + 0.955338i \(0.595492\pi\)
\(812\) −1.82654 + 5.52373i −0.0640990 + 0.193845i
\(813\) 8.55633 0.300084
\(814\) 9.02493 + 1.45344i 0.316324 + 0.0509431i
\(815\) 0 0
\(816\) −1.59764 + 0.236058i −0.0559287 + 0.00826367i
\(817\) 23.1614 + 23.1614i 0.810314 + 0.810314i
\(818\) −19.4245 + 14.0358i −0.679161 + 0.490750i
\(819\) 3.19250 + 3.19250i 0.111555 + 0.111555i
\(820\) 0 0
\(821\) 3.91048 3.91048i 0.136477 0.136477i −0.635568 0.772045i \(-0.719234\pi\)
0.772045 + 0.635568i \(0.219234\pi\)
\(822\) 7.52488 + 1.21186i 0.262460 + 0.0422686i
\(823\) −35.4412 + 35.4412i −1.23540 + 1.23540i −0.273542 + 0.961860i \(0.588195\pi\)
−0.961860 + 0.273542i \(0.911805\pi\)
\(824\) 34.0574 + 17.6887i 1.18645 + 0.616214i
\(825\) 0 0
\(826\) −5.78405 + 4.17945i −0.201253 + 0.145422i
\(827\) 44.0700i 1.53246i 0.642565 + 0.766232i \(0.277870\pi\)
−0.642565 + 0.766232i \(0.722130\pi\)
\(828\) −9.89061 19.6632i −0.343723 0.683344i
\(829\) 15.1609 15.1609i 0.526561 0.526561i −0.392984 0.919545i \(-0.628557\pi\)
0.919545 + 0.392984i \(0.128557\pi\)
\(830\) 0 0
\(831\) 4.70216i 0.163116i
\(832\) −24.1097 + 16.9492i −0.835854 + 0.587607i
\(833\) −2.78749 + 2.78749i −0.0965808 + 0.0965808i
\(834\) 4.15151 + 0.668590i 0.143755 + 0.0231514i
\(835\) 0 0
\(836\) −17.2289 5.69711i −0.595874 0.197039i
\(837\) −33.4958 −1.15779
\(838\) −12.9720 2.08910i −0.448109 0.0721669i
\(839\) 40.3143i 1.39180i 0.718137 + 0.695901i \(0.244995\pi\)
−0.718137 + 0.695901i \(0.755005\pi\)
\(840\) 0 0
\(841\) 6.78056i 0.233812i
\(842\) 4.41396 27.4078i 0.152115 0.944535i
\(843\) −14.9286 −0.514168
\(844\) −14.5909 29.0077i −0.502238 0.998485i
\(845\) 0 0
\(846\) −3.66218 + 22.7398i −0.125908 + 0.781809i
\(847\) 3.29307 3.29307i 0.113151 0.113151i
\(848\) 14.4875 19.5108i 0.497502 0.670005i
\(849\) 6.83575i 0.234602i
\(850\) 0 0
\(851\) 16.7286 16.7286i 0.573450 0.573450i
\(852\) −3.91463 1.29446i −0.134113 0.0443473i
\(853\) 28.6203i 0.979941i 0.871739 + 0.489971i \(0.162992\pi\)
−0.871739 + 0.489971i \(0.837008\pi\)
\(854\) −2.74327 3.79648i −0.0938728 0.129913i
\(855\) 0 0
\(856\) 14.2441 4.50582i 0.486854 0.154006i
\(857\) 7.19794 7.19794i 0.245877 0.245877i −0.573399 0.819276i \(-0.694376\pi\)
0.819276 + 0.573399i \(0.194376\pi\)
\(858\) −0.684634 + 4.25113i −0.0233730 + 0.145131i
\(859\) −18.8135 + 18.8135i −0.641910 + 0.641910i −0.951025 0.309115i \(-0.899967\pi\)
0.309115 + 0.951025i \(0.399967\pi\)
\(860\) 0 0
\(861\) −0.606890 0.606890i −0.0206828 0.0206828i
\(862\) −10.2491 14.1840i −0.349087 0.483110i
\(863\) −19.2328 19.2328i −0.654691 0.654691i 0.299428 0.954119i \(-0.403204\pi\)
−0.954119 + 0.299428i \(0.903204\pi\)
\(864\) 0.280854 21.6293i 0.00955484 0.735843i
\(865\) 0 0
\(866\) 0.0462133 0.286955i 0.00157039 0.00975112i
\(867\) 11.5408 0.391945
\(868\) 3.82843 + 7.61118i 0.129945 + 0.258340i
\(869\) 8.57624 + 8.57624i 0.290929 + 0.290929i
\(870\) 0 0
\(871\) −52.9103 −1.79280
\(872\) −5.46593 2.83888i −0.185100 0.0961367i
\(873\) −18.0423 18.0423i −0.610638 0.610638i
\(874\) −38.0660 + 27.5058i −1.28760 + 0.930398i
\(875\) 0 0
\(876\) 6.04981 + 12.0274i 0.204404 + 0.406369i
\(877\) 35.4397i 1.19671i −0.801229 0.598357i \(-0.795820\pi\)
0.801229 0.598357i \(-0.204180\pi\)
\(878\) −3.03020 4.19357i −0.102264 0.141526i
\(879\) −9.83458 −0.331712
\(880\) 0 0
\(881\) 30.2010 1.01750 0.508748 0.860915i \(-0.330108\pi\)
0.508748 + 0.860915i \(0.330108\pi\)
\(882\) −14.1181 19.5384i −0.475380 0.657891i
\(883\) 28.9931i 0.975696i 0.872928 + 0.487848i \(0.162218\pi\)
−0.872928 + 0.487848i \(0.837782\pi\)
\(884\) −3.83634 + 1.92968i −0.129030 + 0.0649023i
\(885\) 0 0
\(886\) −4.51664 + 3.26364i −0.151740 + 0.109644i
\(887\) −5.33418 5.33418i −0.179104 0.179104i 0.611861 0.790965i \(-0.290421\pi\)
−0.790965 + 0.611861i \(0.790421\pi\)
\(888\) 10.1202 3.20131i 0.339612 0.107429i
\(889\) 7.25724 0.243400
\(890\) 0 0
\(891\) 4.14379 + 4.14379i 0.138822 + 0.138822i
\(892\) −5.50493 + 2.76898i −0.184319 + 0.0927125i
\(893\) 49.1447 1.64456
\(894\) −2.45769 + 15.2606i −0.0821974 + 0.510392i
\(895\) 0 0
\(896\) −4.94687 + 2.40831i −0.165263 + 0.0804561i
\(897\) 7.87991 + 7.87991i 0.263103 + 0.263103i
\(898\) 31.4758 + 43.5602i 1.05036 + 1.45362i
\(899\) −37.0507 37.0507i −1.23571 1.23571i
\(900\) 0 0
\(901\) 2.50388 2.50388i 0.0834163 0.0834163i
\(902\) −0.683531 + 4.24428i −0.0227591 + 0.141319i
\(903\) 1.02602 1.02602i 0.0341439 0.0341439i
\(904\) −10.6371 5.52467i −0.353785 0.183748i
\(905\) 0 0
\(906\) 1.82607 + 2.52715i 0.0606672 + 0.0839589i
\(907\) 26.2683i 0.872226i −0.899892 0.436113i \(-0.856355\pi\)
0.899892 0.436113i \(-0.143645\pi\)
\(908\) −5.85407 + 17.7036i −0.194274 + 0.587514i
\(909\) 2.40270 2.40270i 0.0796924 0.0796924i
\(910\) 0 0
\(911\) 33.5196i 1.11055i 0.831665 + 0.555277i \(0.187388\pi\)
−0.831665 + 0.555277i \(0.812612\pi\)
\(912\) −20.8447 + 3.07988i −0.690236 + 0.101985i
\(913\) 6.03459 6.03459i 0.199716 0.199716i
\(914\) −5.76028 + 35.7676i −0.190533 + 1.18309i
\(915\) 0 0
\(916\) −6.87940 + 3.46034i −0.227302 + 0.114333i
\(917\) −0.584935 −0.0193163
\(918\) 0.501151 3.11182i 0.0165405 0.102705i
\(919\) 25.7545i 0.849564i −0.905296 0.424782i \(-0.860351\pi\)
0.905296 0.424782i \(-0.139649\pi\)
\(920\) 0 0
\(921\) 14.1425i 0.466011i
\(922\) 24.5130 + 3.94775i 0.807292 + 0.130012i
\(923\) −10.9635 −0.360868
\(924\) −0.252375 + 0.763221i −0.00830254 + 0.0251081i
\(925\) 0 0
\(926\) 16.9136 + 2.72390i 0.555816 + 0.0895128i
\(927\) −24.1790 + 24.1790i −0.794141 + 0.794141i
\(928\) 24.2354 23.6141i 0.795565 0.775170i
\(929\) 9.06425i 0.297388i 0.988883 + 0.148694i \(0.0475070\pi\)
−0.988883 + 0.148694i \(0.952493\pi\)
\(930\) 0 0
\(931\) −36.3688 + 36.3688i −1.19194 + 1.19194i
\(932\) −31.3062 + 15.7470i −1.02547 + 0.515811i
\(933\) 4.71788i 0.154456i
\(934\) 39.3707 28.4486i 1.28825 0.930865i
\(935\) 0 0
\(936\) −7.91970 25.0363i −0.258864 0.818338i
\(937\) 3.38621 3.38621i 0.110623 0.110623i −0.649629 0.760251i \(-0.725076\pi\)
0.760251 + 0.649629i \(0.225076\pi\)
\(938\) −9.75212 1.57055i −0.318418 0.0512804i
\(939\) −0.837719 + 0.837719i −0.0273379 + 0.0273379i
\(940\) 0 0
\(941\) −16.9347 16.9347i −0.552054 0.552054i 0.374979 0.927033i \(-0.377650\pi\)
−0.927033 + 0.374979i \(0.877650\pi\)
\(942\) −5.60159 + 4.04761i −0.182510 + 0.131878i
\(943\) 7.86722 + 7.86722i 0.256192 + 0.256192i
\(944\) 41.0583 6.06651i 1.33633 0.197448i
\(945\) 0 0
\(946\) −7.17548 1.15559i −0.233295 0.0375716i
\(947\) 1.08633 0.0353011 0.0176505 0.999844i \(-0.494381\pi\)
0.0176505 + 0.999844i \(0.494381\pi\)
\(948\) 13.3713 + 4.42150i 0.434279 + 0.143604i
\(949\) 25.3140 + 25.3140i 0.821727 + 0.821727i
\(950\) 0 0
\(951\) −2.38416 −0.0773117
\(952\) −0.764372 + 0.241792i −0.0247734 + 0.00783654i
\(953\) −10.7914 10.7914i −0.349567 0.349567i 0.510381 0.859948i \(-0.329504\pi\)
−0.859948 + 0.510381i \(0.829504\pi\)
\(954\) 12.6816 + 17.5504i 0.410583 + 0.568217i
\(955\) 0 0
\(956\) 15.8345 47.8859i 0.512124 1.54874i
\(957\) 4.94385i 0.159812i
\(958\) −26.8807 + 19.4235i −0.868475 + 0.627544i
\(959\) 3.78359 0.122178
\(960\) 0 0
\(961\) −45.7317 −1.47522
\(962\) 22.8770 16.5305i 0.737583 0.532964i
\(963\) 13.3115i 0.428956i
\(964\) 7.54853 22.8279i 0.243122 0.735237i
\(965\) 0 0
\(966\) 1.21848 + 1.68628i 0.0392038 + 0.0542552i
\(967\) 31.4724 + 31.4724i 1.01208 + 1.01208i 0.999926 + 0.0121587i \(0.00387033\pi\)
0.0121587 + 0.999926i \(0.496130\pi\)
\(968\) −25.8250 + 8.16917i −0.830046 + 0.262567i
\(969\) −3.07030 −0.0986323
\(970\) 0 0
\(971\) −23.1234 23.1234i −0.742066 0.742066i 0.230909 0.972975i \(-0.425830\pi\)
−0.972975 + 0.230909i \(0.925830\pi\)
\(972\) 28.2438 + 9.33942i 0.905921 + 0.299562i
\(973\) 2.08742 0.0669196
\(974\) 10.4891 + 1.68925i 0.336094 + 0.0541271i
\(975\) 0 0
\(976\) 3.98188 + 26.9495i 0.127457 + 0.862632i
\(977\) −15.3820 15.3820i −0.492114 0.492114i 0.416858 0.908972i \(-0.363131\pi\)
−0.908972 + 0.416858i \(0.863131\pi\)
\(978\) 12.7211 9.19207i 0.406777 0.293930i
\(979\) 0.936080 + 0.936080i 0.0299173 + 0.0299173i
\(980\) 0 0
\(981\) 3.88052 3.88052i 0.123896 0.123896i
\(982\) −7.34496 1.18289i −0.234387 0.0377475i
\(983\) 38.5198 38.5198i 1.22859 1.22859i 0.264093 0.964497i \(-0.414927\pi\)
0.964497 0.264093i \(-0.0850726\pi\)
\(984\) 1.50552 + 4.75937i 0.0479943 + 0.151723i
\(985\) 0 0
\(986\) 3.99641 2.88773i 0.127272 0.0919642i
\(987\) 2.17705i 0.0692964i
\(988\) −50.0533 + 25.1769i −1.59241 + 0.800982i
\(989\) −13.3005 + 13.3005i −0.422931 + 0.422931i
\(990\) 0 0
\(991\) 22.0556i 0.700619i 0.936634 + 0.350310i \(0.113924\pi\)
−0.936634 + 0.350310i \(0.886076\pi\)
\(992\) 0.643375 49.5480i 0.0204272 1.57315i
\(993\) 1.02841 1.02841i 0.0326356 0.0326356i
\(994\) −2.02073 0.325433i −0.0640936 0.0103221i
\(995\) 0 0
\(996\) 3.11114 9.40856i 0.0985804 0.298122i
\(997\) −0.840040 −0.0266043 −0.0133022 0.999912i \(-0.504234\pi\)
−0.0133022 + 0.999912i \(0.504234\pi\)
\(998\) 26.8668 + 4.32684i 0.850455 + 0.136964i
\(999\) 20.7159i 0.655422i
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 400.2.j.d.307.7 18
4.3 odd 2 1600.2.j.d.1007.4 18
5.2 odd 4 80.2.s.b.3.7 yes 18
5.3 odd 4 400.2.s.d.243.3 18
5.4 even 2 80.2.j.b.67.3 yes 18
15.2 even 4 720.2.z.g.163.3 18
15.14 odd 2 720.2.bd.g.307.7 18
16.5 even 4 1600.2.s.d.207.6 18
16.11 odd 4 400.2.s.d.107.3 18
20.3 even 4 1600.2.s.d.943.6 18
20.7 even 4 320.2.s.b.303.4 18
20.19 odd 2 320.2.j.b.47.6 18
40.19 odd 2 640.2.j.c.607.4 18
40.27 even 4 640.2.s.c.223.6 18
40.29 even 2 640.2.j.d.607.6 18
40.37 odd 4 640.2.s.d.223.4 18
80.19 odd 4 640.2.s.d.287.4 18
80.27 even 4 80.2.j.b.43.3 18
80.29 even 4 640.2.s.c.287.6 18
80.37 odd 4 320.2.j.b.143.4 18
80.43 even 4 inner 400.2.j.d.43.7 18
80.53 odd 4 1600.2.j.d.143.6 18
80.59 odd 4 80.2.s.b.27.7 yes 18
80.67 even 4 640.2.j.d.543.4 18
80.69 even 4 320.2.s.b.207.4 18
80.77 odd 4 640.2.j.c.543.6 18
240.59 even 4 720.2.z.g.667.3 18
240.107 odd 4 720.2.bd.g.523.7 18
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
80.2.j.b.43.3 18 80.27 even 4
80.2.j.b.67.3 yes 18 5.4 even 2
80.2.s.b.3.7 yes 18 5.2 odd 4
80.2.s.b.27.7 yes 18 80.59 odd 4
320.2.j.b.47.6 18 20.19 odd 2
320.2.j.b.143.4 18 80.37 odd 4
320.2.s.b.207.4 18 80.69 even 4
320.2.s.b.303.4 18 20.7 even 4
400.2.j.d.43.7 18 80.43 even 4 inner
400.2.j.d.307.7 18 1.1 even 1 trivial
400.2.s.d.107.3 18 16.11 odd 4
400.2.s.d.243.3 18 5.3 odd 4
640.2.j.c.543.6 18 80.77 odd 4
640.2.j.c.607.4 18 40.19 odd 2
640.2.j.d.543.4 18 80.67 even 4
640.2.j.d.607.6 18 40.29 even 2
640.2.s.c.223.6 18 40.27 even 4
640.2.s.c.287.6 18 80.29 even 4
640.2.s.d.223.4 18 40.37 odd 4
640.2.s.d.287.4 18 80.19 odd 4
720.2.z.g.163.3 18 15.2 even 4
720.2.z.g.667.3 18 240.59 even 4
720.2.bd.g.307.7 18 15.14 odd 2
720.2.bd.g.523.7 18 240.107 odd 4
1600.2.j.d.143.6 18 80.53 odd 4
1600.2.j.d.1007.4 18 4.3 odd 2
1600.2.s.d.207.6 18 16.5 even 4
1600.2.s.d.943.6 18 20.3 even 4