Properties

Label 430.2.l.a.7.18
Level $430$
Weight $2$
Character 430.7
Analytic conductor $3.434$
Analytic rank $0$
Dimension $88$
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] = [430,2,Mod(7,430)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(430, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([3, 10]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("430.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 430 = 2 \cdot 5 \cdot 43 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 430.l (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.43356728692\)
Analytic rank: \(0\)
Dimension: \(88\)
Relative dimension: \(22\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 7.18
Character \(\chi\) \(=\) 430.7
Dual form 430.2.l.a.123.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(0.0996077 - 0.371741i) q^{3} -1.00000i q^{4} +(2.14837 - 0.620072i) q^{5} +(-0.192427 - 0.333294i) q^{6} +(1.10238 + 4.11412i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.46981 + 1.42594i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(0.0996077 - 0.371741i) q^{3} -1.00000i q^{4} +(2.14837 - 0.620072i) q^{5} +(-0.192427 - 0.333294i) q^{6} +(1.10238 + 4.11412i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.46981 + 1.42594i) q^{9} +(1.08067 - 1.95759i) q^{10} +0.0420741 q^{11} +(-0.371741 - 0.0996077i) q^{12} +(0.445268 + 1.66176i) q^{13} +(3.68862 + 2.12963i) q^{14} +(-0.0165118 - 0.860403i) q^{15} -1.00000 q^{16} +(-0.548777 + 0.147044i) q^{17} +(2.75471 - 0.738123i) q^{18} +(-3.77954 - 6.54635i) q^{19} +(-0.620072 - 2.14837i) q^{20} +1.63919 q^{21} +(0.0297509 - 0.0297509i) q^{22} +(-3.00934 - 0.806352i) q^{23} +(-0.333294 + 0.192427i) q^{24} +(4.23102 - 2.66429i) q^{25} +(1.48990 + 0.860192i) q^{26} +(1.59249 - 1.59249i) q^{27} +(4.11412 - 1.10238i) q^{28} +(-3.38993 + 5.87153i) q^{29} +(-0.620072 - 0.596721i) q^{30} +(-5.03145 - 8.71473i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(0.00419090 - 0.0156407i) q^{33} +(-0.284068 + 0.492020i) q^{34} +(4.91937 + 8.15512i) q^{35} +(1.42594 - 2.46981i) q^{36} +(-6.11891 - 1.63956i) q^{37} +(-7.30151 - 1.95643i) q^{38} +0.662098 q^{39} +(-1.95759 - 1.08067i) q^{40} +2.65867 q^{41} +(1.15908 - 1.15908i) q^{42} +(6.19255 - 2.15692i) q^{43} -0.0420741i q^{44} +(6.19026 + 1.53200i) q^{45} +(-2.69810 + 1.55775i) q^{46} +(-3.66812 - 3.66812i) q^{47} +(-0.0996077 + 0.371741i) q^{48} +(-9.64858 + 5.57061i) q^{49} +(1.10784 - 4.87572i) q^{50} +0.218650i q^{51} +(1.66176 - 0.445268i) q^{52} +(7.35064 + 1.96960i) q^{53} -2.25213i q^{54} +(0.0903909 - 0.0260890i) q^{55} +(2.12963 - 3.68862i) q^{56} +(-2.81002 + 0.752942i) q^{57} +(1.75476 + 6.54885i) q^{58} +11.1091i q^{59} +(-0.860403 + 0.0165118i) q^{60} +(0.988247 + 0.570565i) q^{61} +(-9.72002 - 2.60447i) q^{62} +(-3.14385 + 11.7330i) q^{63} +1.00000i q^{64} +(1.98702 + 3.29399i) q^{65} +(-0.00809621 - 0.0140230i) q^{66} +(-1.80106 + 6.72166i) q^{67} +(0.147044 + 0.548777i) q^{68} +(-0.599508 + 1.03838i) q^{69} +(9.24506 + 2.28802i) q^{70} +(-11.4295 - 6.59884i) q^{71} +(-0.738123 - 2.75471i) q^{72} +(12.2318 - 3.27750i) q^{73} +(-5.48606 + 3.16738i) q^{74} +(-0.568985 - 1.83823i) q^{75} +(-6.54635 + 3.77954i) q^{76} +(0.0463815 + 0.173098i) q^{77} +(0.468174 - 0.468174i) q^{78} +(-8.68436 - 5.01392i) q^{79} +(-2.14837 + 0.620072i) q^{80} +(3.84446 + 6.65880i) q^{81} +(1.87996 - 1.87996i) q^{82} +(-3.03214 - 0.812460i) q^{83} -1.63919i q^{84} +(-1.08780 + 0.656188i) q^{85} +(2.85362 - 5.90397i) q^{86} +(1.84503 + 1.84503i) q^{87} +(-0.0297509 - 0.0297509i) q^{88} +(-6.93640 - 12.0142i) q^{89} +(5.46046 - 3.29388i) q^{90} +(-6.34584 + 3.66378i) q^{91} +(-0.806352 + 3.00934i) q^{92} +(-3.74079 + 1.00234i) q^{93} -5.18750 q^{94} +(-12.1791 - 11.7204i) q^{95} +(0.192427 + 0.333294i) q^{96} +(-7.11526 - 7.11526i) q^{97} +(-2.88356 + 10.7616i) q^{98} +(0.103915 + 0.0599953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 88 q + 4 q^{6} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 88 q + 4 q^{6} + 12 q^{7} + 16 q^{13} - 88 q^{16} + 4 q^{17} - 16 q^{21} + 12 q^{23} - 8 q^{25} + 12 q^{28} - 36 q^{30} - 40 q^{31} + 12 q^{33} - 40 q^{35} - 40 q^{36} + 16 q^{38} - 56 q^{41} - 56 q^{43} + 24 q^{46} + 72 q^{47} + 24 q^{50} - 16 q^{52} + 20 q^{53} + 24 q^{55} - 8 q^{56} + 20 q^{57} + 8 q^{60} + 72 q^{61} + 36 q^{62} - 40 q^{66} - 16 q^{67} + 4 q^{68} + 24 q^{71} + 60 q^{73} - 48 q^{76} - 48 q^{77} + 40 q^{78} + 28 q^{81} + 20 q^{86} - 64 q^{87} - 8 q^{90} + 48 q^{91} - 12 q^{92} - 108 q^{93} + 4 q^{95} - 4 q^{96} - 48 q^{97} - 96 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/430\mathbb{Z}\right)^\times\).

\(n\) \(87\) \(261\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) 0.0996077 0.371741i 0.0575085 0.214625i −0.931192 0.364529i \(-0.881230\pi\)
0.988700 + 0.149904i \(0.0478966\pi\)
\(4\) 1.00000i 0.500000i
\(5\) 2.14837 0.620072i 0.960782 0.277305i
\(6\) −0.192427 0.333294i −0.0785581 0.136067i
\(7\) 1.10238 + 4.11412i 0.416659 + 1.55499i 0.781490 + 0.623918i \(0.214460\pi\)
−0.364831 + 0.931074i \(0.618873\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.46981 + 1.42594i 0.823269 + 0.475314i
\(10\) 1.08067 1.95759i 0.341739 0.619043i
\(11\) 0.0420741 0.0126858 0.00634291 0.999980i \(-0.497981\pi\)
0.00634291 + 0.999980i \(0.497981\pi\)
\(12\) −0.371741 0.0996077i −0.107312 0.0287543i
\(13\) 0.445268 + 1.66176i 0.123495 + 0.460890i 0.999782 0.0209003i \(-0.00665324\pi\)
−0.876286 + 0.481791i \(0.839987\pi\)
\(14\) 3.68862 + 2.12963i 0.985825 + 0.569166i
\(15\) −0.0165118 0.860403i −0.00426332 0.222155i
\(16\) −1.00000 −0.250000
\(17\) −0.548777 + 0.147044i −0.133098 + 0.0356635i −0.324753 0.945799i \(-0.605281\pi\)
0.191655 + 0.981462i \(0.438615\pi\)
\(18\) 2.75471 0.738123i 0.649292 0.173977i
\(19\) −3.77954 6.54635i −0.867086 1.50184i −0.864961 0.501838i \(-0.832657\pi\)
−0.00212420 0.999998i \(-0.500676\pi\)
\(20\) −0.620072 2.14837i −0.138652 0.480391i
\(21\) 1.63919 0.357701
\(22\) 0.0297509 0.0297509i 0.00634291 0.00634291i
\(23\) −3.00934 0.806352i −0.627492 0.168136i −0.0689605 0.997619i \(-0.521968\pi\)
−0.558531 + 0.829483i \(0.688635\pi\)
\(24\) −0.333294 + 0.192427i −0.0680333 + 0.0392791i
\(25\) 4.23102 2.66429i 0.846204 0.532859i
\(26\) 1.48990 + 0.860192i 0.292193 + 0.168698i
\(27\) 1.59249 1.59249i 0.306475 0.306475i
\(28\) 4.11412 1.10238i 0.777496 0.208329i
\(29\) −3.38993 + 5.87153i −0.629495 + 1.09032i 0.358159 + 0.933661i \(0.383405\pi\)
−0.987653 + 0.156656i \(0.949929\pi\)
\(30\) −0.620072 0.596721i −0.113209 0.108946i
\(31\) −5.03145 8.71473i −0.903675 1.56521i −0.822686 0.568496i \(-0.807525\pi\)
−0.0809895 0.996715i \(-0.525808\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) 0.00419090 0.0156407i 0.000729543 0.00272269i
\(34\) −0.284068 + 0.492020i −0.0487172 + 0.0843807i
\(35\) 4.91937 + 8.15512i 0.831525 + 1.37847i
\(36\) 1.42594 2.46981i 0.237657 0.411634i
\(37\) −6.11891 1.63956i −1.00594 0.269541i −0.282009 0.959412i \(-0.591001\pi\)
−0.723933 + 0.689870i \(0.757668\pi\)
\(38\) −7.30151 1.95643i −1.18446 0.317375i
\(39\) 0.662098 0.106021
\(40\) −1.95759 1.08067i −0.309522 0.170869i
\(41\) 2.65867 0.415215 0.207607 0.978212i \(-0.433432\pi\)
0.207607 + 0.978212i \(0.433432\pi\)
\(42\) 1.15908 1.15908i 0.178851 0.178851i
\(43\) 6.19255 2.15692i 0.944355 0.328927i
\(44\) 0.0420741i 0.00634291i
\(45\) 6.19026 + 1.53200i 0.922789 + 0.228377i
\(46\) −2.69810 + 1.55775i −0.397814 + 0.229678i
\(47\) −3.66812 3.66812i −0.535050 0.535050i 0.387021 0.922071i \(-0.373504\pi\)
−0.922071 + 0.387021i \(0.873504\pi\)
\(48\) −0.0996077 + 0.371741i −0.0143771 + 0.0536562i
\(49\) −9.64858 + 5.57061i −1.37837 + 0.795802i
\(50\) 1.10784 4.87572i 0.156673 0.689532i
\(51\) 0.218650i 0.0306171i
\(52\) 1.66176 0.445268i 0.230445 0.0617476i
\(53\) 7.35064 + 1.96960i 1.00969 + 0.270545i 0.725499 0.688223i \(-0.241609\pi\)
0.284189 + 0.958768i \(0.408276\pi\)
\(54\) 2.25213i 0.306475i
\(55\) 0.0903909 0.0260890i 0.0121883 0.00351784i
\(56\) 2.12963 3.68862i 0.284583 0.492913i
\(57\) −2.81002 + 0.752942i −0.372196 + 0.0997296i
\(58\) 1.75476 + 6.54885i 0.230411 + 0.859906i
\(59\) 11.1091i 1.44628i 0.690701 + 0.723140i \(0.257302\pi\)
−0.690701 + 0.723140i \(0.742698\pi\)
\(60\) −0.860403 + 0.0165118i −0.111077 + 0.00213166i
\(61\) 0.988247 + 0.570565i 0.126532 + 0.0730533i 0.561930 0.827185i \(-0.310059\pi\)
−0.435398 + 0.900238i \(0.643392\pi\)
\(62\) −9.72002 2.60447i −1.23444 0.330768i
\(63\) −3.14385 + 11.7330i −0.396088 + 1.47822i
\(64\) 1.00000i 0.125000i
\(65\) 1.98702 + 3.29399i 0.246459 + 0.408569i
\(66\) −0.00809621 0.0140230i −0.000996574 0.00172612i
\(67\) −1.80106 + 6.72166i −0.220035 + 0.821182i 0.764298 + 0.644863i \(0.223086\pi\)
−0.984333 + 0.176319i \(0.943581\pi\)
\(68\) 0.147044 + 0.548777i 0.0178317 + 0.0665490i
\(69\) −0.599508 + 1.03838i −0.0721723 + 0.125006i
\(70\) 9.24506 + 2.28802i 1.10500 + 0.273471i
\(71\) −11.4295 6.59884i −1.35644 0.783138i −0.367294 0.930105i \(-0.619716\pi\)
−0.989141 + 0.146967i \(0.953049\pi\)
\(72\) −0.738123 2.75471i −0.0869886 0.324646i
\(73\) 12.2318 3.27750i 1.43162 0.383602i 0.542030 0.840359i \(-0.317656\pi\)
0.889591 + 0.456757i \(0.150989\pi\)
\(74\) −5.48606 + 3.16738i −0.637742 + 0.368200i
\(75\) −0.568985 1.83823i −0.0657008 0.212260i
\(76\) −6.54635 + 3.77954i −0.750918 + 0.433543i
\(77\) 0.0463815 + 0.173098i 0.00528566 + 0.0197263i
\(78\) 0.468174 0.468174i 0.0530103 0.0530103i
\(79\) −8.68436 5.01392i −0.977067 0.564110i −0.0756834 0.997132i \(-0.524114\pi\)
−0.901383 + 0.433022i \(0.857447\pi\)
\(80\) −2.14837 + 0.620072i −0.240195 + 0.0693262i
\(81\) 3.84446 + 6.65880i 0.427162 + 0.739867i
\(82\) 1.87996 1.87996i 0.207607 0.207607i
\(83\) −3.03214 0.812460i −0.332821 0.0891791i 0.0885386 0.996073i \(-0.471780\pi\)
−0.421360 + 0.906894i \(0.638447\pi\)
\(84\) 1.63919i 0.178851i
\(85\) −1.08780 + 0.656188i −0.117988 + 0.0711736i
\(86\) 2.85362 5.90397i 0.307714 0.636641i
\(87\) 1.84503 + 1.84503i 0.197808 + 0.197808i
\(88\) −0.0297509 0.0297509i −0.00317145 0.00317145i
\(89\) −6.93640 12.0142i −0.735257 1.27350i −0.954611 0.297856i \(-0.903728\pi\)
0.219354 0.975645i \(-0.429605\pi\)
\(90\) 5.46046 3.29388i 0.575583 0.347206i
\(91\) −6.34584 + 3.66378i −0.665225 + 0.384068i
\(92\) −0.806352 + 3.00934i −0.0840680 + 0.313746i
\(93\) −3.74079 + 1.00234i −0.387902 + 0.103938i
\(94\) −5.18750 −0.535050
\(95\) −12.1791 11.7204i −1.24955 1.20249i
\(96\) 0.192427 + 0.333294i 0.0196395 + 0.0340167i
\(97\) −7.11526 7.11526i −0.722445 0.722445i 0.246658 0.969103i \(-0.420668\pi\)
−0.969103 + 0.246658i \(0.920668\pi\)
\(98\) −2.88356 + 10.7616i −0.291284 + 1.08709i
\(99\) 0.103915 + 0.0599953i 0.0104438 + 0.00602975i
\(100\) −2.66429 4.23102i −0.266429 0.423102i
\(101\) −2.03224 + 3.51994i −0.202215 + 0.350247i −0.949242 0.314547i \(-0.898147\pi\)
0.747027 + 0.664794i \(0.231481\pi\)
\(102\) 0.154609 + 0.154609i 0.0153085 + 0.0153085i
\(103\) 4.84672 + 18.0882i 0.477561 + 1.78228i 0.611447 + 0.791285i \(0.290588\pi\)
−0.133886 + 0.990997i \(0.542746\pi\)
\(104\) 0.860192 1.48990i 0.0843488 0.146096i
\(105\) 3.52160 1.01642i 0.343673 0.0991922i
\(106\) 6.59041 3.80497i 0.640117 0.369572i
\(107\) 10.2856 + 10.2856i 0.994345 + 0.994345i 0.999984 0.00563890i \(-0.00179493\pi\)
−0.00563890 + 0.999984i \(0.501795\pi\)
\(108\) −1.59249 1.59249i −0.153238 0.153238i
\(109\) 6.37593 3.68115i 0.610704 0.352590i −0.162537 0.986702i \(-0.551968\pi\)
0.773241 + 0.634113i \(0.218634\pi\)
\(110\) 0.0454683 0.0823637i 0.00433523 0.00785307i
\(111\) −1.21898 + 2.11134i −0.115701 + 0.200399i
\(112\) −1.10238 4.11412i −0.104165 0.388748i
\(113\) 3.93692 + 3.93692i 0.370354 + 0.370354i 0.867606 0.497252i \(-0.165658\pi\)
−0.497252 + 0.867606i \(0.665658\pi\)
\(114\) −1.45457 + 2.51939i −0.136233 + 0.235963i
\(115\) −6.96519 + 0.133667i −0.649508 + 0.0124645i
\(116\) 5.87153 + 3.38993i 0.545158 + 0.314747i
\(117\) −1.26985 + 4.73916i −0.117398 + 0.438136i
\(118\) 7.85532 + 7.85532i 0.723140 + 0.723140i
\(119\) −1.20992 2.09564i −0.110913 0.192107i
\(120\) −0.596721 + 0.620072i −0.0544729 + 0.0566046i
\(121\) −10.9982 −0.999839
\(122\) 1.10225 0.295346i 0.0997927 0.0267394i
\(123\) 0.264824 0.988337i 0.0238784 0.0891154i
\(124\) −8.71473 + 5.03145i −0.782606 + 0.451838i
\(125\) 7.43776 8.34744i 0.665253 0.746618i
\(126\) 6.07345 + 10.5195i 0.541066 + 0.937154i
\(127\) −4.14066 4.14066i −0.367424 0.367424i 0.499113 0.866537i \(-0.333659\pi\)
−0.866537 + 0.499113i \(0.833659\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −0.184990 2.51687i −0.0162875 0.221598i
\(130\) 3.73424 + 0.924171i 0.327514 + 0.0810551i
\(131\) 11.9910i 1.04766i 0.851824 + 0.523828i \(0.175497\pi\)
−0.851824 + 0.523828i \(0.824503\pi\)
\(132\) −0.0156407 0.00419090i −0.00136135 0.000364771i
\(133\) 22.7660 22.7660i 1.97406 1.97406i
\(134\) 3.47939 + 6.02648i 0.300573 + 0.520608i
\(135\) 2.43381 4.40873i 0.209469 0.379443i
\(136\) 0.492020 + 0.284068i 0.0421904 + 0.0243586i
\(137\) −4.58660 + 4.58660i −0.391859 + 0.391859i −0.875350 0.483490i \(-0.839369\pi\)
0.483490 + 0.875350i \(0.339369\pi\)
\(138\) 0.310328 + 1.15816i 0.0264169 + 0.0985891i
\(139\) 16.7136 9.64959i 1.41763 0.818467i 0.421537 0.906811i \(-0.361491\pi\)
0.996090 + 0.0883439i \(0.0281575\pi\)
\(140\) 8.15512 4.91937i 0.689233 0.415762i
\(141\) −1.72896 + 0.998217i −0.145605 + 0.0840650i
\(142\) −12.7480 + 3.41581i −1.06979 + 0.286648i
\(143\) 0.0187343 + 0.0699172i 0.00156664 + 0.00584677i
\(144\) −2.46981 1.42594i −0.205817 0.118829i
\(145\) −3.64206 + 14.7163i −0.302457 + 1.22212i
\(146\) 6.33164 10.9667i 0.524010 0.907612i
\(147\) 1.10975 + 4.14165i 0.0915308 + 0.341597i
\(148\) −1.63956 + 6.11891i −0.134771 + 0.502971i
\(149\) −2.49758 4.32594i −0.204610 0.354395i 0.745399 0.666619i \(-0.232259\pi\)
−0.950008 + 0.312225i \(0.898926\pi\)
\(150\) −1.70216 0.897490i −0.138981 0.0732798i
\(151\) 4.57950i 0.372675i 0.982486 + 0.186337i \(0.0596617\pi\)
−0.982486 + 0.186337i \(0.940338\pi\)
\(152\) −1.95643 + 7.30151i −0.158688 + 0.592230i
\(153\) −1.56505 0.419354i −0.126527 0.0339028i
\(154\) 0.155195 + 0.0896021i 0.0125060 + 0.00722034i
\(155\) −16.2132 15.6026i −1.30228 1.25323i
\(156\) 0.662098i 0.0530103i
\(157\) 3.33636 + 12.4515i 0.266270 + 0.993735i 0.961468 + 0.274916i \(0.0886502\pi\)
−0.695198 + 0.718819i \(0.744683\pi\)
\(158\) −9.68614 + 2.59539i −0.770588 + 0.206478i
\(159\) 1.46436 2.53635i 0.116131 0.201145i
\(160\) −1.08067 + 1.95759i −0.0854346 + 0.154761i
\(161\) 13.2697i 1.04580i
\(162\) 7.42693 + 1.99004i 0.583514 + 0.156352i
\(163\) 1.79339 0.480539i 0.140470 0.0376387i −0.187899 0.982188i \(-0.560168\pi\)
0.328369 + 0.944550i \(0.393501\pi\)
\(164\) 2.65867i 0.207607i
\(165\) −0.000694718 0.0362007i −5.40837e−5 0.00281822i
\(166\) −2.71855 + 1.56955i −0.211000 + 0.121821i
\(167\) 1.31319 4.90090i 0.101618 0.379243i −0.896322 0.443404i \(-0.853771\pi\)
0.997940 + 0.0641615i \(0.0204373\pi\)
\(168\) −1.15908 1.15908i −0.0894253 0.0894253i
\(169\) 8.69513 5.02014i 0.668857 0.386164i
\(170\) −0.305196 + 1.23319i −0.0234075 + 0.0945810i
\(171\) 21.5576i 1.64855i
\(172\) −2.15692 6.19255i −0.164464 0.472178i
\(173\) −8.16518 + 8.16518i −0.620787 + 0.620787i −0.945733 0.324946i \(-0.894654\pi\)
0.324946 + 0.945733i \(0.394654\pi\)
\(174\) 2.60926 0.197808
\(175\) 15.6254 + 14.4699i 1.18117 + 1.09382i
\(176\) −0.0420741 −0.00317145
\(177\) 4.12971 + 1.10655i 0.310408 + 0.0831735i
\(178\) −13.4001 3.59054i −1.00438 0.269123i
\(179\) 0.235089 0.407187i 0.0175714 0.0304346i −0.857106 0.515140i \(-0.827740\pi\)
0.874677 + 0.484706i \(0.161073\pi\)
\(180\) 1.53200 6.19026i 0.114189 0.461394i
\(181\) 8.71967 15.1029i 0.648128 1.12259i −0.335442 0.942061i \(-0.608886\pi\)
0.983570 0.180530i \(-0.0577812\pi\)
\(182\) −1.89651 + 7.07787i −0.140579 + 0.524647i
\(183\) 0.310539 0.310539i 0.0229557 0.0229557i
\(184\) 1.55775 + 2.69810i 0.114839 + 0.198907i
\(185\) −14.1623 + 0.271786i −1.04124 + 0.0199821i
\(186\) −1.93638 + 3.35390i −0.141982 + 0.245920i
\(187\) −0.0230893 + 0.00618676i −0.00168846 + 0.000452421i
\(188\) −3.66812 + 3.66812i −0.267525 + 0.267525i
\(189\) 8.30724 + 4.79618i 0.604262 + 0.348871i
\(190\) −16.8995 + 0.324314i −1.22602 + 0.0235282i
\(191\) 0.385625 0.222641i 0.0279028 0.0161097i −0.485984 0.873968i \(-0.661539\pi\)
0.513887 + 0.857858i \(0.328205\pi\)
\(192\) 0.371741 + 0.0996077i 0.0268281 + 0.00718857i
\(193\) 3.23148 3.23148i 0.232607 0.232607i −0.581173 0.813780i \(-0.697406\pi\)
0.813780 + 0.581173i \(0.197406\pi\)
\(194\) −10.0625 −0.722445
\(195\) 1.42243 0.410549i 0.101863 0.0294000i
\(196\) 5.57061 + 9.64858i 0.397901 + 0.689184i
\(197\) −10.6964 + 2.86609i −0.762085 + 0.204200i −0.618872 0.785492i \(-0.712410\pi\)
−0.143213 + 0.989692i \(0.545743\pi\)
\(198\) 0.115902 0.0310558i 0.00823680 0.00220704i
\(199\) −8.47113 −0.600502 −0.300251 0.953860i \(-0.597070\pi\)
−0.300251 + 0.953860i \(0.597070\pi\)
\(200\) −4.87572 1.10784i −0.344766 0.0783363i
\(201\) 2.31932 + 1.33906i 0.163592 + 0.0944499i
\(202\) 1.05196 + 3.92598i 0.0740158 + 0.276231i
\(203\) −27.8932 7.47396i −1.95772 0.524569i
\(204\) 0.218650 0.0153085
\(205\) 5.71182 1.64857i 0.398931 0.115141i
\(206\) 16.2174 + 9.36313i 1.12992 + 0.652361i
\(207\) −6.28269 6.28269i −0.436677 0.436677i
\(208\) −0.445268 1.66176i −0.0308738 0.115223i
\(209\) −0.159021 0.275432i −0.0109997 0.0190520i
\(210\) 1.77143 3.20886i 0.122240 0.221433i
\(211\) 2.28848i 0.157546i 0.996893 + 0.0787728i \(0.0251002\pi\)
−0.996893 + 0.0787728i \(0.974900\pi\)
\(212\) 1.96960 7.35064i 0.135273 0.504844i
\(213\) −3.59153 + 3.59153i −0.246087 + 0.246087i
\(214\) 14.5460 0.994345
\(215\) 11.9665 8.47370i 0.816106 0.577902i
\(216\) −2.25213 −0.153238
\(217\) 30.3069 30.3069i 2.05737 2.05737i
\(218\) 1.90550 7.11143i 0.129057 0.481647i
\(219\) 4.87352i 0.329322i
\(220\) −0.0260890 0.0903909i −0.00175892 0.00609415i
\(221\) −0.488706 0.846464i −0.0328739 0.0569393i
\(222\) 0.630991 + 2.35489i 0.0423493 + 0.158050i
\(223\) −4.66864 4.66864i −0.312635 0.312635i 0.533295 0.845930i \(-0.320954\pi\)
−0.845930 + 0.533295i \(0.820954\pi\)
\(224\) −3.68862 2.12963i −0.246456 0.142292i
\(225\) 14.2489 0.547097i 0.949929 0.0364731i
\(226\) 5.56764 0.370354
\(227\) 13.3702 + 3.58253i 0.887410 + 0.237781i 0.673602 0.739095i \(-0.264746\pi\)
0.213809 + 0.976876i \(0.431413\pi\)
\(228\) 0.752942 + 2.81002i 0.0498648 + 0.186098i
\(229\) 9.54432 + 5.51042i 0.630707 + 0.364139i 0.781026 0.624499i \(-0.214697\pi\)
−0.150319 + 0.988638i \(0.548030\pi\)
\(230\) −4.83062 + 5.01965i −0.318522 + 0.330986i
\(231\) 0.0689675 0.00453773
\(232\) 6.54885 1.75476i 0.429953 0.115205i
\(233\) 24.3141 6.51493i 1.59287 0.426808i 0.649989 0.759944i \(-0.274774\pi\)
0.942879 + 0.333136i \(0.108107\pi\)
\(234\) 2.45317 + 4.24902i 0.160369 + 0.277767i
\(235\) −10.1550 5.60599i −0.662438 0.365694i
\(236\) 11.1091 0.723140
\(237\) −2.72891 + 2.72891i −0.177262 + 0.177262i
\(238\) −2.33738 0.626299i −0.151510 0.0405969i
\(239\) −11.9974 + 6.92668i −0.776044 + 0.448049i −0.835027 0.550210i \(-0.814548\pi\)
0.0589821 + 0.998259i \(0.481215\pi\)
\(240\) 0.0165118 + 0.860403i 0.00106583 + 0.0555387i
\(241\) 1.85397 + 1.07039i 0.119425 + 0.0689499i 0.558522 0.829489i \(-0.311368\pi\)
−0.439098 + 0.898439i \(0.644702\pi\)
\(242\) −7.77692 + 7.77692i −0.499920 + 0.499920i
\(243\) 9.38445 2.51455i 0.602012 0.161309i
\(244\) 0.570565 0.988247i 0.0365267 0.0632660i
\(245\) −17.2746 + 17.9506i −1.10363 + 1.14682i
\(246\) −0.511601 0.886119i −0.0326185 0.0564969i
\(247\) 9.19558 9.19558i 0.585101 0.585101i
\(248\) −2.60447 + 9.72002i −0.165384 + 0.617222i
\(249\) −0.604050 + 1.04624i −0.0382801 + 0.0663031i
\(250\) −0.643243 11.1618i −0.0406822 0.705936i
\(251\) 3.72715 6.45561i 0.235256 0.407475i −0.724091 0.689704i \(-0.757741\pi\)
0.959347 + 0.282229i \(0.0910740\pi\)
\(252\) 11.7330 + 3.14385i 0.739110 + 0.198044i
\(253\) −0.126615 0.0339265i −0.00796025 0.00213294i
\(254\) −5.85578 −0.367424
\(255\) 0.135579 + 0.469741i 0.00849026 + 0.0294163i
\(256\) 1.00000 0.0625000
\(257\) −16.0873 + 16.0873i −1.00350 + 1.00350i −0.00350584 + 0.999994i \(0.501116\pi\)
−0.999994 + 0.00350584i \(0.998884\pi\)
\(258\) −1.91050 1.64889i −0.118943 0.102655i
\(259\) 26.9813i 1.67654i
\(260\) 3.29399 1.98702i 0.204285 0.123230i
\(261\) −16.7450 + 9.66770i −1.03649 + 0.598416i
\(262\) 8.47890 + 8.47890i 0.523828 + 0.523828i
\(263\) −4.09883 + 15.2971i −0.252745 + 0.943257i 0.716586 + 0.697499i \(0.245704\pi\)
−0.969331 + 0.245758i \(0.920963\pi\)
\(264\) −0.0140230 + 0.00809621i −0.000863058 + 0.000498287i
\(265\) 17.0132 0.326496i 1.04511 0.0200565i
\(266\) 32.1960i 1.97406i
\(267\) −5.15709 + 1.38184i −0.315608 + 0.0845670i
\(268\) 6.72166 + 1.80106i 0.410591 + 0.110017i
\(269\) 21.9248i 1.33678i 0.743811 + 0.668390i \(0.233016\pi\)
−0.743811 + 0.668390i \(0.766984\pi\)
\(270\) −1.39648 4.83841i −0.0849871 0.294456i
\(271\) 11.2950 19.5634i 0.686120 1.18839i −0.286964 0.957941i \(-0.592646\pi\)
0.973083 0.230453i \(-0.0740208\pi\)
\(272\) 0.548777 0.147044i 0.0332745 0.00891587i
\(273\) 0.729880 + 2.72395i 0.0441744 + 0.164861i
\(274\) 6.48643i 0.391859i
\(275\) 0.178016 0.112098i 0.0107348 0.00675975i
\(276\) 1.03838 + 0.599508i 0.0625030 + 0.0360861i
\(277\) 13.7531 + 3.68513i 0.826343 + 0.221418i 0.647118 0.762390i \(-0.275974\pi\)
0.179225 + 0.983808i \(0.442641\pi\)
\(278\) 4.99499 18.6416i 0.299580 1.11805i
\(279\) 28.6983i 1.71812i
\(280\) 2.28802 9.24506i 0.136735 0.552498i
\(281\) −14.1397 24.4907i −0.843503 1.46099i −0.886915 0.461933i \(-0.847156\pi\)
0.0434112 0.999057i \(-0.486177\pi\)
\(282\) −0.516715 + 1.92841i −0.0307699 + 0.114835i
\(283\) −0.967269 3.60990i −0.0574982 0.214586i 0.931199 0.364510i \(-0.118764\pi\)
−0.988697 + 0.149924i \(0.952097\pi\)
\(284\) −6.59884 + 11.4295i −0.391569 + 0.678218i
\(285\) −5.57009 + 3.36002i −0.329944 + 0.199030i
\(286\) 0.0626861 + 0.0361918i 0.00370670 + 0.00214007i
\(287\) 2.93085 + 10.9381i 0.173003 + 0.645655i
\(288\) −2.75471 + 0.738123i −0.162323 + 0.0434943i
\(289\) −14.4429 + 8.33861i −0.849582 + 0.490507i
\(290\) 7.83063 + 12.9813i 0.459831 + 0.762288i
\(291\) −3.35377 + 1.93630i −0.196601 + 0.113508i
\(292\) −3.27750 12.2318i −0.191801 0.715811i
\(293\) 1.23033 1.23033i 0.0718766 0.0718766i −0.670255 0.742131i \(-0.733815\pi\)
0.742131 + 0.670255i \(0.233815\pi\)
\(294\) 3.71330 + 2.14388i 0.216564 + 0.125033i
\(295\) 6.88844 + 23.8665i 0.401061 + 1.38956i
\(296\) 3.16738 + 5.48606i 0.184100 + 0.318871i
\(297\) 0.0670027 0.0670027i 0.00388789 0.00388789i
\(298\) −4.82496 1.29284i −0.279502 0.0748924i
\(299\) 5.35986i 0.309969i
\(300\) −1.83823 + 0.568985i −0.106130 + 0.0328504i
\(301\) 15.7003 + 23.0992i 0.904953 + 1.33141i
\(302\) 3.23820 + 3.23820i 0.186337 + 0.186337i
\(303\) 1.10608 + 1.10608i 0.0635425 + 0.0635425i
\(304\) 3.77954 + 6.54635i 0.216771 + 0.375459i
\(305\) 2.47692 + 0.613001i 0.141828 + 0.0351004i
\(306\) −1.40319 + 0.810130i −0.0802148 + 0.0463120i
\(307\) 1.99656 7.45126i 0.113950 0.425266i −0.885257 0.465103i \(-0.846017\pi\)
0.999206 + 0.0398371i \(0.0126839\pi\)
\(308\) 0.173098 0.0463815i 0.00986317 0.00264283i
\(309\) 7.20689 0.409986
\(310\) −22.4972 + 0.431738i −1.27775 + 0.0245211i
\(311\) 1.41494 + 2.45074i 0.0802337 + 0.138969i 0.903350 0.428904i \(-0.141100\pi\)
−0.823117 + 0.567872i \(0.807767\pi\)
\(312\) −0.468174 0.468174i −0.0265051 0.0265051i
\(313\) 2.11703 7.90086i 0.119662 0.446583i −0.879932 0.475100i \(-0.842412\pi\)
0.999593 + 0.0285170i \(0.00907848\pi\)
\(314\) 11.1637 + 6.44535i 0.630003 + 0.363732i
\(315\) 0.521150 + 27.1563i 0.0293634 + 1.53008i
\(316\) −5.01392 + 8.68436i −0.282055 + 0.488533i
\(317\) −12.8399 12.8399i −0.721158 0.721158i 0.247683 0.968841i \(-0.420331\pi\)
−0.968841 + 0.247683i \(0.920331\pi\)
\(318\) −0.758009 2.82893i −0.0425070 0.158638i
\(319\) −0.142628 + 0.247040i −0.00798565 + 0.0138316i
\(320\) 0.620072 + 2.14837i 0.0346631 + 0.120098i
\(321\) 4.84810 2.79905i 0.270594 0.156228i
\(322\) −9.38310 9.38310i −0.522900 0.522900i
\(323\) 3.03673 + 3.03673i 0.168968 + 0.168968i
\(324\) 6.65880 3.84446i 0.369933 0.213581i
\(325\) 6.31137 + 5.84463i 0.350092 + 0.324202i
\(326\) 0.928329 1.60791i 0.0514154 0.0890541i
\(327\) −0.733341 2.73687i −0.0405539 0.151349i
\(328\) −1.87996 1.87996i −0.103804 0.103804i
\(329\) 11.0474 19.1347i 0.609065 1.05493i
\(330\) −0.0260890 0.0251065i −0.00143615 0.00138207i
\(331\) −2.55280 1.47386i −0.140315 0.0810107i 0.428199 0.903684i \(-0.359148\pi\)
−0.568514 + 0.822674i \(0.692481\pi\)
\(332\) −0.812460 + 3.03214i −0.0445896 + 0.166411i
\(333\) −12.7746 12.7746i −0.700044 0.700044i
\(334\) −2.53689 4.39402i −0.138812 0.240430i
\(335\) 0.298559 + 15.5574i 0.0163120 + 0.849993i
\(336\) −1.63919 −0.0894253
\(337\) −3.55118 + 0.951534i −0.193445 + 0.0518334i −0.354241 0.935154i \(-0.615261\pi\)
0.160796 + 0.986988i \(0.448594\pi\)
\(338\) 2.59861 9.69816i 0.141346 0.527511i
\(339\) 1.85566 1.07137i 0.100786 0.0581887i
\(340\) 0.656188 + 1.08780i 0.0355868 + 0.0589942i
\(341\) −0.211694 0.366664i −0.0114639 0.0198560i
\(342\) −15.2435 15.2435i −0.824277 0.824277i
\(343\) −12.4723 12.4723i −0.673442 0.673442i
\(344\) −5.90397 2.85362i −0.318321 0.153857i
\(345\) −0.644097 + 2.60256i −0.0346770 + 0.140117i
\(346\) 11.5473i 0.620787i
\(347\) 12.1562 + 3.25724i 0.652579 + 0.174858i 0.569895 0.821718i \(-0.306984\pi\)
0.0826842 + 0.996576i \(0.473651\pi\)
\(348\) 1.84503 1.84503i 0.0989038 0.0989038i
\(349\) −8.15090 14.1178i −0.436307 0.755707i 0.561094 0.827752i \(-0.310381\pi\)
−0.997401 + 0.0720455i \(0.977047\pi\)
\(350\) 21.2806 0.817081i 1.13749 0.0436748i
\(351\) 3.35543 + 1.93726i 0.179100 + 0.103403i
\(352\) −0.0297509 + 0.0297509i −0.00158573 + 0.00158573i
\(353\) 6.83654 + 25.5143i 0.363872 + 1.35799i 0.868943 + 0.494912i \(0.164800\pi\)
−0.505071 + 0.863078i \(0.668534\pi\)
\(354\) 3.70259 2.13769i 0.196791 0.113617i
\(355\) −28.6467 7.08964i −1.52041 0.376279i
\(356\) −12.0142 + 6.93640i −0.636751 + 0.367628i
\(357\) −0.899551 + 0.241034i −0.0476093 + 0.0127569i
\(358\) −0.121691 0.454158i −0.00643158 0.0240030i
\(359\) 3.04581 + 1.75850i 0.160752 + 0.0928100i 0.578218 0.815883i \(-0.303748\pi\)
−0.417466 + 0.908692i \(0.637082\pi\)
\(360\) −3.29388 5.46046i −0.173603 0.287792i
\(361\) −19.0698 + 33.0299i −1.00367 + 1.73842i
\(362\) −4.51363 16.8451i −0.237231 0.885359i
\(363\) −1.09551 + 4.08849i −0.0574993 + 0.214590i
\(364\) 3.66378 + 6.34584i 0.192034 + 0.332613i
\(365\) 24.2462 14.6259i 1.26910 0.765553i
\(366\) 0.439169i 0.0229557i
\(367\) −5.08901 + 18.9925i −0.265644 + 0.991398i 0.696210 + 0.717838i \(0.254868\pi\)
−0.961855 + 0.273561i \(0.911799\pi\)
\(368\) 3.00934 + 0.806352i 0.156873 + 0.0420340i
\(369\) 6.56640 + 3.79112i 0.341833 + 0.197358i
\(370\) −9.82211 + 10.2065i −0.510627 + 0.530609i
\(371\) 32.4127i 1.68278i
\(372\) 1.00234 + 3.74079i 0.0519690 + 0.193951i
\(373\) 5.79180 1.55191i 0.299888 0.0803548i −0.105737 0.994394i \(-0.533720\pi\)
0.405626 + 0.914039i \(0.367054\pi\)
\(374\) −0.0119519 + 0.0207013i −0.000618018 + 0.00107044i
\(375\) −2.36223 3.59639i −0.121985 0.185717i
\(376\) 5.18750i 0.267525i
\(377\) −11.2665 3.01886i −0.580256 0.155479i
\(378\) 9.26552 2.48269i 0.476567 0.127696i
\(379\) 30.3657i 1.55978i 0.625917 + 0.779889i \(0.284725\pi\)
−0.625917 + 0.779889i \(0.715275\pi\)
\(380\) −11.7204 + 12.1791i −0.601245 + 0.624773i
\(381\) −1.95170 + 1.12681i −0.0999884 + 0.0577283i
\(382\) 0.115247 0.430109i 0.00589656 0.0220063i
\(383\) −14.6859 14.6859i −0.750415 0.750415i 0.224141 0.974557i \(-0.428042\pi\)
−0.974557 + 0.224141i \(0.928042\pi\)
\(384\) 0.333294 0.192427i 0.0170083 0.00981976i
\(385\) 0.206978 + 0.343119i 0.0105486 + 0.0174870i
\(386\) 4.57000i 0.232607i
\(387\) 18.3701 + 3.50305i 0.933802 + 0.178070i
\(388\) −7.11526 + 7.11526i −0.361222 + 0.361222i
\(389\) −13.7334 −0.696309 −0.348154 0.937437i \(-0.613192\pi\)
−0.348154 + 0.937437i \(0.613192\pi\)
\(390\) 0.715511 1.29611i 0.0362313 0.0656313i
\(391\) 1.77003 0.0895142
\(392\) 10.7616 + 2.88356i 0.543543 + 0.145642i
\(393\) 4.45754 + 1.19439i 0.224853 + 0.0602492i
\(394\) −5.53685 + 9.59011i −0.278943 + 0.483143i
\(395\) −21.7662 5.38684i −1.09518 0.271041i
\(396\) 0.0599953 0.103915i 0.00301488 0.00522192i
\(397\) −2.36311 + 8.81924i −0.118601 + 0.442625i −0.999531 0.0306217i \(-0.990251\pi\)
0.880930 + 0.473246i \(0.156918\pi\)
\(398\) −5.98999 + 5.98999i −0.300251 + 0.300251i
\(399\) −6.19539 10.7307i −0.310157 0.537208i
\(400\) −4.23102 + 2.66429i −0.211551 + 0.133215i
\(401\) −0.452590 + 0.783909i −0.0226013 + 0.0391465i −0.877105 0.480299i \(-0.840528\pi\)
0.854504 + 0.519446i \(0.173861\pi\)
\(402\) 2.58686 0.693148i 0.129021 0.0345711i
\(403\) 12.2415 12.2415i 0.609791 0.609791i
\(404\) 3.51994 + 2.03224i 0.175123 + 0.101108i
\(405\) 12.3883 + 11.9217i 0.615578 + 0.592396i
\(406\) −25.0083 + 14.4386i −1.24114 + 0.716574i
\(407\) −0.257448 0.0689829i −0.0127612 0.00341935i
\(408\) 0.154609 0.154609i 0.00765427 0.00765427i
\(409\) 13.8117 0.682946 0.341473 0.939892i \(-0.389074\pi\)
0.341473 + 0.939892i \(0.389074\pi\)
\(410\) 2.87315 5.20458i 0.141895 0.257036i
\(411\) 1.24817 + 2.16189i 0.0615675 + 0.106638i
\(412\) 18.0882 4.84672i 0.891141 0.238781i
\(413\) −45.7042 + 12.2464i −2.24895 + 0.602606i
\(414\) −8.88506 −0.436677
\(415\) −7.01796 + 0.134680i −0.344498 + 0.00661118i
\(416\) −1.48990 0.860192i −0.0730482 0.0421744i
\(417\) −1.92235 7.17429i −0.0941377 0.351327i
\(418\) −0.307204 0.0823152i −0.0150259 0.00402617i
\(419\) 20.0934 0.981625 0.490813 0.871265i \(-0.336700\pi\)
0.490813 + 0.871265i \(0.336700\pi\)
\(420\) −1.01642 3.52160i −0.0495961 0.171836i
\(421\) 7.44354 + 4.29753i 0.362776 + 0.209449i 0.670298 0.742092i \(-0.266166\pi\)
−0.307522 + 0.951541i \(0.599500\pi\)
\(422\) 1.61820 + 1.61820i 0.0787728 + 0.0787728i
\(423\) −3.82901 14.2901i −0.186173 0.694807i
\(424\) −3.80497 6.59041i −0.184786 0.320058i
\(425\) −1.93012 + 2.08425i −0.0936244 + 0.101101i
\(426\) 5.07919i 0.246087i
\(427\) −1.25795 + 4.69474i −0.0608766 + 0.227195i
\(428\) 10.2856 10.2856i 0.497173 0.497173i
\(429\) 0.0278572 0.00134496
\(430\) 2.46976 14.4534i 0.119102 0.697004i
\(431\) −13.0821 −0.630144 −0.315072 0.949068i \(-0.602029\pi\)
−0.315072 + 0.949068i \(0.602029\pi\)
\(432\) −1.59249 + 1.59249i −0.0766189 + 0.0766189i
\(433\) 3.95433 14.7577i 0.190033 0.709212i −0.803464 0.595353i \(-0.797012\pi\)
0.993497 0.113859i \(-0.0363211\pi\)
\(434\) 42.8604i 2.05737i
\(435\) 5.10786 + 2.81976i 0.244903 + 0.135197i
\(436\) −3.68115 6.37593i −0.176295 0.305352i
\(437\) 6.09527 + 22.7479i 0.291576 + 1.08818i
\(438\) −3.44610 3.44610i −0.164661 0.164661i
\(439\) 15.4733 + 8.93354i 0.738502 + 0.426374i 0.821524 0.570173i \(-0.193124\pi\)
−0.0830223 + 0.996548i \(0.526457\pi\)
\(440\) −0.0823637 0.0454683i −0.00392654 0.00216762i
\(441\) −31.7735 −1.51302
\(442\) −0.944108 0.252973i −0.0449066 0.0120327i
\(443\) −0.943762 3.52217i −0.0448395 0.167343i 0.939875 0.341518i \(-0.110941\pi\)
−0.984715 + 0.174175i \(0.944274\pi\)
\(444\) 2.11134 + 1.21898i 0.100200 + 0.0578503i
\(445\) −22.3516 21.5099i −1.05957 1.01967i
\(446\) −6.60245 −0.312635
\(447\) −1.85691 + 0.497556i −0.0878286 + 0.0235336i
\(448\) −4.11412 + 1.10238i −0.194374 + 0.0520823i
\(449\) 12.2629 + 21.2400i 0.578724 + 1.00238i 0.995626 + 0.0934280i \(0.0297825\pi\)
−0.416902 + 0.908951i \(0.636884\pi\)
\(450\) 9.68866 10.4624i 0.456728 0.493201i
\(451\) 0.111861 0.00526734
\(452\) 3.93692 3.93692i 0.185177 0.185177i
\(453\) 1.70239 + 0.456154i 0.0799852 + 0.0214320i
\(454\) 11.9874 6.92092i 0.562596 0.324815i
\(455\) −11.3614 + 11.8060i −0.532633 + 0.553476i
\(456\) 2.51939 + 1.45457i 0.117981 + 0.0681166i
\(457\) 1.63646 1.63646i 0.0765506 0.0765506i −0.667795 0.744345i \(-0.732762\pi\)
0.744345 + 0.667795i \(0.232762\pi\)
\(458\) 10.6453 2.85240i 0.497423 0.133284i
\(459\) −0.639757 + 1.10809i −0.0298613 + 0.0517213i
\(460\) 0.133667 + 6.96519i 0.00623227 + 0.324754i
\(461\) 1.20661 + 2.08991i 0.0561976 + 0.0973370i 0.892756 0.450541i \(-0.148769\pi\)
−0.836558 + 0.547878i \(0.815436\pi\)
\(462\) 0.0487674 0.0487674i 0.00226887 0.00226887i
\(463\) −1.62402 + 6.06094i −0.0754748 + 0.281676i −0.993341 0.115215i \(-0.963244\pi\)
0.917866 + 0.396891i \(0.129911\pi\)
\(464\) 3.38993 5.87153i 0.157374 0.272579i
\(465\) −7.41510 + 4.47297i −0.343867 + 0.207429i
\(466\) 12.5859 21.7994i 0.583030 1.00984i
\(467\) −27.9577 7.49123i −1.29373 0.346653i −0.454652 0.890669i \(-0.650236\pi\)
−0.839074 + 0.544017i \(0.816903\pi\)
\(468\) 4.73916 + 1.26985i 0.219068 + 0.0586991i
\(469\) −29.6392 −1.36861
\(470\) −11.1447 + 3.21663i −0.514066 + 0.148372i
\(471\) 4.96105 0.228593
\(472\) 7.85532 7.85532i 0.361570 0.361570i
\(473\) 0.260546 0.0907505i 0.0119799 0.00417271i
\(474\) 3.85926i 0.177262i
\(475\) −33.4327 17.6279i −1.53400 0.808826i
\(476\) −2.09564 + 1.20992i −0.0960534 + 0.0554564i
\(477\) 15.3461 + 15.3461i 0.702651 + 0.702651i
\(478\) −3.58551 + 13.3813i −0.163997 + 0.612047i
\(479\) 22.7586 13.1397i 1.03987 0.600367i 0.120070 0.992765i \(-0.461688\pi\)
0.919795 + 0.392399i \(0.128355\pi\)
\(480\) 0.620072 + 0.596721i 0.0283023 + 0.0272365i
\(481\) 10.8982i 0.496916i
\(482\) 2.06784 0.554075i 0.0941873 0.0252374i
\(483\) −4.93290 1.32177i −0.224455 0.0601424i
\(484\) 10.9982i 0.499920i
\(485\) −19.6982 10.8743i −0.894449 0.493775i
\(486\) 4.85775 8.41386i 0.220352 0.381661i
\(487\) −12.9423 + 3.46789i −0.586474 + 0.157145i −0.539841 0.841767i \(-0.681516\pi\)
−0.0466327 + 0.998912i \(0.514849\pi\)
\(488\) −0.295346 1.10225i −0.0133697 0.0498963i
\(489\) 0.714544i 0.0323128i
\(490\) 0.478002 + 24.9079i 0.0215939 + 1.12523i
\(491\) −18.5997 10.7385i −0.839391 0.484623i 0.0176661 0.999844i \(-0.494376\pi\)
−0.857057 + 0.515221i \(0.827710\pi\)
\(492\) −0.988337 0.264824i −0.0445577 0.0119392i
\(493\) 0.996941 3.72063i 0.0449000 0.167569i
\(494\) 13.0045i 0.585101i
\(495\) 0.260449 + 0.0644576i 0.0117063 + 0.00289715i
\(496\) 5.03145 + 8.71473i 0.225919 + 0.391303i
\(497\) 14.5488 54.2969i 0.652603 2.43555i
\(498\) 0.312679 + 1.16693i 0.0140115 + 0.0522916i
\(499\) −15.5825 + 26.9897i −0.697568 + 1.20822i 0.271739 + 0.962371i \(0.412401\pi\)
−0.969307 + 0.245853i \(0.920932\pi\)
\(500\) −8.34744 7.43776i −0.373309 0.332627i
\(501\) −1.69106 0.976334i −0.0755510 0.0436194i
\(502\) −1.92931 7.20030i −0.0861095 0.321365i
\(503\) −27.2377 + 7.29831i −1.21447 + 0.325415i −0.808513 0.588478i \(-0.799727\pi\)
−0.405954 + 0.913894i \(0.633061\pi\)
\(504\) 10.5195 6.07345i 0.468577 0.270533i
\(505\) −2.18339 + 8.82227i −0.0971595 + 0.392586i
\(506\) −0.113520 + 0.0655410i −0.00504659 + 0.00291365i
\(507\) −1.00009 3.73238i −0.0444155 0.165761i
\(508\) −4.14066 + 4.14066i −0.183712 + 0.183712i
\(509\) 32.0128 + 18.4826i 1.41894 + 0.819226i 0.996206 0.0870272i \(-0.0277367\pi\)
0.422735 + 0.906253i \(0.361070\pi\)
\(510\) 0.428026 + 0.236289i 0.0189533 + 0.0104630i
\(511\) 26.9680 + 46.7100i 1.19300 + 2.06633i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −16.4439 4.40613i −0.726016 0.194536i
\(514\) 22.7509i 1.00350i
\(515\) 21.6285 + 35.8549i 0.953067 + 1.57995i
\(516\) −2.51687 + 0.184990i −0.110799 + 0.00814373i
\(517\) −0.154333 0.154333i −0.00678755 0.00678755i
\(518\) −19.0787 19.0787i −0.838269 0.838269i
\(519\) 2.22202 + 3.84865i 0.0975357 + 0.168937i
\(520\) 0.924171 3.73424i 0.0405276 0.163757i
\(521\) −32.8438 + 18.9624i −1.43891 + 0.830758i −0.997774 0.0666804i \(-0.978759\pi\)
−0.441140 + 0.897438i \(0.645426\pi\)
\(522\) −5.00437 + 18.6766i −0.219035 + 0.817451i
\(523\) −2.05168 + 0.549745i −0.0897136 + 0.0240387i −0.303397 0.952864i \(-0.598121\pi\)
0.213683 + 0.976903i \(0.431454\pi\)
\(524\) 11.9910 0.523828
\(525\) 6.93546 4.36729i 0.302688 0.190604i
\(526\) 7.91834 + 13.7150i 0.345256 + 0.598001i
\(527\) 4.04260 + 4.04260i 0.176098 + 0.176098i
\(528\) −0.00419090 + 0.0156407i −0.000182386 + 0.000680673i
\(529\) −11.5126 6.64682i −0.500549 0.288992i
\(530\) 11.7993 12.2610i 0.512529 0.532585i
\(531\) −15.8409 + 27.4373i −0.687438 + 1.19068i
\(532\) −22.7660 22.7660i −0.987032 0.987032i
\(533\) 1.18382 + 4.41808i 0.0512770 + 0.191368i
\(534\) −2.66950 + 4.62372i −0.115521 + 0.200088i
\(535\) 28.4751 + 15.7195i 1.23109 + 0.679612i
\(536\) 6.02648 3.47939i 0.260304 0.150287i
\(537\) −0.127951 0.127951i −0.00552150 0.00552150i
\(538\) 15.5032 + 15.5032i 0.668390 + 0.668390i
\(539\) −0.405955 + 0.234378i −0.0174857 + 0.0100954i
\(540\) −4.40873 2.43381i −0.189722 0.104734i
\(541\) 1.41662 2.45365i 0.0609051 0.105491i −0.833965 0.551817i \(-0.813935\pi\)
0.894870 + 0.446326i \(0.147268\pi\)
\(542\) −5.84670 21.8202i −0.251137 0.937257i
\(543\) −4.74582 4.74582i −0.203663 0.203663i
\(544\) 0.284068 0.492020i 0.0121793 0.0210952i
\(545\) 11.4153 11.8620i 0.488978 0.508113i
\(546\) 2.44223 + 1.41002i 0.104518 + 0.0603433i
\(547\) 2.39309 8.93113i 0.102321 0.381867i −0.895706 0.444646i \(-0.853330\pi\)
0.998027 + 0.0627786i \(0.0199962\pi\)
\(548\) 4.58660 + 4.58660i 0.195930 + 0.195930i
\(549\) 1.62719 + 2.81837i 0.0694466 + 0.120285i
\(550\) 0.0466115 0.205142i 0.00198752 0.00874727i
\(551\) 51.2495 2.18330
\(552\) 1.15816 0.310328i 0.0492946 0.0132084i
\(553\) 11.0544 41.2557i 0.470082 1.75437i
\(554\) 12.3307 7.11913i 0.523881 0.302463i
\(555\) −1.30964 + 5.29180i −0.0555913 + 0.224624i
\(556\) −9.64959 16.7136i −0.409234 0.708813i
\(557\) 18.1321 + 18.1321i 0.768284 + 0.768284i 0.977804 0.209521i \(-0.0671903\pi\)
−0.209521 + 0.977804i \(0.567190\pi\)
\(558\) −20.2927 20.2927i −0.859060 0.859060i
\(559\) 6.34164 + 9.33015i 0.268223 + 0.394623i
\(560\) −4.91937 8.15512i −0.207881 0.344617i
\(561\) 0.00919949i 0.000388403i
\(562\) −27.3158 7.31924i −1.15225 0.308744i
\(563\) 18.1061 18.1061i 0.763082 0.763082i −0.213796 0.976878i \(-0.568583\pi\)
0.976878 + 0.213796i \(0.0685829\pi\)
\(564\) 0.998217 + 1.72896i 0.0420325 + 0.0728025i
\(565\) 10.8991 + 6.01680i 0.458531 + 0.253129i
\(566\) −3.23655 1.86862i −0.136042 0.0785440i
\(567\) −23.1571 + 23.1571i −0.972506 + 0.972506i
\(568\) 3.41581 + 12.7480i 0.143324 + 0.534893i
\(569\) 12.8917 7.44300i 0.540446 0.312027i −0.204813 0.978801i \(-0.565659\pi\)
0.745260 + 0.666774i \(0.232325\pi\)
\(570\) −1.56276 + 6.31454i −0.0654568 + 0.264487i
\(571\) 24.9852 14.4252i 1.04560 0.603676i 0.124184 0.992259i \(-0.460369\pi\)
0.921414 + 0.388583i \(0.127035\pi\)
\(572\) 0.0699172 0.0187343i 0.00292339 0.000783319i
\(573\) −0.0443534 0.165529i −0.00185289 0.00691508i
\(574\) 9.80683 + 5.66198i 0.409329 + 0.236326i
\(575\) −14.8810 + 4.60609i −0.620579 + 0.192087i
\(576\) −1.42594 + 2.46981i −0.0594143 + 0.102909i
\(577\) −11.8523 44.2332i −0.493416 1.84145i −0.538727 0.842480i \(-0.681095\pi\)
0.0453113 0.998973i \(-0.485572\pi\)
\(578\) −4.31638 + 16.1090i −0.179538 + 0.670044i
\(579\) −0.879392 1.52315i −0.0365463 0.0633000i
\(580\) 14.7163 + 3.64206i 0.611059 + 0.151228i
\(581\) 13.3702i 0.554691i
\(582\) −1.00230 + 3.74064i −0.0415467 + 0.155055i
\(583\) 0.309272 + 0.0828691i 0.0128087 + 0.00343209i
\(584\) −10.9667 6.33164i −0.453806 0.262005i
\(585\) 0.210501 + 10.9689i 0.00870315 + 0.453508i
\(586\) 1.73995i 0.0718766i
\(587\) −4.11306 15.3501i −0.169764 0.633568i −0.997384 0.0722798i \(-0.976973\pi\)
0.827620 0.561288i \(-0.189694\pi\)
\(588\) 4.14165 1.10975i 0.170799 0.0457654i
\(589\) −38.0331 + 65.8753i −1.56713 + 2.71434i
\(590\) 21.7470 + 12.0053i 0.895311 + 0.494250i
\(591\) 4.26177i 0.175306i
\(592\) 6.11891 + 1.63956i 0.251486 + 0.0673853i
\(593\) 38.9930 10.4481i 1.60125 0.429054i 0.655830 0.754908i \(-0.272319\pi\)
0.945420 + 0.325855i \(0.105652\pi\)
\(594\) 0.0947562i 0.00388789i
\(595\) −3.89880 3.75198i −0.159835 0.153816i
\(596\) −4.32594 + 2.49758i −0.177197 + 0.102305i
\(597\) −0.843789 + 3.14907i −0.0345340 + 0.128883i
\(598\) −3.79000 3.79000i −0.154984 0.154984i
\(599\) −7.38493 + 4.26369i −0.301740 + 0.174210i −0.643224 0.765678i \(-0.722404\pi\)
0.341484 + 0.939887i \(0.389070\pi\)
\(600\) −0.897490 + 1.70216i −0.0366399 + 0.0694903i
\(601\) 47.0697i 1.92001i −0.279981 0.960006i \(-0.590328\pi\)
0.279981 0.960006i \(-0.409672\pi\)
\(602\) 27.4354 + 5.23176i 1.11818 + 0.213230i
\(603\) −14.0330 + 14.0330i −0.571468 + 0.571468i
\(604\) 4.57950 0.186337
\(605\) −23.6283 + 6.81970i −0.960627 + 0.277260i
\(606\) 1.56423 0.0635425
\(607\) 42.2140 + 11.3112i 1.71341 + 0.459108i 0.976257 0.216614i \(-0.0695013\pi\)
0.737157 + 0.675722i \(0.236168\pi\)
\(608\) 7.30151 + 1.95643i 0.296115 + 0.0793438i
\(609\) −5.55675 + 9.62457i −0.225171 + 0.390007i
\(610\) 2.18490 1.31799i 0.0884641 0.0533637i
\(611\) 4.46225 7.72884i 0.180523 0.312675i
\(612\) −0.419354 + 1.56505i −0.0169514 + 0.0632634i
\(613\) −21.9575 + 21.9575i −0.886855 + 0.886855i −0.994220 0.107365i \(-0.965759\pi\)
0.107365 + 0.994220i \(0.465759\pi\)
\(614\) −3.85706 6.68062i −0.155658 0.269608i
\(615\) −0.0438994 2.28753i −0.00177019 0.0922420i
\(616\) 0.0896021 0.155195i 0.00361017 0.00625300i
\(617\) 26.6007 7.12763i 1.07090 0.286948i 0.320039 0.947404i \(-0.396304\pi\)
0.750864 + 0.660456i \(0.229637\pi\)
\(618\) 5.09604 5.09604i 0.204993 0.204993i
\(619\) 19.9121 + 11.4962i 0.800334 + 0.462073i 0.843588 0.536991i \(-0.180439\pi\)
−0.0432538 + 0.999064i \(0.513772\pi\)
\(620\) −15.6026 + 16.2132i −0.626617 + 0.651138i
\(621\) −6.07647 + 3.50825i −0.243840 + 0.140781i
\(622\) 2.73345 + 0.732425i 0.109601 + 0.0293676i
\(623\) 41.7813 41.7813i 1.67393 1.67393i
\(624\) −0.662098 −0.0265051
\(625\) 10.8031 22.5454i 0.432123 0.901815i
\(626\) −4.08979 7.08372i −0.163461 0.283122i
\(627\) −0.118229 + 0.0316794i −0.00472161 + 0.00126515i
\(628\) 12.4515 3.33636i 0.496867 0.133135i
\(629\) 3.59900 0.143502
\(630\) 19.5709 + 18.8339i 0.779724 + 0.750360i
\(631\) 38.5122 + 22.2350i 1.53315 + 0.885163i 0.999214 + 0.0396364i \(0.0126200\pi\)
0.533933 + 0.845527i \(0.320713\pi\)
\(632\) 2.59539 + 9.68614i 0.103239 + 0.385294i
\(633\) 0.850722 + 0.227950i 0.0338132 + 0.00906021i
\(634\) −18.1583 −0.721158
\(635\) −11.4632 6.32818i −0.454903 0.251126i
\(636\) −2.53635 1.46436i −0.100573 0.0580657i
\(637\) −13.5532 13.5532i −0.536999 0.536999i
\(638\) 0.0738299 + 0.275537i 0.00292295 + 0.0109086i
\(639\) −18.8191 32.5957i −0.744474 1.28947i
\(640\) 1.95759 + 1.08067i 0.0773804 + 0.0427173i
\(641\) 43.0878i 1.70187i −0.525273 0.850934i \(-0.676037\pi\)
0.525273 0.850934i \(-0.323963\pi\)
\(642\) 1.44890 5.40735i 0.0571833 0.213411i
\(643\) 30.3838 30.3838i 1.19822 1.19822i 0.223521 0.974699i \(-0.428245\pi\)
0.974699 0.223521i \(-0.0717553\pi\)
\(644\) −13.2697 −0.522900
\(645\) −1.95807 5.29247i −0.0770989 0.208391i
\(646\) 4.29458 0.168968
\(647\) 20.1476 20.1476i 0.792084 0.792084i −0.189749 0.981833i \(-0.560767\pi\)
0.981833 + 0.189749i \(0.0607673\pi\)
\(648\) 1.99004 7.42693i 0.0781761 0.291757i
\(649\) 0.467405i 0.0183473i
\(650\) 8.59559 0.330033i 0.337147 0.0129450i
\(651\) −8.24752 14.2851i −0.323246 0.559878i
\(652\) −0.480539 1.79339i −0.0188193 0.0702348i
\(653\) −18.6680 18.6680i −0.730536 0.730536i 0.240190 0.970726i \(-0.422790\pi\)
−0.970726 + 0.240190i \(0.922790\pi\)
\(654\) −2.45381 1.41671i −0.0959515 0.0553976i
\(655\) 7.43527 + 25.7611i 0.290520 + 1.00657i
\(656\) −2.65867 −0.103804
\(657\) 34.8837 + 9.34705i 1.36094 + 0.364663i
\(658\) −5.71857 21.3420i −0.222933 0.831998i
\(659\) 16.6120 + 9.59093i 0.647111 + 0.373609i 0.787348 0.616508i \(-0.211453\pi\)
−0.140238 + 0.990118i \(0.544787\pi\)
\(660\) −0.0362007 0.000694718i −0.00140911 2.70418e-5i
\(661\) 29.5021 1.14750 0.573749 0.819031i \(-0.305488\pi\)
0.573749 + 0.819031i \(0.305488\pi\)
\(662\) −2.84728 + 0.762927i −0.110663 + 0.0296520i
\(663\) −0.363344 + 0.0973578i −0.0141111 + 0.00378106i
\(664\) 1.56955 + 2.71855i 0.0609105 + 0.105500i
\(665\) 34.7933 63.0265i 1.34923 2.44406i
\(666\) −18.0660 −0.700044
\(667\) 14.9360 14.9360i 0.578324 0.578324i
\(668\) −4.90090 1.31319i −0.189621 0.0508089i
\(669\) −2.20055 + 1.27049i −0.0850784 + 0.0491200i
\(670\) 11.2119 + 10.7897i 0.433153 + 0.416841i
\(671\) 0.0415796 + 0.0240060i 0.00160516 + 0.000926741i
\(672\) −1.15908 + 1.15908i −0.0447126 + 0.0447126i
\(673\) −45.1569 + 12.0998i −1.74067 + 0.466411i −0.982596 0.185756i \(-0.940527\pi\)
−0.758075 + 0.652167i \(0.773860\pi\)
\(674\) −1.83822 + 3.18390i −0.0708057 + 0.122639i
\(675\) 2.49500 10.9807i 0.0960326 0.422649i
\(676\) −5.02014 8.69513i −0.193082 0.334428i
\(677\) 2.21836 2.21836i 0.0852586 0.0852586i −0.663191 0.748450i \(-0.730798\pi\)
0.748450 + 0.663191i \(0.230798\pi\)
\(678\) 0.554580 2.06972i 0.0212985 0.0794872i
\(679\) 21.4293 37.1167i 0.822383 1.42441i
\(680\) 1.23319 + 0.305196i 0.0472905 + 0.0117037i
\(681\) 2.66355 4.61340i 0.102067 0.176786i
\(682\) −0.408961 0.109581i −0.0156599 0.00419606i
\(683\) 8.83110 + 2.36629i 0.337913 + 0.0905435i 0.423785 0.905763i \(-0.360701\pi\)
−0.0858725 + 0.996306i \(0.527368\pi\)
\(684\) −21.5576 −0.824277
\(685\) −7.00970 + 12.6977i −0.267827 + 0.485156i
\(686\) −17.6385 −0.673442
\(687\) 2.99914 2.99914i 0.114424 0.114424i
\(688\) −6.19255 + 2.15692i −0.236089 + 0.0822318i
\(689\) 13.0920i 0.498767i
\(690\) 1.38484 + 2.29574i 0.0527201 + 0.0873971i
\(691\) 32.3897 18.7002i 1.23216 0.711389i 0.264682 0.964336i \(-0.414733\pi\)
0.967480 + 0.252946i \(0.0813996\pi\)
\(692\) 8.16518 + 8.16518i 0.310393 + 0.310393i
\(693\) −0.132275 + 0.493656i −0.00502470 + 0.0187524i
\(694\) 10.8989 6.29251i 0.413718 0.238860i
\(695\) 29.9236 31.0945i 1.13507 1.17948i
\(696\) 2.60926i 0.0989038i
\(697\) −1.45902 + 0.390943i −0.0552642 + 0.0148080i
\(698\) −15.7463 4.21921i −0.596007 0.159700i
\(699\) 9.68747i 0.366414i
\(700\) 14.4699 15.6254i 0.546910 0.590585i
\(701\) −19.5573 + 33.8743i −0.738669 + 1.27941i 0.214425 + 0.976740i \(0.431212\pi\)
−0.953095 + 0.302672i \(0.902121\pi\)
\(702\) 3.74250 1.00280i 0.141252 0.0378482i
\(703\) 12.3935 + 46.2533i 0.467431 + 1.74448i
\(704\) 0.0420741i 0.00158573i
\(705\) −3.09549 + 3.21663i −0.116583 + 0.121145i
\(706\) 22.8755 + 13.2072i 0.860931 + 0.497059i
\(707\) −16.7217 4.48057i −0.628885 0.168509i
\(708\) 1.10655 4.12971i 0.0415867 0.155204i
\(709\) 3.84401i 0.144365i −0.997391 0.0721825i \(-0.977004\pi\)
0.997391 0.0721825i \(-0.0229964\pi\)
\(710\) −25.2694 + 15.2431i −0.948343 + 0.572064i
\(711\) −14.2991 24.7668i −0.536259 0.928828i
\(712\) −3.59054 + 13.4001i −0.134561 + 0.502190i
\(713\) 8.11424 + 30.2827i 0.303881 + 1.13410i
\(714\) −0.465642 + 0.806516i −0.0174262 + 0.0301831i
\(715\) 0.0836019 + 0.138592i 0.00312654 + 0.00518304i
\(716\) −0.407187 0.235089i −0.0152173 0.00878570i
\(717\) 1.37990 + 5.14986i 0.0515333 + 0.192325i
\(718\) 3.39716 0.910265i 0.126781 0.0339708i
\(719\) 43.5847 25.1637i 1.62544 0.938446i 0.640005 0.768370i \(-0.278932\pi\)
0.985431 0.170076i \(-0.0544012\pi\)
\(720\) −6.19026 1.53200i −0.230697 0.0570943i
\(721\) −69.0741 + 39.8799i −2.57245 + 1.48521i
\(722\) 9.87126 + 36.8401i 0.367370 + 1.37105i
\(723\) 0.582578 0.582578i 0.0216663 0.0216663i
\(724\) −15.1029 8.71967i −0.561295 0.324064i
\(725\) 1.30063 + 33.8744i 0.0483041 + 1.25806i
\(726\) 2.11636 + 3.66564i 0.0785455 + 0.136045i
\(727\) −6.03201 + 6.03201i −0.223715 + 0.223715i −0.810061 0.586346i \(-0.800566\pi\)
0.586346 + 0.810061i \(0.300566\pi\)
\(728\) 7.07787 + 1.89651i 0.262323 + 0.0702893i
\(729\) 19.3277i 0.715841i
\(730\) 6.80256 27.4867i 0.251774 1.01733i
\(731\) −3.08117 + 2.09425i −0.113961 + 0.0774586i
\(732\) −0.310539 0.310539i −0.0114779 0.0114779i
\(733\) −5.40913 5.40913i −0.199791 0.199791i 0.600119 0.799910i \(-0.295120\pi\)
−0.799910 + 0.600119i \(0.795120\pi\)
\(734\) 9.83122 + 17.0282i 0.362877 + 0.628521i
\(735\) 4.95228 + 8.20968i 0.182668 + 0.302819i
\(736\) 2.69810 1.55775i 0.0994535 0.0574195i
\(737\) −0.0757781 + 0.282808i −0.00279132 + 0.0104174i
\(738\) 7.32387 1.96243i 0.269595 0.0722379i
\(739\) −22.8015 −0.838767 −0.419384 0.907809i \(-0.637754\pi\)
−0.419384 + 0.907809i \(0.637754\pi\)
\(740\) 0.271786 + 14.1623i 0.00999105 + 0.520618i
\(741\) −2.50242 4.33433i −0.0919289 0.159225i
\(742\) 22.9192 + 22.9192i 0.841391 + 0.841391i
\(743\) −8.56583 + 31.9681i −0.314250 + 1.17280i 0.610436 + 0.792065i \(0.290994\pi\)
−0.924686 + 0.380731i \(0.875673\pi\)
\(744\) 3.35390 + 1.93638i 0.122960 + 0.0709910i
\(745\) −8.04813 7.74505i −0.294861 0.283757i
\(746\) 2.99806 5.19279i 0.109767 0.190122i
\(747\) −6.33029 6.33029i −0.231613 0.231613i
\(748\) 0.00618676 + 0.0230893i 0.000226210 + 0.000844229i
\(749\) −30.9776 + 53.6547i −1.13190 + 1.96050i
\(750\) −4.21338 0.872684i −0.153851 0.0318659i
\(751\) 9.83885 5.68046i 0.359025 0.207283i −0.309628 0.950858i \(-0.600205\pi\)
0.668653 + 0.743575i \(0.266871\pi\)
\(752\) 3.66812 + 3.66812i 0.133762 + 0.133762i
\(753\) −2.02856 2.02856i −0.0739249 0.0739249i
\(754\) −10.1013 + 5.83199i −0.367868 + 0.212388i
\(755\) 2.83962 + 9.83848i 0.103344 + 0.358059i
\(756\) 4.79618 8.30724i 0.174436 0.302131i
\(757\) −9.01058 33.6279i −0.327495 1.22223i −0.911780 0.410680i \(-0.865292\pi\)
0.584285 0.811549i \(-0.301375\pi\)
\(758\) 21.4718 + 21.4718i 0.779889 + 0.779889i
\(759\) −0.0252238 + 0.0436888i −0.000915564 + 0.00158580i
\(760\) 0.324314 + 16.8995i 0.0117641 + 0.613009i
\(761\) −20.9714 12.1078i −0.760212 0.438909i 0.0691598 0.997606i \(-0.477968\pi\)
−0.829372 + 0.558697i \(0.811302\pi\)
\(762\) −0.583281 + 2.17683i −0.0211300 + 0.0788584i
\(763\) 22.1734 + 22.1734i 0.802729 + 0.802729i
\(764\) −0.222641 0.385625i −0.00805485 0.0139514i
\(765\) −3.62234 + 0.0695154i −0.130966 + 0.00251334i
\(766\) −20.7690 −0.750415
\(767\) −18.4607 + 4.94653i −0.666577 + 0.178609i
\(768\) 0.0996077 0.371741i 0.00359428 0.0134140i
\(769\) 15.4907 8.94358i 0.558610 0.322514i −0.193977 0.981006i \(-0.562139\pi\)
0.752588 + 0.658492i \(0.228805\pi\)
\(770\) 0.388977 + 0.0962664i 0.0140178 + 0.00346920i
\(771\) 4.37790 + 7.58274i 0.157666 + 0.273086i
\(772\) −3.23148 3.23148i −0.116303 0.116303i
\(773\) −12.9294 12.9294i −0.465038 0.465038i 0.435265 0.900302i \(-0.356655\pi\)
−0.900302 + 0.435265i \(0.856655\pi\)
\(774\) 15.4666 10.5126i 0.555936 0.377866i
\(775\) −44.5068 23.4669i −1.59873 0.842957i
\(776\) 10.0625i 0.361222i
\(777\) −10.0301 2.68755i −0.359827 0.0964153i
\(778\) −9.71095 + 9.71095i −0.348154 + 0.348154i
\(779\) −10.0486 17.4046i −0.360027 0.623585i
\(780\) −0.410549 1.42243i −0.0147000 0.0509313i
\(781\) −0.480887 0.277640i −0.0172075 0.00993475i
\(782\) 1.25160 1.25160i 0.0447571 0.0447571i
\(783\) 3.95193 + 14.7488i 0.141231 + 0.527080i
\(784\) 9.64858 5.57061i 0.344592 0.198950i
\(785\) 14.8886 + 24.6816i 0.531395 + 0.880925i
\(786\) 3.99652 2.30739i 0.142551 0.0823019i
\(787\) 23.5119 6.29999i 0.838108 0.224570i 0.185860 0.982576i \(-0.440493\pi\)
0.652248 + 0.758006i \(0.273826\pi\)
\(788\) 2.86609 + 10.6964i 0.102100 + 0.381043i
\(789\) 5.27827 + 3.04741i 0.187911 + 0.108491i
\(790\) −19.2001 + 11.5820i −0.683110 + 0.412069i
\(791\) −11.8570 + 20.5369i −0.421586 + 0.730209i
\(792\) −0.0310558 0.115902i −0.00110352 0.00411840i
\(793\) −0.508109 + 1.89629i −0.0180435 + 0.0673391i
\(794\) 4.56517 + 7.90711i 0.162012 + 0.280613i
\(795\) 1.57328 6.35703i 0.0557983 0.225461i
\(796\) 8.47113i 0.300251i
\(797\) −1.43297 + 5.34790i −0.0507583 + 0.189433i −0.986650 0.162855i \(-0.947930\pi\)
0.935892 + 0.352288i \(0.114596\pi\)
\(798\) −11.9686 3.20697i −0.423683 0.113526i
\(799\) 2.55236 + 1.47360i 0.0902958 + 0.0521323i
\(800\) −1.10784 + 4.87572i −0.0391681 + 0.172383i
\(801\) 39.5636i 1.39791i
\(802\) 0.234278 + 0.874336i 0.00827263 + 0.0308739i
\(803\) 0.514641 0.137898i 0.0181613 0.00486630i
\(804\) 1.33906 2.31932i 0.0472250 0.0817960i
\(805\) −8.22818 28.5083i −0.290005 1.00479i
\(806\) 17.3121i 0.609791i
\(807\) 8.15036 + 2.18388i 0.286906 + 0.0768763i
\(808\) 3.92598 1.05196i 0.138115 0.0370079i
\(809\) 0.153827i 0.00540827i 0.999996 + 0.00270413i \(0.000860753\pi\)
−0.999996 + 0.00270413i \(0.999139\pi\)
\(810\) 17.1898 0.329885i 0.603987 0.0115910i
\(811\) 23.7054 13.6863i 0.832411 0.480593i −0.0222666 0.999752i \(-0.507088\pi\)
0.854677 + 0.519160i \(0.173755\pi\)
\(812\) −7.47396 + 27.8932i −0.262284 + 0.978859i
\(813\) −6.14747 6.14747i −0.215601 0.215601i
\(814\) −0.230821 + 0.133265i −0.00809028 + 0.00467092i
\(815\) 3.55491 2.14441i 0.124523 0.0751155i
\(816\) 0.218650i 0.00765427i
\(817\) −37.5249 32.3865i −1.31283 1.13306i
\(818\) 9.76637 9.76637i 0.341473 0.341473i
\(819\) −20.8973 −0.730212
\(820\) −1.64857 5.71182i −0.0575705 0.199465i
\(821\) 44.2460 1.54420 0.772099 0.635502i \(-0.219207\pi\)
0.772099 + 0.635502i \(0.219207\pi\)
\(822\) 2.41127 + 0.646098i 0.0841027 + 0.0225353i
\(823\) −14.2514 3.81864i −0.496771 0.133109i 0.00172993 0.999999i \(-0.499449\pi\)
−0.498501 + 0.866889i \(0.666116\pi\)
\(824\) 9.36313 16.2174i 0.326180 0.564961i
\(825\) −0.0239395 0.0773418i −0.000833468 0.00269270i
\(826\) −23.6582 + 40.9772i −0.823175 + 1.42578i
\(827\) −10.0054 + 37.3406i −0.347921 + 1.29846i 0.541241 + 0.840867i \(0.317955\pi\)
−0.889162 + 0.457592i \(0.848712\pi\)
\(828\) −6.28269 + 6.28269i −0.218339 + 0.218339i
\(829\) −12.4133 21.5005i −0.431132 0.746743i 0.565839 0.824516i \(-0.308552\pi\)
−0.996971 + 0.0777727i \(0.975219\pi\)
\(830\) −4.86722 + 5.05768i −0.168944 + 0.175555i
\(831\) 2.73983 4.74552i 0.0950436 0.164620i
\(832\) −1.66176 + 0.445268i −0.0576113 + 0.0154369i
\(833\) 4.47579 4.47579i 0.155077 0.155077i
\(834\) −6.43230 3.71369i −0.222732 0.128594i
\(835\) −0.217685 11.3432i −0.00753330 0.392549i
\(836\) −0.275432 + 0.159021i −0.00952601 + 0.00549985i
\(837\) −21.8907 5.86559i −0.756653 0.202745i
\(838\) 14.2082 14.2082i 0.490813 0.490813i
\(839\) −16.9353 −0.584670 −0.292335 0.956316i \(-0.594432\pi\)
−0.292335 + 0.956316i \(0.594432\pi\)
\(840\) −3.20886 1.77143i −0.110716 0.0611201i
\(841\) −8.48328 14.6935i −0.292527 0.506671i
\(842\) 8.30219 2.22456i 0.286112 0.0766635i
\(843\) −10.5126 + 2.81684i −0.362073 + 0.0970173i
\(844\) 2.28848 0.0787728
\(845\) 15.5676 16.1767i 0.535540 0.556497i
\(846\) −12.8121 7.39708i −0.440490 0.254317i
\(847\) −12.1242 45.2480i −0.416592 1.55474i
\(848\) −7.35064 1.96960i −0.252422 0.0676363i
\(849\) −1.43829 −0.0493621
\(850\) 0.108989 + 2.83859i 0.00373830 + 0.0973628i
\(851\) 17.0918 + 9.86798i 0.585901 + 0.338270i
\(852\) 3.59153 + 3.59153i 0.123044 + 0.123044i
\(853\) 3.13017 + 11.6819i 0.107175 + 0.399982i 0.998583 0.0532197i \(-0.0169484\pi\)
−0.891408 + 0.453202i \(0.850282\pi\)
\(854\) 2.43018 + 4.20919i 0.0831590 + 0.144036i
\(855\) −13.3673 46.3139i −0.457152 1.58390i
\(856\) 14.5460i 0.497173i
\(857\) −7.67014 + 28.6254i −0.262007 + 0.977824i 0.702050 + 0.712128i \(0.252268\pi\)
−0.964057 + 0.265696i \(0.914398\pi\)
\(858\) 0.0196980 0.0196980i 0.000672478 0.000672478i
\(859\) −51.9937 −1.77400 −0.887001 0.461768i \(-0.847215\pi\)
−0.887001 + 0.461768i \(0.847215\pi\)
\(860\) −8.47370 11.9665i −0.288951 0.408053i
\(861\) 4.35807 0.148523
\(862\) −9.25046 + 9.25046i −0.315072 + 0.315072i
\(863\) −1.88538 + 7.03632i −0.0641790 + 0.239519i −0.990562 0.137062i \(-0.956234\pi\)
0.926383 + 0.376582i \(0.122901\pi\)
\(864\) 2.25213i 0.0766189i
\(865\) −12.4789 + 22.6049i −0.424294 + 0.768588i
\(866\) −7.63917 13.2314i −0.259590 0.449622i
\(867\) 1.66118 + 6.19961i 0.0564166 + 0.210550i
\(868\) −30.3069 30.3069i −1.02868 1.02868i
\(869\) −0.365387 0.210956i −0.0123949 0.00715619i
\(870\) 5.60567 1.61793i 0.190050 0.0548530i
\(871\) −11.9718 −0.405648
\(872\) −7.11143 1.90550i −0.240823 0.0645284i
\(873\) −7.42735 27.7193i −0.251378 0.938155i
\(874\) 20.3952 + 11.7752i 0.689877 + 0.398301i
\(875\) 42.5416 + 21.3978i 1.43817 + 0.723378i
\(876\) −4.87352 −0.164661
\(877\) −16.7221 + 4.48067i −0.564665 + 0.151302i −0.529849 0.848092i \(-0.677751\pi\)
−0.0348163 + 0.999394i \(0.511085\pi\)
\(878\) 17.2583 4.62434i 0.582438 0.156064i
\(879\) −0.334813 0.579914i −0.0112930 0.0195600i
\(880\) −0.0903909 + 0.0260890i −0.00304708 + 0.000879460i
\(881\) 23.1981 0.781564 0.390782 0.920483i \(-0.372205\pi\)
0.390782 + 0.920483i \(0.372205\pi\)
\(882\) −22.4673 + 22.4673i −0.756512 + 0.756512i
\(883\) −36.3992 9.75314i −1.22493 0.328219i −0.412327 0.911036i \(-0.635284\pi\)
−0.812604 + 0.582816i \(0.801951\pi\)
\(884\) −0.846464 + 0.488706i −0.0284697 + 0.0164370i
\(885\) 9.55829 0.183431i 0.321299 0.00616596i
\(886\) −3.15789 1.82321i −0.106091 0.0612519i
\(887\) −34.4304 + 34.4304i −1.15606 + 1.15606i −0.170744 + 0.985315i \(0.554617\pi\)
−0.985315 + 0.170744i \(0.945383\pi\)
\(888\) 2.35489 0.630991i 0.0790249 0.0211747i
\(889\) 12.4706 21.5997i 0.418251 0.724432i
\(890\) −31.0148 + 0.595197i −1.03962 + 0.0199510i
\(891\) 0.161752 + 0.280163i 0.00541890 + 0.00938581i
\(892\) −4.66864 + 4.66864i −0.156317 + 0.156317i
\(893\) −10.1490 + 37.8766i −0.339623 + 1.26749i
\(894\) −0.961205 + 1.66486i −0.0321475 + 0.0556811i
\(895\) 0.252574 1.02056i 0.00844263 0.0341136i
\(896\) −2.12963 + 3.68862i −0.0711458 + 0.123228i
\(897\) −1.99248 0.533884i −0.0665270 0.0178259i
\(898\) 23.6902 + 6.34777i 0.790552 + 0.211828i
\(899\) 68.2251 2.27543
\(900\) −0.547097 14.2489i −0.0182366 0.474965i
\(901\) −4.32348 −0.144036
\(902\) 0.0790978 0.0790978i 0.00263367 0.00263367i
\(903\) 10.1508 3.53561i 0.337797 0.117658i
\(904\) 5.56764i 0.185177i
\(905\) 9.36821 37.8535i 0.311410 1.25829i
\(906\) 1.52632 0.881221i 0.0507086 0.0292766i
\(907\) 0.934659 + 0.934659i 0.0310349 + 0.0310349i 0.722454 0.691419i \(-0.243014\pi\)
−0.691419 + 0.722454i \(0.743014\pi\)
\(908\) 3.58253 13.3702i 0.118890 0.443705i
\(909\) −10.0385 + 5.79571i −0.332955 + 0.192231i
\(910\) 0.314380 + 16.3819i 0.0104216 + 0.543054i
\(911\) 11.6084i 0.384602i −0.981336 0.192301i \(-0.938405\pi\)
0.981336 0.192301i \(-0.0615950\pi\)
\(912\) 2.81002 0.752942i 0.0930490 0.0249324i
\(913\) −0.127575 0.0341835i −0.00422211 0.00113131i
\(914\) 2.31431i 0.0765506i
\(915\) 0.474598 0.859711i 0.0156897 0.0284212i
\(916\) 5.51042 9.54432i 0.182069 0.315353i
\(917\) −49.3323 + 13.2186i −1.62910 + 0.436515i
\(918\) 0.331162 + 1.23591i 0.0109300 + 0.0407913i
\(919\) 0.327708i 0.0108101i −0.999985 0.00540505i \(-0.998280\pi\)
0.999985 0.00540505i \(-0.00172049\pi\)
\(920\) 5.01965 + 4.83062i 0.165493 + 0.159261i
\(921\) −2.57107 1.48441i −0.0847195 0.0489128i
\(922\) 2.33100 + 0.624589i 0.0767673 + 0.0205697i
\(923\) 5.87651 21.9314i 0.193428 0.721882i
\(924\) 0.0689675i 0.00226887i
\(925\) −30.2575 + 9.36558i −0.994860 + 0.307938i
\(926\) 3.13737 + 5.43409i 0.103100 + 0.178575i
\(927\) −13.8223 + 51.5855i −0.453983 + 1.69429i
\(928\) −1.75476 6.54885i −0.0576027 0.214976i
\(929\) 25.4695 44.1144i 0.835626 1.44735i −0.0578931 0.998323i \(-0.518438\pi\)
0.893519 0.449025i \(-0.148228\pi\)
\(930\) −2.08040 + 8.40613i −0.0682190 + 0.275648i
\(931\) 72.9344 + 42.1087i 2.39033 + 1.38006i
\(932\) −6.51493 24.3141i −0.213404 0.796434i
\(933\) 1.05198 0.281877i 0.0344403 0.00922825i
\(934\) −25.0661 + 14.4719i −0.820189 + 0.473537i
\(935\) −0.0457682 + 0.0276085i −0.00149678 + 0.000902895i
\(936\) 4.24902 2.45317i 0.138883 0.0801844i
\(937\) −11.2128 41.8467i −0.366306 1.36707i −0.865642 0.500663i \(-0.833090\pi\)
0.499337 0.866408i \(-0.333577\pi\)
\(938\) −20.9581 + 20.9581i −0.684305 + 0.684305i
\(939\) −2.72620 1.57397i −0.0889662 0.0513647i
\(940\) −5.60599 + 10.1550i −0.182847 + 0.331219i
\(941\) 8.07395 + 13.9845i 0.263203 + 0.455882i 0.967091 0.254429i \(-0.0818877\pi\)
−0.703888 + 0.710311i \(0.748554\pi\)
\(942\) 3.50799 3.50799i 0.114296 0.114296i
\(943\) −8.00086 2.14382i −0.260544 0.0698125i
\(944\) 11.1091i 0.361570i
\(945\) 20.8210 + 5.15291i 0.677308 + 0.167624i
\(946\) 0.120064 0.248404i 0.00390360 0.00807632i
\(947\) 18.1941 + 18.1941i 0.591227 + 0.591227i 0.937963 0.346736i \(-0.112710\pi\)
−0.346736 + 0.937963i \(0.612710\pi\)
\(948\) 2.72891 + 2.72891i 0.0886308 + 0.0886308i
\(949\) 10.8928 + 18.8670i 0.353597 + 0.612448i
\(950\) −36.1053 + 11.1757i −1.17141 + 0.362586i
\(951\) −6.05205 + 3.49415i −0.196251 + 0.113306i
\(952\) −0.626299 + 2.33738i −0.0202985 + 0.0757549i
\(953\) −25.9113 + 6.94291i −0.839349 + 0.224903i −0.652788 0.757541i \(-0.726401\pi\)
−0.186561 + 0.982443i \(0.559734\pi\)
\(954\) 21.7027 0.702651
\(955\) 0.690413 0.717431i 0.0223412 0.0232155i
\(956\) 6.92668 + 11.9974i 0.224025 + 0.388022i
\(957\) 0.0776278 + 0.0776278i 0.00250935 + 0.00250935i
\(958\) 6.80159 25.3839i 0.219749 0.820116i
\(959\) −23.9260 13.8137i −0.772610 0.446066i
\(960\) 0.860403 0.0165118i 0.0277694 0.000532915i
\(961\) −35.1310 + 60.8487i −1.13326 + 1.96286i
\(962\) −7.70621 7.70621i −0.248458 0.248458i
\(963\) 10.7367 + 40.0701i 0.345987 + 1.29124i
\(964\) 1.07039 1.85397i 0.0344750 0.0597124i
\(965\) 4.93867 8.94617i 0.158981 0.287987i
\(966\) −4.42271 + 2.55345i −0.142298 + 0.0821561i
\(967\) 21.1492 + 21.1492i 0.680114 + 0.680114i 0.960026 0.279912i \(-0.0903052\pi\)
−0.279912 + 0.960026i \(0.590305\pi\)
\(968\) 7.77692 + 7.77692i 0.249960 + 0.249960i
\(969\) 1.43136 0.826395i 0.0459818 0.0265476i
\(970\) −21.6180 + 6.23947i −0.694112 + 0.200337i
\(971\) −18.0736 + 31.3044i −0.580009 + 1.00461i 0.415468 + 0.909608i \(0.363618\pi\)
−0.995477 + 0.0949978i \(0.969716\pi\)
\(972\) −2.51455 9.38445i −0.0806544 0.301006i
\(973\) 58.1242 + 58.1242i 1.86338 + 1.86338i
\(974\) −6.69945 + 11.6038i −0.214664 + 0.371809i
\(975\) 2.80135 1.76402i 0.0897150 0.0564940i
\(976\) −0.988247 0.570565i −0.0316330 0.0182633i
\(977\) −4.60018 + 17.1681i −0.147173 + 0.549256i 0.852476 + 0.522766i \(0.175100\pi\)
−0.999649 + 0.0264905i \(0.991567\pi\)
\(978\) −0.505259 0.505259i −0.0161564 0.0161564i
\(979\) −0.291843 0.505486i −0.00932733 0.0161554i
\(980\) 17.9506 + 17.2746i 0.573410 + 0.551816i
\(981\) 20.9964 0.670364
\(982\) −20.7452 + 5.55867i −0.662007 + 0.177384i
\(983\) −9.42805 + 35.1860i −0.300708 + 1.12226i 0.635869 + 0.771797i \(0.280642\pi\)
−0.936577 + 0.350461i \(0.886025\pi\)
\(984\) −0.886119 + 0.511601i −0.0282484 + 0.0163092i
\(985\) −21.2026 + 12.7900i −0.675572 + 0.407522i
\(986\) −1.92594 3.33583i −0.0613345 0.106234i
\(987\) −6.01275 6.01275i −0.191388 0.191388i
\(988\) −9.19558 9.19558i −0.292550 0.292550i
\(989\) −20.3748 + 1.49755i −0.647880 + 0.0476192i
\(990\) 0.229744 0.138587i 0.00730174 0.00440459i
\(991\) 28.3357i 0.900114i −0.893000 0.450057i \(-0.851404\pi\)
0.893000 0.450057i \(-0.148596\pi\)
\(992\) 9.72002 + 2.60447i 0.308611 + 0.0826920i
\(993\) −0.802173 + 0.802173i −0.0254562 + 0.0254562i
\(994\) −28.1061 48.6812i −0.891472 1.54407i
\(995\) −18.1991 + 5.25271i −0.576952 + 0.166522i
\(996\) 1.04624 + 0.604050i 0.0331515 + 0.0191400i
\(997\) 4.24866 4.24866i 0.134556 0.134556i −0.636621 0.771177i \(-0.719668\pi\)
0.771177 + 0.636621i \(0.219668\pi\)
\(998\) 8.06609 + 30.1031i 0.255328 + 0.952896i
\(999\) −12.3553 + 7.13334i −0.390904 + 0.225689i
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 430.2.l.a.7.18 88
5.3 odd 4 inner 430.2.l.a.93.7 yes 88
43.37 odd 6 inner 430.2.l.a.37.7 yes 88
215.123 even 12 inner 430.2.l.a.123.18 yes 88
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
430.2.l.a.7.18 88 1.1 even 1 trivial
430.2.l.a.37.7 yes 88 43.37 odd 6 inner
430.2.l.a.93.7 yes 88 5.3 odd 4 inner
430.2.l.a.123.18 yes 88 215.123 even 12 inner