Properties

Label 370.2.ba.a.283.9
Level $370$
Weight $2$
Character 370.283
Analytic conductor $2.954$
Analytic rank $0$
Dimension $108$
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] = [370,2,Mod(17,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([9, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 370 = 2 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 370.ba (of order \(36\), degree \(12\), 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: \(2.95446487479\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(9\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 283.9
Character \(\chi\) \(=\) 370.283
Dual form 370.2.ba.a.17.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.173648 - 0.984808i) q^{2} +(2.40138 + 1.68147i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.06638 + 1.96541i) q^{5} +(2.07292 - 2.07292i) q^{6} +(-0.0272851 + 0.311870i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.91325 + 5.25661i) q^{9} +O(q^{10})\) \(q+(0.173648 - 0.984808i) q^{2} +(2.40138 + 1.68147i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-1.06638 + 1.96541i) q^{5} +(2.07292 - 2.07292i) q^{6} +(-0.0272851 + 0.311870i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(1.91325 + 5.25661i) q^{9} +(1.75038 + 1.39147i) q^{10} +(-0.336134 - 0.194067i) q^{11} +(-1.68147 - 2.40138i) q^{12} +(1.10478 + 0.402107i) q^{13} +(0.302394 + 0.0810263i) q^{14} +(-5.86555 + 2.92663i) q^{15} +(0.766044 + 0.642788i) q^{16} +(0.856703 + 2.35377i) q^{17} +(5.50898 - 0.971381i) q^{18} +(3.50398 - 5.00421i) q^{19} +(1.67428 - 1.48216i) q^{20} +(-0.589921 + 0.703041i) q^{21} +(-0.249487 + 0.297328i) q^{22} +(0.00670387 + 0.0116114i) q^{23} +(-2.65688 + 1.23892i) q^{24} +(-2.72568 - 4.19174i) q^{25} +(0.587841 - 1.01817i) q^{26} +(-1.96814 + 7.34521i) q^{27} +(0.132306 - 0.283730i) q^{28} +(1.46909 + 5.48271i) q^{29} +(1.86362 + 6.28464i) q^{30} +(-1.63301 - 1.63301i) q^{31} +(0.766044 - 0.642788i) q^{32} +(-0.480868 - 1.03123i) q^{33} +(2.46678 - 0.434959i) q^{34} +(-0.583857 - 0.386198i) q^{35} -5.59396i q^{36} +(-2.74292 - 5.42922i) q^{37} +(-4.31972 - 4.31972i) q^{38} +(1.97687 + 2.82326i) q^{39} +(-1.16891 - 1.90622i) q^{40} +(3.16243 - 8.68870i) q^{41} +(0.589921 + 0.703041i) q^{42} -9.85100 q^{43} +(0.249487 + 0.297328i) q^{44} +(-12.3716 - 1.84521i) q^{45} +(0.0125992 - 0.00458572i) q^{46} +(3.99887 + 1.07149i) q^{47} +(0.758740 + 2.83166i) q^{48} +(6.79714 + 1.19852i) q^{49} +(-4.60137 + 1.95638i) q^{50} +(-1.90052 + 7.09282i) q^{51} +(-0.900625 - 0.755714i) q^{52} +(-0.404022 - 4.61800i) q^{53} +(6.89186 + 3.21373i) q^{54} +(0.739866 - 0.453692i) q^{55} +(-0.256445 - 0.179565i) q^{56} +(16.8288 - 6.12518i) q^{57} +(5.65452 - 0.494706i) q^{58} +(-0.834962 - 9.54366i) q^{59} +(6.51278 - 0.743992i) q^{60} +(-2.39133 - 5.12822i) q^{61} +(-1.89178 + 1.32464i) q^{62} +(-1.69158 + 0.453258i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-1.96842 + 1.74255i) q^{65} +(-1.09906 + 0.294492i) q^{66} +(13.1456 + 1.15009i) q^{67} -2.50483i q^{68} +(-0.00342569 + 0.0391559i) q^{69} +(-0.481716 + 0.507924i) q^{70} +(-0.00507722 - 0.0287943i) q^{71} +(-5.50898 - 0.971381i) q^{72} +(-1.83480 + 1.83480i) q^{73} +(-5.82304 + 1.75848i) q^{74} +(0.502866 - 14.6491i) q^{75} +(-5.00421 + 3.50398i) q^{76} +(0.0696951 - 0.0995349i) q^{77} +(3.12365 - 1.45658i) q^{78} +(-11.5452 - 1.01007i) q^{79} +(-2.08023 + 0.820138i) q^{80} +(-4.22131 + 3.54210i) q^{81} +(-8.00755 - 4.62316i) q^{82} +(14.8888 + 6.94277i) q^{83} +(0.794799 - 0.458877i) q^{84} +(-5.53970 - 0.826235i) q^{85} +(-1.71061 + 9.70134i) q^{86} +(-5.69115 + 15.6363i) q^{87} +(0.336134 - 0.194067i) q^{88} +(-13.5048 + 1.18152i) q^{89} +(-3.96548 + 11.8633i) q^{90} +(-0.155549 + 0.333577i) q^{91} +(-0.00232823 - 0.0132041i) q^{92} +(-1.17563 - 6.66735i) q^{93} +(1.74961 - 3.75205i) q^{94} +(6.09875 + 12.2231i) q^{95} +(2.92039 - 0.255501i) q^{96} +(7.27335 - 4.19927i) q^{97} +(2.36062 - 6.48575i) q^{98} +(0.377026 - 2.13822i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 6 q^{3} + 6 q^{5} - 54 q^{8} - 12 q^{10} + 36 q^{11} - 6 q^{12} + 6 q^{13} + 12 q^{14} + 24 q^{15} + 12 q^{19} - 6 q^{20} - 42 q^{21} - 6 q^{22} - 6 q^{24} - 18 q^{25} - 6 q^{26} + 6 q^{27} - 12 q^{30} + 6 q^{33} - 54 q^{35} + 12 q^{37} + 48 q^{38} - 12 q^{40} + 48 q^{41} + 42 q^{42} + 6 q^{44} - 90 q^{45} + 6 q^{46} - 12 q^{47} - 12 q^{49} - 12 q^{50} - 12 q^{51} + 6 q^{52} + 36 q^{53} - 18 q^{54} + 36 q^{57} + 6 q^{58} + 24 q^{59} - 54 q^{60} - 36 q^{61} + 54 q^{62} - 96 q^{63} - 54 q^{64} - 18 q^{65} - 42 q^{67} - 96 q^{69} - 12 q^{70} - 48 q^{71} + 84 q^{73} + 42 q^{74} + 252 q^{75} - 6 q^{76} - 66 q^{77} - 24 q^{78} + 66 q^{79} + 6 q^{80} - 108 q^{81} + 36 q^{82} + 48 q^{83} - 36 q^{85} + 108 q^{87} - 36 q^{88} - 66 q^{89} + 6 q^{90} - 18 q^{91} - 12 q^{92} - 12 q^{93} + 18 q^{94} + 90 q^{95} + 12 q^{96} - 72 q^{97} - 24 q^{98} - 42 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).

\(n\) \(261\) \(297\)
\(\chi(n)\) \(e\left(\frac{29}{36}\right)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.173648 0.984808i 0.122788 0.696364i
\(3\) 2.40138 + 1.68147i 1.38644 + 0.970795i 0.998800 + 0.0489834i \(0.0155982\pi\)
0.387639 + 0.921811i \(0.373291\pi\)
\(4\) −0.939693 0.342020i −0.469846 0.171010i
\(5\) −1.06638 + 1.96541i −0.476898 + 0.878958i
\(6\) 2.07292 2.07292i 0.846264 0.846264i
\(7\) −0.0272851 + 0.311870i −0.0103128 + 0.117876i −0.999606 0.0280651i \(-0.991065\pi\)
0.989293 + 0.145941i \(0.0466210\pi\)
\(8\) −0.500000 + 0.866025i −0.176777 + 0.306186i
\(9\) 1.91325 + 5.25661i 0.637749 + 1.75220i
\(10\) 1.75038 + 1.39147i 0.553518 + 0.440020i
\(11\) −0.336134 0.194067i −0.101348 0.0585133i 0.448469 0.893798i \(-0.351969\pi\)
−0.549817 + 0.835285i \(0.685303\pi\)
\(12\) −1.68147 2.40138i −0.485397 0.693219i
\(13\) 1.10478 + 0.402107i 0.306411 + 0.111524i 0.490649 0.871357i \(-0.336760\pi\)
−0.184238 + 0.982882i \(0.558982\pi\)
\(14\) 0.302394 + 0.0810263i 0.0808183 + 0.0216552i
\(15\) −5.86555 + 2.92663i −1.51448 + 0.755652i
\(16\) 0.766044 + 0.642788i 0.191511 + 0.160697i
\(17\) 0.856703 + 2.35377i 0.207781 + 0.570874i 0.999183 0.0404229i \(-0.0128705\pi\)
−0.791402 + 0.611296i \(0.790648\pi\)
\(18\) 5.50898 0.971381i 1.29848 0.228957i
\(19\) 3.50398 5.00421i 0.803869 1.14804i −0.182454 0.983214i \(-0.558404\pi\)
0.986322 0.164829i \(-0.0527072\pi\)
\(20\) 1.67428 1.48216i 0.374380 0.331421i
\(21\) −0.589921 + 0.703041i −0.128731 + 0.153416i
\(22\) −0.249487 + 0.297328i −0.0531909 + 0.0633905i
\(23\) 0.00670387 + 0.0116114i 0.00139785 + 0.00242115i 0.866723 0.498789i \(-0.166222\pi\)
−0.865326 + 0.501210i \(0.832888\pi\)
\(24\) −2.65688 + 1.23892i −0.542334 + 0.252894i
\(25\) −2.72568 4.19174i −0.545136 0.838348i
\(26\) 0.587841 1.01817i 0.115285 0.199680i
\(27\) −1.96814 + 7.34521i −0.378769 + 1.41359i
\(28\) 0.132306 0.283730i 0.0250034 0.0536200i
\(29\) 1.46909 + 5.48271i 0.272803 + 1.01811i 0.957300 + 0.289098i \(0.0933553\pi\)
−0.684497 + 0.729016i \(0.739978\pi\)
\(30\) 1.86362 + 6.28464i 0.340249 + 1.14741i
\(31\) −1.63301 1.63301i −0.293298 0.293298i 0.545084 0.838382i \(-0.316498\pi\)
−0.838382 + 0.545084i \(0.816498\pi\)
\(32\) 0.766044 0.642788i 0.135419 0.113630i
\(33\) −0.480868 1.03123i −0.0837084 0.179513i
\(34\) 2.46678 0.434959i 0.423049 0.0745949i
\(35\) −0.583857 0.386198i −0.0986898 0.0652793i
\(36\) 5.59396i 0.932327i
\(37\) −2.74292 5.42922i −0.450934 0.892557i
\(38\) −4.31972 4.31972i −0.700751 0.700751i
\(39\) 1.97687 + 2.82326i 0.316553 + 0.452084i
\(40\) −1.16891 1.90622i −0.184820 0.301399i
\(41\) 3.16243 8.68870i 0.493888 1.35695i −0.403207 0.915109i \(-0.632104\pi\)
0.897095 0.441838i \(-0.145673\pi\)
\(42\) 0.589921 + 0.703041i 0.0910268 + 0.108482i
\(43\) −9.85100 −1.50226 −0.751132 0.660152i \(-0.770492\pi\)
−0.751132 + 0.660152i \(0.770492\pi\)
\(44\) 0.249487 + 0.297328i 0.0376117 + 0.0448238i
\(45\) −12.3716 1.84521i −1.84425 0.275067i
\(46\) 0.0125992 0.00458572i 0.00185764 0.000676127i
\(47\) 3.99887 + 1.07149i 0.583294 + 0.156293i 0.538387 0.842698i \(-0.319034\pi\)
0.0449077 + 0.998991i \(0.485701\pi\)
\(48\) 0.758740 + 2.83166i 0.109515 + 0.408714i
\(49\) 6.79714 + 1.19852i 0.971019 + 0.171217i
\(50\) −4.60137 + 1.95638i −0.650731 + 0.276674i
\(51\) −1.90052 + 7.09282i −0.266125 + 0.993194i
\(52\) −0.900625 0.755714i −0.124894 0.104799i
\(53\) −0.404022 4.61800i −0.0554967 0.634330i −0.972105 0.234545i \(-0.924640\pi\)
0.916609 0.399786i \(-0.130915\pi\)
\(54\) 6.89186 + 3.21373i 0.937863 + 0.437333i
\(55\) 0.739866 0.453692i 0.0997635 0.0611758i
\(56\) −0.256445 0.179565i −0.0342689 0.0239953i
\(57\) 16.8288 6.12518i 2.22903 0.811300i
\(58\) 5.65452 0.494706i 0.742475 0.0649581i
\(59\) −0.834962 9.54366i −0.108703 1.24248i −0.833111 0.553107i \(-0.813442\pi\)
0.724408 0.689372i \(-0.242113\pi\)
\(60\) 6.51278 0.743992i 0.840796 0.0960490i
\(61\) −2.39133 5.12822i −0.306178 0.656602i 0.691667 0.722217i \(-0.256877\pi\)
−0.997845 + 0.0656153i \(0.979099\pi\)
\(62\) −1.89178 + 1.32464i −0.240256 + 0.168229i
\(63\) −1.69158 + 0.453258i −0.213119 + 0.0571051i
\(64\) −0.500000 0.866025i −0.0625000 0.108253i
\(65\) −1.96842 + 1.74255i −0.244152 + 0.216137i
\(66\) −1.09906 + 0.294492i −0.135285 + 0.0362495i
\(67\) 13.1456 + 1.15009i 1.60599 + 0.140506i 0.854576 0.519326i \(-0.173817\pi\)
0.751413 + 0.659832i \(0.229373\pi\)
\(68\) 2.50483i 0.303755i
\(69\) −0.00342569 + 0.0391559i −0.000412405 + 0.00471381i
\(70\) −0.481716 + 0.507924i −0.0575761 + 0.0607086i
\(71\) −0.00507722 0.0287943i −0.000602555 0.00341726i 0.984505 0.175357i \(-0.0561078\pi\)
−0.985108 + 0.171939i \(0.944997\pi\)
\(72\) −5.50898 0.971381i −0.649239 0.114478i
\(73\) −1.83480 + 1.83480i −0.214747 + 0.214747i −0.806281 0.591533i \(-0.798523\pi\)
0.591533 + 0.806281i \(0.298523\pi\)
\(74\) −5.82304 + 1.75848i −0.676914 + 0.204419i
\(75\) 0.502866 14.6491i 0.0580659 1.69153i
\(76\) −5.00421 + 3.50398i −0.574022 + 0.401934i
\(77\) 0.0696951 0.0995349i 0.00794250 0.0113431i
\(78\) 3.12365 1.45658i 0.353684 0.164926i
\(79\) −11.5452 1.01007i −1.29894 0.113642i −0.583381 0.812199i \(-0.698270\pi\)
−0.715555 + 0.698557i \(0.753826\pi\)
\(80\) −2.08023 + 0.820138i −0.232577 + 0.0916942i
\(81\) −4.22131 + 3.54210i −0.469035 + 0.393567i
\(82\) −8.00755 4.62316i −0.884286 0.510543i
\(83\) 14.8888 + 6.94277i 1.63426 + 0.762068i 0.999939 0.0110008i \(-0.00350174\pi\)
0.634322 + 0.773069i \(0.281280\pi\)
\(84\) 0.794799 0.458877i 0.0867196 0.0500676i
\(85\) −5.53970 0.826235i −0.600865 0.0896178i
\(86\) −1.71061 + 9.70134i −0.184460 + 1.04612i
\(87\) −5.69115 + 15.6363i −0.610155 + 1.67639i
\(88\) 0.336134 0.194067i 0.0358320 0.0206876i
\(89\) −13.5048 + 1.18152i −1.43151 + 0.125241i −0.776374 0.630273i \(-0.782943\pi\)
−0.655133 + 0.755514i \(0.727387\pi\)
\(90\) −3.96548 + 11.8633i −0.417999 + 1.25050i
\(91\) −0.155549 + 0.333577i −0.0163060 + 0.0349683i
\(92\) −0.00232823 0.0132041i −0.000242735 0.00137662i
\(93\) −1.17563 6.66735i −0.121908 0.691372i
\(94\) 1.74961 3.75205i 0.180459 0.386995i
\(95\) 6.09875 + 12.2231i 0.625719 + 1.25407i
\(96\) 2.92039 0.255501i 0.298061 0.0260770i
\(97\) 7.27335 4.19927i 0.738497 0.426371i −0.0830256 0.996547i \(-0.526458\pi\)
0.821523 + 0.570176i \(0.193125\pi\)
\(98\) 2.36062 6.48575i 0.238459 0.655160i
\(99\) 0.377026 2.13822i 0.0378925 0.214899i
\(100\) 1.12764 + 4.87118i 0.112764 + 0.487118i
\(101\) −17.0070 + 9.81897i −1.69226 + 0.977024i −0.739563 + 0.673087i \(0.764968\pi\)
−0.952692 + 0.303937i \(0.901699\pi\)
\(102\) 6.65505 + 3.10330i 0.658948 + 0.307272i
\(103\) −1.57751 0.910774i −0.155436 0.0897412i 0.420264 0.907402i \(-0.361937\pi\)
−0.575701 + 0.817660i \(0.695271\pi\)
\(104\) −0.900625 + 0.755714i −0.0883136 + 0.0741039i
\(105\) −0.752685 1.90914i −0.0734546 0.186313i
\(106\) −4.61800 0.404022i −0.448539 0.0392421i
\(107\) −7.91100 + 3.68896i −0.764785 + 0.356625i −0.765551 0.643375i \(-0.777534\pi\)
0.000766612 1.00000i \(0.499756\pi\)
\(108\) 4.36166 6.22910i 0.419701 0.599395i
\(109\) −15.5737 + 10.9048i −1.49169 + 1.04449i −0.508677 + 0.860957i \(0.669865\pi\)
−0.983013 + 0.183535i \(0.941246\pi\)
\(110\) −0.318323 0.807409i −0.0303509 0.0769834i
\(111\) 2.54223 17.6497i 0.241298 1.67524i
\(112\) −0.221368 + 0.221368i −0.0209173 + 0.0209173i
\(113\) 3.85114 + 0.679059i 0.362285 + 0.0638805i 0.351828 0.936065i \(-0.385560\pi\)
0.0104569 + 0.999945i \(0.496671\pi\)
\(114\) −3.10984 17.6368i −0.291263 1.65183i
\(115\) −0.0299701 0.000793682i −0.00279473 7.40113e-5i
\(116\) 0.494706 5.65452i 0.0459323 0.525009i
\(117\) 6.57673i 0.608019i
\(118\) −9.54366 0.834962i −0.878565 0.0768645i
\(119\) −0.757447 + 0.202957i −0.0694350 + 0.0186051i
\(120\) 0.398243 6.54303i 0.0363544 0.597294i
\(121\) −5.42468 9.39581i −0.493152 0.854165i
\(122\) −5.46556 + 1.46449i −0.494829 + 0.132589i
\(123\) 22.2040 15.5474i 2.00206 1.40186i
\(124\) 0.976008 + 2.09306i 0.0876481 + 0.187962i
\(125\) 11.1451 0.887108i 0.996847 0.0793453i
\(126\) 0.152632 + 1.74459i 0.0135975 + 0.155420i
\(127\) −3.67812 + 0.321794i −0.326380 + 0.0285546i −0.249168 0.968460i \(-0.580157\pi\)
−0.0772117 + 0.997015i \(0.524602\pi\)
\(128\) −0.939693 + 0.342020i −0.0830579 + 0.0302306i
\(129\) −23.6560 16.5641i −2.08280 1.45839i
\(130\) 1.37426 + 2.24110i 0.120531 + 0.196558i
\(131\) 5.81671 + 2.71238i 0.508209 + 0.236982i 0.659772 0.751466i \(-0.270653\pi\)
−0.151563 + 0.988448i \(0.548431\pi\)
\(132\) 0.0991686 + 1.13350i 0.00863152 + 0.0986587i
\(133\) 1.46506 + 1.22933i 0.127036 + 0.106596i
\(134\) 3.41532 12.7462i 0.295039 1.10110i
\(135\) −12.3376 11.7010i −1.06185 1.00706i
\(136\) −2.46678 0.434959i −0.211524 0.0372975i
\(137\) 5.42345 + 20.2406i 0.463357 + 1.72927i 0.662281 + 0.749256i \(0.269589\pi\)
−0.198924 + 0.980015i \(0.563745\pi\)
\(138\) 0.0379661 + 0.0101730i 0.00323189 + 0.000865983i
\(139\) 4.90332 1.78466i 0.415894 0.151373i −0.125594 0.992082i \(-0.540084\pi\)
0.541487 + 0.840709i \(0.317861\pi\)
\(140\) 0.416559 + 0.562598i 0.0352056 + 0.0475482i
\(141\) 7.80113 + 9.29702i 0.656973 + 0.782950i
\(142\) −0.0292385 −0.00245364
\(143\) −0.293318 0.349563i −0.0245285 0.0292319i
\(144\) −1.91325 + 5.25661i −0.159437 + 0.438050i
\(145\) −12.3424 2.95928i −1.02498 0.245754i
\(146\) 1.48832 + 2.12554i 0.123174 + 0.175911i
\(147\) 14.3073 + 14.3073i 1.18004 + 1.18004i
\(148\) 0.720603 + 6.03993i 0.0592332 + 0.496479i
\(149\) 20.1592i 1.65151i 0.564030 + 0.825754i \(0.309250\pi\)
−0.564030 + 0.825754i \(0.690750\pi\)
\(150\) −14.3392 3.03902i −1.17079 0.248135i
\(151\) 6.88308 1.21367i 0.560137 0.0987673i 0.113591 0.993528i \(-0.463765\pi\)
0.446547 + 0.894760i \(0.352654\pi\)
\(152\) 2.58178 + 5.53664i 0.209410 + 0.449081i
\(153\) −10.7338 + 9.00670i −0.867773 + 0.728148i
\(154\) −0.0859203 0.0859203i −0.00692366 0.00692366i
\(155\) 4.95095 1.46814i 0.397670 0.117923i
\(156\) −0.892038 3.32913i −0.0714202 0.266544i
\(157\) 2.35549 5.05137i 0.187989 0.403143i −0.789613 0.613605i \(-0.789719\pi\)
0.977602 + 0.210462i \(0.0674967\pi\)
\(158\) −2.99953 + 11.1944i −0.238630 + 0.890578i
\(159\) 6.79479 11.7689i 0.538862 0.933336i
\(160\) 0.446450 + 2.19105i 0.0352949 + 0.173217i
\(161\) −0.00380418 + 0.00177392i −0.000299811 + 0.000139804i
\(162\) 2.75527 + 4.77226i 0.216474 + 0.374944i
\(163\) 4.19715 5.00197i 0.328746 0.391785i −0.576201 0.817308i \(-0.695465\pi\)
0.904947 + 0.425523i \(0.139910\pi\)
\(164\) −5.94342 + 7.08309i −0.464103 + 0.553097i
\(165\) 2.53957 + 0.154571i 0.197705 + 0.0120334i
\(166\) 9.42272 13.4570i 0.731345 1.04447i
\(167\) −6.62705 + 1.16853i −0.512816 + 0.0904233i −0.424067 0.905631i \(-0.639398\pi\)
−0.0887489 + 0.996054i \(0.528287\pi\)
\(168\) −0.313890 0.862407i −0.0242172 0.0665361i
\(169\) −8.89973 7.46776i −0.684594 0.574443i
\(170\) −1.77564 + 5.31206i −0.136185 + 0.407417i
\(171\) 33.0091 + 8.84477i 2.52427 + 0.676376i
\(172\) 9.25691 + 3.36924i 0.705833 + 0.256902i
\(173\) 6.90376 + 9.85959i 0.524883 + 0.749611i 0.990817 0.135209i \(-0.0431705\pi\)
−0.465934 + 0.884819i \(0.654282\pi\)
\(174\) 14.4105 + 8.31990i 1.09246 + 0.630730i
\(175\) 1.38165 0.735686i 0.104443 0.0556127i
\(176\) −0.132750 0.364726i −0.0100064 0.0274923i
\(177\) 14.0423 24.3219i 1.05548 1.82815i
\(178\) −1.18152 + 13.5048i −0.0885585 + 1.01223i
\(179\) −4.02933 + 4.02933i −0.301166 + 0.301166i −0.841470 0.540304i \(-0.818309\pi\)
0.540304 + 0.841470i \(0.318309\pi\)
\(180\) 10.9944 + 5.96527i 0.819477 + 0.444625i
\(181\) −2.12208 0.772374i −0.157733 0.0574101i 0.261947 0.965082i \(-0.415635\pi\)
−0.419680 + 0.907672i \(0.637858\pi\)
\(182\) 0.301498 + 0.211111i 0.0223485 + 0.0156486i
\(183\) 2.88044 16.3358i 0.212928 1.20757i
\(184\) −0.0134077 −0.000988432
\(185\) 13.5956 + 0.398621i 0.999570 + 0.0293072i
\(186\) −6.77021 −0.496416
\(187\) 0.168822 0.957439i 0.0123455 0.0700149i
\(188\) −3.39123 2.37457i −0.247331 0.173183i
\(189\) −2.23705 0.814220i −0.162722 0.0592258i
\(190\) 13.0965 3.88357i 0.950118 0.281744i
\(191\) 14.0913 14.0913i 1.01961 1.01961i 0.0198100 0.999804i \(-0.493694\pi\)
0.999804 0.0198100i \(-0.00630615\pi\)
\(192\) 0.255501 2.92039i 0.0184392 0.210761i
\(193\) −1.73772 + 3.00982i −0.125084 + 0.216652i −0.921766 0.387747i \(-0.873253\pi\)
0.796682 + 0.604399i \(0.206587\pi\)
\(194\) −2.87247 7.89205i −0.206231 0.566616i
\(195\) −7.65696 + 0.874699i −0.548326 + 0.0626385i
\(196\) −5.97730 3.45100i −0.426950 0.246500i
\(197\) 9.25092 + 13.2117i 0.659101 + 0.941293i 0.999999 + 0.00119328i \(0.000379834\pi\)
−0.340899 + 0.940100i \(0.610731\pi\)
\(198\) −2.04027 0.742596i −0.144995 0.0527740i
\(199\) 7.33397 + 1.96513i 0.519892 + 0.139305i 0.509216 0.860638i \(-0.329935\pi\)
0.0106751 + 0.999943i \(0.496602\pi\)
\(200\) 4.99299 0.264639i 0.353058 0.0187128i
\(201\) 29.6337 + 24.8657i 2.09020 + 1.75389i
\(202\) 6.71657 + 18.4536i 0.472576 + 1.29839i
\(203\) −1.74998 + 0.308568i −0.122824 + 0.0216573i
\(204\) 4.21179 6.01506i 0.294884 0.421138i
\(205\) 13.7045 + 15.4809i 0.957166 + 1.08123i
\(206\) −1.17087 + 1.39539i −0.0815782 + 0.0972212i
\(207\) −0.0482106 + 0.0574552i −0.00335087 + 0.00399341i
\(208\) 0.587841 + 1.01817i 0.0407595 + 0.0705975i
\(209\) −2.14896 + 1.00207i −0.148646 + 0.0693150i
\(210\) −2.01084 + 0.409731i −0.138761 + 0.0282741i
\(211\) 10.5615 18.2931i 0.727084 1.25935i −0.231026 0.972948i \(-0.574208\pi\)
0.958110 0.286399i \(-0.0924584\pi\)
\(212\) −1.19979 + 4.47768i −0.0824020 + 0.307528i
\(213\) 0.0362243 0.0776833i 0.00248205 0.00532278i
\(214\) 2.25918 + 8.43139i 0.154435 + 0.576358i
\(215\) 10.5049 19.3613i 0.716427 1.32043i
\(216\) −5.37707 5.37707i −0.365863 0.365863i
\(217\) 0.553846 0.464732i 0.0375975 0.0315480i
\(218\) 8.03481 + 17.2307i 0.544186 + 1.16701i
\(219\) −7.49122 + 1.32090i −0.506210 + 0.0892585i
\(220\) −0.850419 + 0.173282i −0.0573352 + 0.0116827i
\(221\) 2.94489i 0.198095i
\(222\) −16.9402 5.56846i −1.13695 0.373731i
\(223\) −2.62290 2.62290i −0.175643 0.175643i 0.613811 0.789453i \(-0.289636\pi\)
−0.789453 + 0.613811i \(0.789636\pi\)
\(224\) 0.179565 + 0.256445i 0.0119977 + 0.0171345i
\(225\) 16.8194 22.3477i 1.12129 1.48984i
\(226\) 1.33749 3.67471i 0.0889682 0.244438i
\(227\) 2.76287 + 3.29266i 0.183378 + 0.218541i 0.849900 0.526944i \(-0.176662\pi\)
−0.666522 + 0.745485i \(0.732218\pi\)
\(228\) −17.9088 −1.18604
\(229\) −6.48887 7.73314i −0.428797 0.511020i 0.507778 0.861488i \(-0.330467\pi\)
−0.936575 + 0.350468i \(0.886023\pi\)
\(230\) −0.00442263 + 0.0296526i −0.000291620 + 0.00195524i
\(231\) 0.334729 0.121831i 0.0220236 0.00801592i
\(232\) −5.48271 1.46909i −0.359958 0.0964503i
\(233\) −5.39873 20.1483i −0.353682 1.31996i −0.882135 0.470997i \(-0.843894\pi\)
0.528452 0.848963i \(-0.322773\pi\)
\(234\) 6.47681 + 1.14204i 0.423402 + 0.0746573i
\(235\) −6.37022 + 6.71680i −0.415547 + 0.438156i
\(236\) −2.47952 + 9.25368i −0.161403 + 0.602363i
\(237\) −26.0260 21.8384i −1.69057 1.41856i
\(238\) 0.0683446 + 0.781183i 0.00443012 + 0.0506365i
\(239\) 4.32466 + 2.01662i 0.279739 + 0.130444i 0.557425 0.830228i \(-0.311790\pi\)
−0.277686 + 0.960672i \(0.589567\pi\)
\(240\) −6.37447 1.52838i −0.411470 0.0986563i
\(241\) −10.4356 7.30711i −0.672219 0.470692i 0.186961 0.982367i \(-0.440136\pi\)
−0.859179 + 0.511675i \(0.829025\pi\)
\(242\) −10.1951 + 3.71070i −0.655363 + 0.238533i
\(243\) 6.63325 0.580334i 0.425523 0.0372285i
\(244\) 0.493159 + 5.63684i 0.0315713 + 0.360861i
\(245\) −9.60389 + 12.0811i −0.613570 + 0.771833i
\(246\) −11.4555 24.5664i −0.730376 1.56630i
\(247\) 5.88336 4.11957i 0.374349 0.262122i
\(248\) 2.23074 0.597725i 0.141652 0.0379556i
\(249\) 24.0797 + 41.7073i 1.52599 + 2.64309i
\(250\) 1.06169 11.1298i 0.0671474 0.703911i
\(251\) −20.6988 + 5.54623i −1.30650 + 0.350075i −0.843903 0.536495i \(-0.819748\pi\)
−0.462594 + 0.886570i \(0.653081\pi\)
\(252\) 1.74459 + 0.152632i 0.109899 + 0.00961491i
\(253\) 0.00520400i 0.000327172i
\(254\) −0.321794 + 3.67812i −0.0201911 + 0.230786i
\(255\) −11.9136 11.2989i −0.746061 0.707566i
\(256\) 0.173648 + 0.984808i 0.0108530 + 0.0615505i
\(257\) −5.36755 0.946444i −0.334819 0.0590375i 0.00371156 0.999993i \(-0.498819\pi\)
−0.338530 + 0.940956i \(0.609930\pi\)
\(258\) −20.4203 + 20.4203i −1.27131 + 1.27131i
\(259\) 1.76805 0.707299i 0.109861 0.0439494i
\(260\) 2.44570 0.964222i 0.151676 0.0597985i
\(261\) −26.0097 + 18.2122i −1.60996 + 1.12731i
\(262\) 3.68123 5.25735i 0.227427 0.324800i
\(263\) 10.6815 4.98087i 0.658649 0.307133i −0.0644055 0.997924i \(-0.520515\pi\)
0.723055 + 0.690791i \(0.242737\pi\)
\(264\) 1.13350 + 0.0991686i 0.0697622 + 0.00610340i
\(265\) 9.50710 + 4.13045i 0.584016 + 0.253732i
\(266\) 1.46506 1.22933i 0.0898284 0.0753749i
\(267\) −34.4169 19.8706i −2.10628 1.21606i
\(268\) −11.9595 5.57679i −0.730540 0.340656i
\(269\) −27.8195 + 16.0616i −1.69618 + 0.979292i −0.746865 + 0.664976i \(0.768442\pi\)
−0.949318 + 0.314316i \(0.898225\pi\)
\(270\) −13.6656 + 10.1183i −0.831662 + 0.615779i
\(271\) −2.74395 + 15.5617i −0.166683 + 0.945306i 0.780629 + 0.624994i \(0.214899\pi\)
−0.947312 + 0.320312i \(0.896212\pi\)
\(272\) −0.856703 + 2.35377i −0.0519452 + 0.142718i
\(273\) −0.934431 + 0.539494i −0.0565543 + 0.0326517i
\(274\) 20.8749 1.82631i 1.26110 0.110332i
\(275\) 0.102715 + 1.93795i 0.00619396 + 0.116863i
\(276\) 0.0166112 0.0356228i 0.000999876 0.00214424i
\(277\) −2.59339 14.7078i −0.155822 0.883709i −0.958031 0.286665i \(-0.907453\pi\)
0.802209 0.597043i \(-0.203658\pi\)
\(278\) −0.906096 5.13873i −0.0543440 0.308200i
\(279\) 5.45975 11.7085i 0.326867 0.700968i
\(280\) 0.626386 0.312536i 0.0374337 0.0186776i
\(281\) −14.2475 + 1.24649i −0.849934 + 0.0743596i −0.503795 0.863823i \(-0.668063\pi\)
−0.346140 + 0.938183i \(0.612508\pi\)
\(282\) 10.5104 6.06820i 0.625887 0.361356i
\(283\) −8.12456 + 22.3220i −0.482955 + 1.32691i 0.423993 + 0.905665i \(0.360628\pi\)
−0.906948 + 0.421242i \(0.861594\pi\)
\(284\) −0.00507722 + 0.0287943i −0.000301277 + 0.00170863i
\(285\) −5.90735 + 39.6073i −0.349921 + 2.34613i
\(286\) −0.395187 + 0.228161i −0.0233679 + 0.0134914i
\(287\) 2.62346 + 1.22334i 0.154858 + 0.0722114i
\(288\) 4.84451 + 2.79698i 0.285466 + 0.164814i
\(289\) 8.21645 6.89442i 0.483321 0.405554i
\(290\) −5.05755 + 11.6410i −0.296990 + 0.683583i
\(291\) 24.5270 + 2.14584i 1.43780 + 0.125791i
\(292\) 2.35169 1.09661i 0.137622 0.0641743i
\(293\) 0.601744 0.859379i 0.0351543 0.0502055i −0.801190 0.598410i \(-0.795799\pi\)
0.836344 + 0.548204i \(0.184688\pi\)
\(294\) 16.5743 11.6055i 0.966634 0.676844i
\(295\) 19.6476 + 8.53609i 1.14393 + 0.496991i
\(296\) 6.07330 + 0.339167i 0.353003 + 0.0197137i
\(297\) 2.08702 2.08702i 0.121101 0.121101i
\(298\) 19.8530 + 3.50061i 1.15005 + 0.202785i
\(299\) 0.00273726 + 0.0155238i 0.000158300 + 0.000897763i
\(300\) −5.48283 + 13.5937i −0.316551 + 0.784831i
\(301\) 0.268786 3.07223i 0.0154926 0.177081i
\(302\) 6.98927i 0.402187i
\(303\) −57.3505 5.01752i −3.29470 0.288249i
\(304\) 5.90085 1.58113i 0.338437 0.0906839i
\(305\) 12.6291 + 0.768674i 0.723142 + 0.0440141i
\(306\) 7.00597 + 12.1347i 0.400505 + 0.693694i
\(307\) 12.6578 3.39165i 0.722418 0.193571i 0.121168 0.992632i \(-0.461336\pi\)
0.601250 + 0.799061i \(0.294669\pi\)
\(308\) −0.0995349 + 0.0696951i −0.00567153 + 0.00397125i
\(309\) −2.25676 4.83964i −0.128383 0.275317i
\(310\) −0.586107 5.13068i −0.0332886 0.291403i
\(311\) −1.16219 13.2839i −0.0659019 0.753262i −0.955205 0.295944i \(-0.904366\pi\)
0.889303 0.457318i \(-0.151190\pi\)
\(312\) −3.43345 + 0.300388i −0.194381 + 0.0170061i
\(313\) −32.7610 + 11.9240i −1.85176 + 0.673987i −0.867460 + 0.497508i \(0.834249\pi\)
−0.984304 + 0.176479i \(0.943529\pi\)
\(314\) −4.56560 3.19687i −0.257652 0.180410i
\(315\) 0.913026 3.80800i 0.0514432 0.214556i
\(316\) 10.5035 + 4.89785i 0.590866 + 0.275525i
\(317\) −1.77993 20.3447i −0.0999708 1.14267i −0.866061 0.499939i \(-0.833356\pi\)
0.766090 0.642733i \(-0.222200\pi\)
\(318\) −10.4102 8.73521i −0.583776 0.489846i
\(319\) 0.570202 2.12802i 0.0319252 0.119146i
\(320\) 2.23528 0.0591958i 0.124956 0.00330915i
\(321\) −25.2002 4.44347i −1.40654 0.248010i
\(322\) 0.00108638 + 0.00405442i 6.05416e−5 + 0.000225944i
\(323\) 14.7806 + 3.96046i 0.822416 + 0.220366i
\(324\) 5.17821 1.88471i 0.287678 0.104706i
\(325\) −1.32575 5.72697i −0.0735394 0.317675i
\(326\) −4.19715 5.00197i −0.232459 0.277034i
\(327\) −55.7345 −3.08213
\(328\) 5.94342 + 7.08309i 0.328171 + 0.391098i
\(329\) −0.443276 + 1.21789i −0.0244386 + 0.0671445i
\(330\) 0.593215 2.47415i 0.0326554 0.136197i
\(331\) 13.7145 + 19.5863i 0.753815 + 1.07656i 0.994374 + 0.105925i \(0.0337803\pi\)
−0.240559 + 0.970634i \(0.577331\pi\)
\(332\) −11.6164 11.6164i −0.637530 0.637530i
\(333\) 23.2914 24.8059i 1.27636 1.35935i
\(334\) 6.72928i 0.368210i
\(335\) −16.2786 + 24.6101i −0.889392 + 1.34459i
\(336\) −0.903812 + 0.159366i −0.0493070 + 0.00869415i
\(337\) −8.19542 17.5751i −0.446433 0.957379i −0.992795 0.119829i \(-0.961765\pi\)
0.546361 0.837549i \(-0.316012\pi\)
\(338\) −8.89973 + 7.46776i −0.484081 + 0.406193i
\(339\) 8.10624 + 8.10624i 0.440270 + 0.440270i
\(340\) 4.92302 + 2.67110i 0.266988 + 0.144860i
\(341\) 0.231997 + 0.865825i 0.0125634 + 0.0468871i
\(342\) 14.4424 30.9718i 0.780954 1.67476i
\(343\) −1.12643 + 4.20388i −0.0608213 + 0.226988i
\(344\) 4.92550 8.53122i 0.265565 0.459972i
\(345\) −0.0733043 0.0484878i −0.00394657 0.00261050i
\(346\) 10.9086 5.08677i 0.586451 0.273467i
\(347\) 14.5642 + 25.2259i 0.781846 + 1.35420i 0.930865 + 0.365363i \(0.119055\pi\)
−0.149019 + 0.988834i \(0.547612\pi\)
\(348\) 10.6959 12.7468i 0.573358 0.683302i
\(349\) 3.60664 4.29823i 0.193059 0.230079i −0.660828 0.750538i \(-0.729795\pi\)
0.853887 + 0.520459i \(0.174239\pi\)
\(350\) −0.484589 1.48841i −0.0259024 0.0795588i
\(351\) −5.12793 + 7.32344i −0.273709 + 0.390896i
\(352\) −0.382237 + 0.0673987i −0.0203733 + 0.00359236i
\(353\) −0.524853 1.44202i −0.0279351 0.0767510i 0.924941 0.380110i \(-0.124114\pi\)
−0.952876 + 0.303359i \(0.901892\pi\)
\(354\) −21.5140 18.0524i −1.14346 0.959474i
\(355\) 0.0620069 + 0.0207268i 0.00329099 + 0.00110006i
\(356\) 13.0945 + 3.50865i 0.694006 + 0.185958i
\(357\) −2.16018 0.786243i −0.114329 0.0416124i
\(358\) 3.26843 + 4.66780i 0.172742 + 0.246701i
\(359\) −18.7642 10.8335i −0.990338 0.571772i −0.0849628 0.996384i \(-0.527077\pi\)
−0.905375 + 0.424612i \(0.860410\pi\)
\(360\) 7.78381 9.79155i 0.410243 0.516060i
\(361\) −6.26580 17.2151i −0.329779 0.906060i
\(362\) −1.12914 + 1.95572i −0.0593460 + 0.102790i
\(363\) 2.77202 31.6843i 0.145493 1.66300i
\(364\) 0.260259 0.260259i 0.0136413 0.0136413i
\(365\) −1.64955 5.56273i −0.0863414 0.291167i
\(366\) −15.5874 5.67335i −0.814767 0.296551i
\(367\) 28.8773 + 20.2201i 1.50738 + 1.05548i 0.978369 + 0.206869i \(0.0663273\pi\)
0.529015 + 0.848613i \(0.322562\pi\)
\(368\) −0.00232823 + 0.0132041i −0.000121367 + 0.000688309i
\(369\) 51.7236 2.69262
\(370\) 2.75342 13.3199i 0.143144 0.692467i
\(371\) 1.45124 0.0753446
\(372\) −1.17563 + 6.66735i −0.0609538 + 0.345686i
\(373\) 0.564989 + 0.395610i 0.0292540 + 0.0204839i 0.588112 0.808779i \(-0.299871\pi\)
−0.558858 + 0.829263i \(0.688760\pi\)
\(374\) −0.913578 0.332515i −0.0472400 0.0171940i
\(375\) 28.2553 + 16.6098i 1.45910 + 0.857727i
\(376\) −2.92737 + 2.92737i −0.150968 + 0.150968i
\(377\) −0.581618 + 6.64792i −0.0299548 + 0.342385i
\(378\) −1.19031 + 2.06168i −0.0612230 + 0.106041i
\(379\) 4.33956 + 11.9229i 0.222908 + 0.612436i 0.999853 0.0171329i \(-0.00545383\pi\)
−0.776945 + 0.629569i \(0.783232\pi\)
\(380\) −1.55040 13.5719i −0.0795336 0.696223i
\(381\) −9.37365 5.41188i −0.480227 0.277259i
\(382\) −11.4303 16.3242i −0.584826 0.835219i
\(383\) −13.3364 4.85405i −0.681458 0.248030i −0.0219844 0.999758i \(-0.506998\pi\)
−0.659473 + 0.751728i \(0.729221\pi\)
\(384\) −2.83166 0.758740i −0.144502 0.0387193i
\(385\) 0.121306 + 0.243121i 0.00618231 + 0.0123906i
\(386\) 2.66235 + 2.23397i 0.135510 + 0.113706i
\(387\) −18.8474 51.7828i −0.958068 2.63227i
\(388\) −8.27095 + 1.45839i −0.419894 + 0.0740386i
\(389\) 10.7789 15.3939i 0.546511 0.780499i −0.446963 0.894552i \(-0.647495\pi\)
0.993475 + 0.114053i \(0.0363834\pi\)
\(390\) −0.468207 + 7.69253i −0.0237086 + 0.389526i
\(391\) −0.0215875 + 0.0257269i −0.00109173 + 0.00130107i
\(392\) −4.43652 + 5.28723i −0.224078 + 0.267046i
\(393\) 9.40738 + 16.2941i 0.474540 + 0.821927i
\(394\) 14.6174 6.81619i 0.736413 0.343395i
\(395\) 14.2967 21.6139i 0.719347 1.08751i
\(396\) −1.08560 + 1.88032i −0.0545536 + 0.0944896i
\(397\) −6.29374 + 23.4886i −0.315874 + 1.17886i 0.607299 + 0.794473i \(0.292253\pi\)
−0.923173 + 0.384384i \(0.874414\pi\)
\(398\) 3.20881 6.88131i 0.160843 0.344929i
\(399\) 1.45109 + 5.41553i 0.0726452 + 0.271116i
\(400\) 0.606405 4.96309i 0.0303203 0.248155i
\(401\) −5.78637 5.78637i −0.288957 0.288957i 0.547711 0.836668i \(-0.315500\pi\)
−0.836668 + 0.547711i \(0.815500\pi\)
\(402\) 29.6337 24.8657i 1.47800 1.24019i
\(403\) −1.14748 2.46077i −0.0571599 0.122580i
\(404\) 19.3396 3.41009i 0.962181 0.169658i
\(405\) −2.46017 12.0738i −0.122247 0.599953i
\(406\) 1.77697i 0.0881898i
\(407\) −0.131642 + 2.35725i −0.00652526 + 0.116845i
\(408\) −5.19231 5.19231i −0.257057 0.257057i
\(409\) 11.1168 + 15.8764i 0.549690 + 0.785039i 0.993829 0.110919i \(-0.0353794\pi\)
−0.444139 + 0.895958i \(0.646490\pi\)
\(410\) 17.6255 10.8081i 0.870460 0.533774i
\(411\) −21.0101 + 57.7248i −1.03635 + 2.84735i
\(412\) 1.17087 + 1.39539i 0.0576845 + 0.0687457i
\(413\) 2.99916 0.147579
\(414\) 0.0482106 + 0.0574552i 0.00236942 + 0.00282377i
\(415\) −29.5225 + 21.8590i −1.44920 + 1.07302i
\(416\) 1.10478 0.402107i 0.0541663 0.0197149i
\(417\) 14.7756 + 3.95910i 0.723563 + 0.193878i
\(418\) 0.613689 + 2.29032i 0.0300165 + 0.112023i
\(419\) −10.4583 1.84409i −0.510923 0.0900895i −0.0877573 0.996142i \(-0.527970\pi\)
−0.423165 + 0.906052i \(0.639081\pi\)
\(420\) 0.0543272 + 2.05144i 0.00265090 + 0.100100i
\(421\) 4.45633 16.6313i 0.217188 0.810558i −0.768196 0.640214i \(-0.778845\pi\)
0.985385 0.170344i \(-0.0544878\pi\)
\(422\) −16.1812 13.5776i −0.787687 0.660948i
\(423\) 2.01841 + 23.0705i 0.0981383 + 1.12173i
\(424\) 4.20131 + 1.95910i 0.204034 + 0.0951425i
\(425\) 7.53130 10.0067i 0.365322 0.485396i
\(426\) −0.0702129 0.0491636i −0.00340182 0.00238198i
\(427\) 1.66459 0.605860i 0.0805551 0.0293196i
\(428\) 8.69560 0.760767i 0.420318 0.0367730i
\(429\) −0.116591 1.33264i −0.00562906 0.0643404i
\(430\) −17.2430 13.7073i −0.831530 0.661027i
\(431\) −11.6799 25.0476i −0.562601 1.20650i −0.957675 0.287853i \(-0.907059\pi\)
0.395074 0.918649i \(-0.370719\pi\)
\(432\) −6.22910 + 4.36166i −0.299697 + 0.209850i
\(433\) −29.4483 + 7.89066i −1.41520 + 0.379201i −0.883777 0.467908i \(-0.845008\pi\)
−0.531420 + 0.847109i \(0.678341\pi\)
\(434\) −0.361497 0.626131i −0.0173524 0.0300553i
\(435\) −24.6628 27.8596i −1.18249 1.33577i
\(436\) 18.3642 4.92066i 0.879484 0.235657i
\(437\) 0.0815963 + 0.00713875i 0.00390328 + 0.000341493i
\(438\) 7.60679i 0.363466i
\(439\) 2.92342 33.4148i 0.139527 1.59480i −0.527359 0.849643i \(-0.676818\pi\)
0.666886 0.745160i \(-0.267627\pi\)
\(440\) 0.0229759 + 0.867589i 0.00109533 + 0.0413607i
\(441\) 6.70447 + 38.0229i 0.319260 + 1.81062i
\(442\) 2.90015 + 0.511374i 0.137946 + 0.0243236i
\(443\) −8.71645 + 8.71645i −0.414131 + 0.414131i −0.883175 0.469044i \(-0.844599\pi\)
0.469044 + 0.883175i \(0.344599\pi\)
\(444\) −8.42549 + 15.7158i −0.399856 + 0.745841i
\(445\) 12.0790 27.8024i 0.572602 1.31796i
\(446\) −3.03852 + 2.12759i −0.143878 + 0.100745i
\(447\) −33.8971 + 48.4100i −1.60328 + 2.28972i
\(448\) 0.283730 0.132306i 0.0134050 0.00625085i
\(449\) 19.6067 + 1.71536i 0.925297 + 0.0809530i 0.539835 0.841771i \(-0.318487\pi\)
0.385462 + 0.922724i \(0.374042\pi\)
\(450\) −19.0875 20.4445i −0.899793 0.963764i
\(451\) −2.74919 + 2.30684i −0.129454 + 0.108625i
\(452\) −3.38663 1.95527i −0.159294 0.0919683i
\(453\) 18.5697 + 8.65918i 0.872479 + 0.406844i
\(454\) 3.72240 2.14913i 0.174701 0.100864i
\(455\) −0.489741 0.661437i −0.0229594 0.0310086i
\(456\) −3.10984 + 17.6368i −0.145631 + 0.825917i
\(457\) −1.18190 + 3.24723i −0.0552868 + 0.151899i −0.964262 0.264952i \(-0.914644\pi\)
0.908975 + 0.416851i \(0.136866\pi\)
\(458\) −8.74243 + 5.04745i −0.408507 + 0.235852i
\(459\) −18.9751 + 1.66010i −0.885680 + 0.0774870i
\(460\) 0.0284342 + 0.00950457i 0.00132575 + 0.000443153i
\(461\) −7.96715 + 17.0856i −0.371067 + 0.795756i 0.628768 + 0.777593i \(0.283560\pi\)
−0.999835 + 0.0181630i \(0.994218\pi\)
\(462\) −0.0618555 0.350800i −0.00287778 0.0163207i
\(463\) 3.73116 + 21.1604i 0.173402 + 0.983409i 0.939973 + 0.341250i \(0.110850\pi\)
−0.766571 + 0.642159i \(0.778039\pi\)
\(464\) −2.39883 + 5.14431i −0.111363 + 0.238819i
\(465\) 14.3578 + 4.79931i 0.665825 + 0.222563i
\(466\) −20.7797 + 1.81799i −0.962601 + 0.0842167i
\(467\) 14.0856 8.13232i 0.651804 0.376319i −0.137343 0.990524i \(-0.543856\pi\)
0.789147 + 0.614204i \(0.210523\pi\)
\(468\) 2.24937 6.18010i 0.103977 0.285675i
\(469\) −0.717358 + 4.06834i −0.0331245 + 0.187858i
\(470\) 5.50858 + 7.43980i 0.254092 + 0.343173i
\(471\) 14.1501 8.16958i 0.652004 0.376435i
\(472\) 8.68253 + 4.04873i 0.399646 + 0.186358i
\(473\) 3.31125 + 1.91175i 0.152252 + 0.0879025i
\(474\) −26.0260 + 21.8384i −1.19541 + 1.00307i
\(475\) −30.5271 1.04791i −1.40068 0.0480816i
\(476\) 0.781183 + 0.0683446i 0.0358054 + 0.00313257i
\(477\) 23.5020 10.9592i 1.07608 0.501785i
\(478\) 2.73695 3.90878i 0.125185 0.178783i
\(479\) −17.5752 + 12.3063i −0.803031 + 0.562288i −0.901463 0.432856i \(-0.857506\pi\)
0.0984325 + 0.995144i \(0.468617\pi\)
\(480\) −2.61207 + 6.01223i −0.119224 + 0.274419i
\(481\) −0.847201 7.10104i −0.0386290 0.323780i
\(482\) −9.00823 + 9.00823i −0.410314 + 0.410314i
\(483\) −0.0121181 0.00213674i −0.000551392 9.72252e-5i
\(484\) 1.88397 + 10.6845i 0.0856350 + 0.485660i
\(485\) 0.497159 + 18.7731i 0.0225748 + 0.852444i
\(486\) 0.580334 6.63325i 0.0263245 0.300890i
\(487\) 8.94574i 0.405370i −0.979244 0.202685i \(-0.935033\pi\)
0.979244 0.202685i \(-0.0649667\pi\)
\(488\) 5.63684 + 0.493159i 0.255168 + 0.0223243i
\(489\) 18.4896 4.95428i 0.836129 0.224040i
\(490\) 10.2299 + 11.5558i 0.462138 + 0.522040i
\(491\) 0.779741 + 1.35055i 0.0351892 + 0.0609495i 0.883084 0.469216i \(-0.155463\pi\)
−0.847894 + 0.530165i \(0.822130\pi\)
\(492\) −26.1824 + 7.01555i −1.18039 + 0.316286i
\(493\) −11.6465 + 8.15495i −0.524531 + 0.367281i
\(494\) −3.03535 6.50933i −0.136567 0.292869i
\(495\) 3.80043 + 3.02116i 0.170817 + 0.135791i
\(496\) −0.201280 2.30064i −0.00903775 0.103302i
\(497\) 0.00911863 0.000797777i 0.000409026 3.57852e-5i
\(498\) 45.2551 16.4715i 2.02793 0.738106i
\(499\) 10.3500 + 7.24715i 0.463330 + 0.324427i 0.781826 0.623497i \(-0.214289\pi\)
−0.318496 + 0.947924i \(0.603178\pi\)
\(500\) −10.7764 2.97824i −0.481934 0.133191i
\(501\) −17.8789 8.33707i −0.798771 0.372473i
\(502\) 1.86766 + 21.3474i 0.0833577 + 0.952783i
\(503\) −16.5761 13.9090i −0.739094 0.620173i 0.193500 0.981100i \(-0.438016\pi\)
−0.932594 + 0.360927i \(0.882460\pi\)
\(504\) 0.453258 1.69158i 0.0201897 0.0753491i
\(505\) −1.16248 43.8964i −0.0517299 1.95336i
\(506\) −0.00512494 0.000903665i −0.000227831 4.01728e-5i
\(507\) −8.81487 32.8975i −0.391482 1.46103i
\(508\) 3.56636 + 0.955603i 0.158232 + 0.0423980i
\(509\) −11.3975 + 4.14836i −0.505187 + 0.183873i −0.582025 0.813171i \(-0.697740\pi\)
0.0768386 + 0.997044i \(0.475517\pi\)
\(510\) −13.1960 + 9.77061i −0.584331 + 0.432650i
\(511\) −0.522158 0.622283i −0.0230989 0.0275282i
\(512\) 1.00000 0.0441942
\(513\) 29.8606 + 35.5865i 1.31838 + 1.57118i
\(514\) −1.86413 + 5.12166i −0.0822233 + 0.225907i
\(515\) 3.47226 2.12922i 0.153006 0.0938246i
\(516\) 16.5641 + 23.6560i 0.729195 + 1.04140i
\(517\) −1.13621 1.13621i −0.0499705 0.0499705i
\(518\) −0.389535 1.86401i −0.0171152 0.0819000i
\(519\) 35.2851i 1.54884i
\(520\) −0.524883 2.57598i −0.0230176 0.112964i
\(521\) −34.5118 + 6.08536i −1.51199 + 0.266604i −0.867279 0.497823i \(-0.834133\pi\)
−0.644710 + 0.764427i \(0.723022\pi\)
\(522\) 13.4190 + 28.7771i 0.587333 + 1.25954i
\(523\) −14.9576 + 12.5509i −0.654050 + 0.548813i −0.908297 0.418326i \(-0.862617\pi\)
0.254247 + 0.967139i \(0.418172\pi\)
\(524\) −4.53823 4.53823i −0.198254 0.198254i
\(525\) 4.55490 + 0.556531i 0.198792 + 0.0242890i
\(526\) −3.05037 11.3841i −0.133003 0.496372i
\(527\) 2.44474 5.24275i 0.106494 0.228378i
\(528\) 0.294492 1.09906i 0.0128161 0.0478305i
\(529\) 11.4999 19.9184i 0.499996 0.866019i
\(530\) 5.71859 8.64542i 0.248400 0.375533i
\(531\) 48.5698 22.6484i 2.10775 0.982859i
\(532\) −0.956248 1.65627i −0.0414586 0.0718084i
\(533\) 6.98758 8.32747i 0.302666 0.360703i
\(534\) −25.5451 + 30.4435i −1.10545 + 1.31742i
\(535\) 1.18579 19.4822i 0.0512660 0.842288i
\(536\) −7.56880 + 10.8094i −0.326922 + 0.466894i
\(537\) −16.4511 + 2.90078i −0.709919 + 0.125178i
\(538\) 10.9868 + 30.1859i 0.473673 + 1.30141i
\(539\) −2.05215 1.72196i −0.0883925 0.0741701i
\(540\) 7.59156 + 15.2150i 0.326689 + 0.654750i
\(541\) −9.60490 2.57362i −0.412947 0.110649i 0.0463635 0.998925i \(-0.485237\pi\)
−0.459310 + 0.888276i \(0.651903\pi\)
\(542\) 14.8488 + 5.40452i 0.637811 + 0.232144i
\(543\) −3.79721 5.42297i −0.162954 0.232722i
\(544\) 2.16925 + 1.25242i 0.0930057 + 0.0536969i
\(545\) −4.82502 42.2374i −0.206681 1.80925i
\(546\) 0.369036 + 1.01392i 0.0157933 + 0.0433917i
\(547\) −8.96809 + 15.5332i −0.383448 + 0.664151i −0.991553 0.129706i \(-0.958597\pi\)
0.608105 + 0.793857i \(0.291930\pi\)
\(548\) 1.82631 20.8749i 0.0780163 0.891730i
\(549\) 22.3818 22.3818i 0.955234 0.955234i
\(550\) 1.92634 + 0.235366i 0.0821395 + 0.0100361i
\(551\) 32.5843 + 11.8597i 1.38814 + 0.505240i
\(552\) −0.0321971 0.0225447i −0.00137040 0.000959565i
\(553\) 0.630024 3.57304i 0.0267913 0.151941i
\(554\) −14.9347 −0.634516
\(555\) 31.9780 + 23.8178i 1.35739 + 1.01101i
\(556\) −5.21800 −0.221292
\(557\) 6.21244 35.2325i 0.263229 1.49285i −0.510800 0.859699i \(-0.670651\pi\)
0.774030 0.633149i \(-0.218238\pi\)
\(558\) −10.5825 7.40996i −0.447994 0.313689i
\(559\) −10.8832 3.96116i −0.460310 0.167539i
\(560\) −0.199017 0.671141i −0.00841001 0.0283609i
\(561\) 2.01531 2.01531i 0.0850864 0.0850864i
\(562\) −1.24649 + 14.2475i −0.0525802 + 0.600994i
\(563\) 8.19926 14.2015i 0.345558 0.598523i −0.639897 0.768460i \(-0.721023\pi\)
0.985455 + 0.169937i \(0.0543565\pi\)
\(564\) −4.15089 11.4045i −0.174784 0.480215i
\(565\) −5.44140 + 6.84493i −0.228921 + 0.287969i
\(566\) 20.5721 + 11.8773i 0.864710 + 0.499241i
\(567\) −0.989497 1.41315i −0.0415550 0.0593466i
\(568\) 0.0274752 + 0.0100002i 0.00115283 + 0.000419598i
\(569\) −23.4576 6.28544i −0.983392 0.263499i −0.268920 0.963163i \(-0.586667\pi\)
−0.714473 + 0.699663i \(0.753333\pi\)
\(570\) 37.9797 + 12.6953i 1.59080 + 0.531749i
\(571\) 22.8411 + 19.1660i 0.955871 + 0.802071i 0.980277 0.197631i \(-0.0633247\pi\)
−0.0244052 + 0.999702i \(0.507769\pi\)
\(572\) 0.156071 + 0.428802i 0.00652567 + 0.0179291i
\(573\) 57.5328 10.1446i 2.40347 0.423796i
\(574\) 1.66031 2.37117i 0.0693001 0.0989709i
\(575\) 0.0303995 0.0597500i 0.00126775 0.00249175i
\(576\) 3.59573 4.28522i 0.149822 0.178551i
\(577\) −8.50243 + 10.1328i −0.353961 + 0.421834i −0.913416 0.407026i \(-0.866566\pi\)
0.559456 + 0.828860i \(0.311010\pi\)
\(578\) −5.36291 9.28883i −0.223068 0.386364i
\(579\) −9.23385 + 4.30582i −0.383746 + 0.178944i
\(580\) 10.5859 + 7.00215i 0.439556 + 0.290749i
\(581\) −2.57149 + 4.45395i −0.106683 + 0.184781i
\(582\) 6.37231 23.7818i 0.264141 0.985787i
\(583\) −0.760394 + 1.63067i −0.0314923 + 0.0675355i
\(584\) −0.671585 2.50639i −0.0277904 0.103715i
\(585\) −12.9260 7.01327i −0.534423 0.289963i
\(586\) −0.741832 0.741832i −0.0306448 0.0306448i
\(587\) 23.6119 19.8127i 0.974568 0.817760i −0.00869307 0.999962i \(-0.502767\pi\)
0.983261 + 0.182203i \(0.0583227\pi\)
\(588\) −8.55105 18.3378i −0.352639 0.756238i
\(589\) −13.8940 + 2.44989i −0.572492 + 0.100946i
\(590\) 11.8182 17.8668i 0.486547 0.735565i
\(591\) 47.2814i 1.94490i
\(592\) 1.38863 5.92214i 0.0570724 0.243398i
\(593\) −14.4784 14.4784i −0.594556 0.594556i 0.344303 0.938859i \(-0.388115\pi\)
−0.938859 + 0.344303i \(0.888115\pi\)
\(594\) −1.69291 2.41772i −0.0694608 0.0992003i
\(595\) 0.408829 1.70512i 0.0167604 0.0699032i
\(596\) 6.89486 18.9435i 0.282425 0.775955i
\(597\) 14.3074 + 17.0509i 0.585562 + 0.697845i
\(598\) 0.0157633 0.000644608
\(599\) 15.4300 + 18.3888i 0.630454 + 0.751346i 0.982830 0.184512i \(-0.0590706\pi\)
−0.352376 + 0.935859i \(0.614626\pi\)
\(600\) 12.4351 + 7.76005i 0.507659 + 0.316803i
\(601\) 5.94026 2.16208i 0.242308 0.0881930i −0.218011 0.975946i \(-0.569957\pi\)
0.460320 + 0.887753i \(0.347735\pi\)
\(602\) −2.97889 0.798190i −0.121410 0.0325318i
\(603\) 19.1052 + 71.3016i 0.778024 + 2.90362i
\(604\) −6.88308 1.21367i −0.280069 0.0493837i
\(605\) 24.2514 0.642236i 0.985959 0.0261106i
\(606\) −14.9001 + 55.6079i −0.605275 + 2.25892i
\(607\) −1.30406 1.09424i −0.0529303 0.0444138i 0.615939 0.787794i \(-0.288777\pi\)
−0.668869 + 0.743380i \(0.733221\pi\)
\(608\) −0.532435 6.08576i −0.0215931 0.246810i
\(609\) −4.72121 2.20154i −0.191313 0.0892108i
\(610\) 2.95002 12.3038i 0.119443 0.498166i
\(611\) 3.98701 + 2.79174i 0.161297 + 0.112942i
\(612\) 13.1669 4.79236i 0.532241 0.193720i
\(613\) 33.6625 2.94509i 1.35962 0.118951i 0.616100 0.787668i \(-0.288712\pi\)
0.743517 + 0.668717i \(0.233156\pi\)
\(614\) −1.14212 13.0544i −0.0460920 0.526835i
\(615\) 6.87919 + 60.2193i 0.277396 + 2.42827i
\(616\) 0.0513522 + 0.110125i 0.00206904 + 0.00443707i
\(617\) 5.79408 4.05706i 0.233261 0.163331i −0.451103 0.892472i \(-0.648969\pi\)
0.684363 + 0.729141i \(0.260080\pi\)
\(618\) −5.15800 + 1.38208i −0.207485 + 0.0555954i
\(619\) −16.6182 28.7836i −0.667942 1.15691i −0.978479 0.206349i \(-0.933842\pi\)
0.310536 0.950562i \(-0.399491\pi\)
\(620\) −5.15451 0.313730i −0.207010 0.0125997i
\(621\) −0.0984827 + 0.0263884i −0.00395197 + 0.00105893i
\(622\) −13.2839 1.16219i −0.532637 0.0465997i
\(623\) 4.24399i 0.170032i
\(624\) −0.300388 + 3.43345i −0.0120252 + 0.137448i
\(625\) −10.1413 + 22.8507i −0.405654 + 0.914027i
\(626\) 6.05400 + 34.3339i 0.241966 + 1.37226i
\(627\) −6.84542 1.20703i −0.273380 0.0482042i
\(628\) −3.94111 + 3.94111i −0.157267 + 0.157267i
\(629\) 10.4293 11.1074i 0.415842 0.442883i
\(630\) −3.59160 1.56041i −0.143093 0.0621681i
\(631\) −12.2667 + 8.58925i −0.488331 + 0.341933i −0.791669 0.610950i \(-0.790788\pi\)
0.303339 + 0.952883i \(0.401899\pi\)
\(632\) 6.64734 9.49339i 0.264417 0.377627i
\(633\) 56.1214 26.1698i 2.23062 1.04016i
\(634\) −20.3447 1.77993i −0.807991 0.0706901i
\(635\) 3.28980 7.57216i 0.130552 0.300492i
\(636\) −10.4102 + 8.73521i −0.412792 + 0.346374i
\(637\) 7.02741 + 4.05728i 0.278436 + 0.160755i
\(638\) −1.99668 0.931067i −0.0790493 0.0368613i
\(639\) 0.141646 0.0817796i 0.00560345 0.00323515i
\(640\) 0.329857 2.21160i 0.0130387 0.0874213i
\(641\) 2.99988 17.0132i 0.118488 0.671979i −0.866476 0.499219i \(-0.833620\pi\)
0.984964 0.172760i \(-0.0552686\pi\)
\(642\) −8.75193 + 24.0457i −0.345411 + 0.949009i
\(643\) 4.22417 2.43883i 0.166585 0.0961779i −0.414390 0.910100i \(-0.636005\pi\)
0.580975 + 0.813922i \(0.302672\pi\)
\(644\) 0.00418148 0.000365832i 0.000164773 1.44158e-5i
\(645\) 57.7815 28.8302i 2.27515 1.13519i
\(646\) 6.46692 13.8684i 0.254438 0.545643i
\(647\) 2.63817 + 14.9618i 0.103717 + 0.588210i 0.991725 + 0.128381i \(0.0409781\pi\)
−0.888008 + 0.459829i \(0.847911\pi\)
\(648\) −0.956894 5.42681i −0.0375903 0.213185i
\(649\) −1.57145 + 3.36998i −0.0616847 + 0.132283i
\(650\) −5.87018 + 0.311132i −0.230247 + 0.0122036i
\(651\) 2.11143 0.184726i 0.0827533 0.00723998i
\(652\) −5.65481 + 3.26481i −0.221459 + 0.127860i
\(653\) −11.0554 + 30.3745i −0.432632 + 1.18865i 0.511558 + 0.859249i \(0.329068\pi\)
−0.944191 + 0.329399i \(0.893154\pi\)
\(654\) −9.67819 + 54.8878i −0.378447 + 2.14628i
\(655\) −11.5337 + 8.53981i −0.450661 + 0.333678i
\(656\) 8.00755 4.62316i 0.312642 0.180504i
\(657\) −13.1553 6.13440i −0.513236 0.239326i
\(658\) 1.12241 + 0.648027i 0.0437563 + 0.0252627i
\(659\) −27.1627 + 22.7922i −1.05811 + 0.887860i −0.993923 0.110078i \(-0.964890\pi\)
−0.0641874 + 0.997938i \(0.520446\pi\)
\(660\) −2.33355 1.01383i −0.0908332 0.0394634i
\(661\) −3.90332 0.341496i −0.151822 0.0132827i 0.0109915 0.999940i \(-0.496501\pi\)
−0.162813 + 0.986657i \(0.552057\pi\)
\(662\) 21.6702 10.1050i 0.842237 0.392741i
\(663\) −4.95173 + 7.07180i −0.192309 + 0.274646i
\(664\) −13.4570 + 9.42272i −0.522234 + 0.365672i
\(665\) −3.97844 + 1.56851i −0.154277 + 0.0608242i
\(666\) −20.3845 27.2450i −0.789885 1.05572i
\(667\) −0.0538136 + 0.0538136i −0.00208367 + 0.00208367i
\(668\) 6.62705 + 1.16853i 0.256408 + 0.0452117i
\(669\) −1.88827 10.7089i −0.0730048 0.414031i
\(670\) 21.4094 + 20.3047i 0.827118 + 0.784440i
\(671\) −0.191412 + 2.18785i −0.00738937 + 0.0844608i
\(672\) 0.917754i 0.0354031i
\(673\) −31.1298 2.72350i −1.19996 0.104983i −0.530407 0.847743i \(-0.677961\pi\)
−0.669558 + 0.742760i \(0.733516\pi\)
\(674\) −18.7313 + 5.01902i −0.721501 + 0.193326i
\(675\) 36.1537 11.7708i 1.39156 0.453056i
\(676\) 5.80888 + 10.0613i 0.223419 + 0.386972i
\(677\) −15.3623 + 4.11631i −0.590420 + 0.158203i −0.541645 0.840607i \(-0.682198\pi\)
−0.0487749 + 0.998810i \(0.515532\pi\)
\(678\) 9.39072 6.57545i 0.360648 0.252529i
\(679\) 1.11117 + 2.38292i 0.0426429 + 0.0914481i
\(680\) 3.48539 4.38440i 0.133659 0.168134i
\(681\) 1.09821 + 12.5526i 0.0420835 + 0.481016i
\(682\) 0.892957 0.0781236i 0.0341931 0.00299151i
\(683\) −17.6432 + 6.42159i −0.675098 + 0.245715i −0.656741 0.754116i \(-0.728066\pi\)
−0.0183565 + 0.999832i \(0.505843\pi\)
\(684\) −27.9933 19.6011i −1.07035 0.749469i
\(685\) −45.5645 10.9248i −1.74093 0.417415i
\(686\) 3.94441 + 1.83931i 0.150598 + 0.0702252i
\(687\) −2.57926 29.4810i −0.0984048 1.12477i
\(688\) −7.54631 6.33210i −0.287700 0.241409i
\(689\) 1.41057 5.26433i 0.0537386 0.200555i
\(690\) −0.0604803 + 0.0637708i −0.00230245 + 0.00242771i
\(691\) −41.3698 7.29461i −1.57378 0.277500i −0.682477 0.730907i \(-0.739097\pi\)
−0.891304 + 0.453407i \(0.850209\pi\)
\(692\) −3.11523 11.6262i −0.118423 0.441962i
\(693\) 0.656560 + 0.175925i 0.0249406 + 0.00668283i
\(694\) 27.3717 9.96249i 1.03902 0.378171i
\(695\) −1.72119 + 11.5402i −0.0652885 + 0.437743i
\(696\) −10.6959 12.7468i −0.405426 0.483167i
\(697\) 23.1605 0.877266
\(698\) −3.60664 4.29823i −0.136513 0.162690i
\(699\) 20.9143 57.4616i 0.791052 2.17340i
\(700\) −1.54994 + 0.218767i −0.0585824 + 0.00826863i
\(701\) 9.78480 + 13.9741i 0.369567 + 0.527796i 0.960262 0.279098i \(-0.0900356\pi\)
−0.590696 + 0.806894i \(0.701147\pi\)
\(702\) 6.32173 + 6.32173i 0.238598 + 0.238598i
\(703\) −36.7801 5.29773i −1.38719 0.199808i
\(704\) 0.388134i 0.0146283i
\(705\) −26.5914 + 5.41829i −1.00149 + 0.204065i
\(706\) −1.51125 + 0.266475i −0.0568768 + 0.0100289i
\(707\) −2.59821 5.57188i −0.0977157 0.209552i
\(708\) −21.5140 + 18.0524i −0.808546 + 0.678451i
\(709\) 16.9411 + 16.9411i 0.636235 + 0.636235i 0.949625 0.313390i \(-0.101465\pi\)
−0.313390 + 0.949625i \(0.601465\pi\)
\(710\) 0.0311793 0.0574657i 0.00117014 0.00215665i
\(711\) −16.7793 62.6210i −0.629271 2.34847i
\(712\) 5.72918 12.2863i 0.214710 0.460447i
\(713\) 0.00801414 0.0299092i 0.000300132 0.00112011i
\(714\) −1.14941 + 1.99084i −0.0430156 + 0.0745052i
\(715\) 0.999823 0.203725i 0.0373912 0.00761887i
\(716\) 5.16445 2.40822i 0.193004 0.0899994i
\(717\) 6.99428 + 12.1144i 0.261206 + 0.452422i
\(718\) −13.9273 + 16.5979i −0.519763 + 0.619429i
\(719\) 26.0148 31.0032i 0.970188 1.15622i −0.0175098 0.999847i \(-0.505574\pi\)
0.987697 0.156378i \(-0.0499817\pi\)
\(720\) −8.29115 9.36584i −0.308993 0.349044i
\(721\) 0.327086 0.467127i 0.0121813 0.0173967i
\(722\) −18.0416 + 3.18123i −0.671440 + 0.118393i
\(723\) −12.7733 35.0943i −0.475044 1.30517i
\(724\) 1.72994 + 1.45159i 0.0642926 + 0.0539479i
\(725\) 18.9778 21.1021i 0.704819 0.783714i
\(726\) −30.7216 8.23184i −1.14019 0.305512i
\(727\) 35.8270 + 13.0400i 1.32875 + 0.483625i 0.906251 0.422739i \(-0.138931\pi\)
0.422497 + 0.906364i \(0.361154\pi\)
\(728\) −0.211111 0.301498i −0.00782430 0.0111743i
\(729\) 31.2216 + 18.0258i 1.15635 + 0.667621i
\(730\) −5.76467 + 0.658531i −0.213360 + 0.0243733i
\(731\) −8.43938 23.1870i −0.312142 0.857603i
\(732\) −8.29388 + 14.3654i −0.306551 + 0.530961i
\(733\) 2.35173 26.8804i 0.0868631 0.992850i −0.820262 0.571988i \(-0.806172\pi\)
0.907125 0.420862i \(-0.138272\pi\)
\(734\) 24.9274 24.9274i 0.920088 0.920088i
\(735\) −43.3766 + 12.8627i −1.59997 + 0.474448i
\(736\) 0.0125992 + 0.00458572i 0.000464411 + 0.000169032i
\(737\) −4.19548 2.93771i −0.154542 0.108212i
\(738\) 8.98171 50.9378i 0.330621 1.87505i
\(739\) 38.3506 1.41075 0.705375 0.708835i \(-0.250779\pi\)
0.705375 + 0.708835i \(0.250779\pi\)
\(740\) −12.6394 5.02456i −0.464633 0.184706i
\(741\) 21.0551 0.773479
\(742\) 0.252005 1.42919i 0.00925140 0.0524673i
\(743\) 7.01510 + 4.91203i 0.257359 + 0.180205i 0.695135 0.718879i \(-0.255345\pi\)
−0.437776 + 0.899084i \(0.644234\pi\)
\(744\) 6.36191 + 2.31555i 0.233239 + 0.0848921i
\(745\) −39.6212 21.4973i −1.45161 0.787602i
\(746\) 0.487709 0.487709i 0.0178563 0.0178563i
\(747\) −8.00941 + 91.5479i −0.293049 + 3.34956i
\(748\) −0.486105 + 0.841958i −0.0177737 + 0.0307850i
\(749\) −0.934624 2.56786i −0.0341504 0.0938275i
\(750\) 21.2639 24.9417i 0.776449 0.910743i
\(751\) −25.3632 14.6434i −0.925515 0.534346i −0.0401246 0.999195i \(-0.512775\pi\)
−0.885390 + 0.464848i \(0.846109\pi\)
\(752\) 2.37457 + 3.39123i 0.0865915 + 0.123666i
\(753\) −59.0315 21.4857i −2.15123 0.782983i
\(754\) 6.44593 + 1.72718i 0.234747 + 0.0629002i
\(755\) −4.95460 + 14.8223i −0.180316 + 0.539440i
\(756\) 1.82366 + 1.53023i 0.0663259 + 0.0556541i
\(757\) −4.62252 12.7003i −0.168008 0.461599i 0.826904 0.562343i \(-0.190100\pi\)
−0.994912 + 0.100744i \(0.967878\pi\)
\(758\) 12.4953 2.20325i 0.453849 0.0800258i
\(759\) 0.00875034 0.0124968i 0.000317617 0.000453605i
\(760\) −13.6349 0.829892i −0.494591 0.0301033i
\(761\) 20.5234 24.4588i 0.743972 0.886632i −0.252750 0.967532i \(-0.581335\pi\)
0.996722 + 0.0808999i \(0.0257794\pi\)
\(762\) −6.95738 + 8.29148i −0.252039 + 0.300369i
\(763\) −2.97596 5.15451i −0.107737 0.186606i
\(764\) −18.0611 + 8.42201i −0.653426 + 0.304698i
\(765\) −6.25562 30.7008i −0.226172 1.10999i
\(766\) −7.09614 + 12.2909i −0.256394 + 0.444088i
\(767\) 2.91512 10.8794i 0.105259 0.392832i
\(768\) −1.23892 + 2.65688i −0.0447059 + 0.0958720i
\(769\) 13.1603 + 49.1148i 0.474572 + 1.77113i 0.623020 + 0.782206i \(0.285905\pi\)
−0.148448 + 0.988920i \(0.547428\pi\)
\(770\) 0.260492 0.0772453i 0.00938749 0.00278373i
\(771\) −11.2981 11.2981i −0.406892 0.406892i
\(772\) 2.66235 2.23397i 0.0958199 0.0804025i
\(773\) 2.76903 + 5.93821i 0.0995952 + 0.213583i 0.949792 0.312883i \(-0.101295\pi\)
−0.850197 + 0.526465i \(0.823517\pi\)
\(774\) −54.2690 + 9.56908i −1.95066 + 0.343954i
\(775\) −2.39409 + 11.2962i −0.0859984 + 0.405773i
\(776\) 8.39854i 0.301490i
\(777\) 5.43507 + 1.27442i 0.194982 + 0.0457197i
\(778\) −13.2882 13.2882i −0.476407 0.476407i
\(779\) −32.3989 46.2705i −1.16081 1.65781i
\(780\) 7.49436 + 1.79689i 0.268341 + 0.0643389i
\(781\) −0.00388140 + 0.0106641i −0.000138887 + 0.000381590i
\(782\) 0.0215875 + 0.0257269i 0.000771966 + 0.000919994i
\(783\) −43.1630 −1.54252
\(784\) 4.43652 + 5.28723i 0.158447 + 0.188830i
\(785\) 7.41617 + 10.0162i 0.264694 + 0.357492i
\(786\) 17.6801 6.43503i 0.630628 0.229530i
\(787\) 17.1626 + 4.59870i 0.611780 + 0.163926i 0.551388 0.834249i \(-0.314098\pi\)
0.0603915 + 0.998175i \(0.480765\pi\)
\(788\) −4.17436 15.5789i −0.148705 0.554976i
\(789\) 34.0255 + 5.99962i 1.21134 + 0.213592i
\(790\) −18.8030 17.8328i −0.668979 0.634461i
\(791\) −0.316857 + 1.18253i −0.0112661 + 0.0420458i
\(792\) 1.66324 + 1.39562i 0.0591006 + 0.0495913i
\(793\) −0.579799 6.62713i −0.0205893 0.235336i
\(794\) 22.0388 + 10.2769i 0.782129 + 0.364713i
\(795\) 15.8850 + 25.9047i 0.563381 + 0.918744i
\(796\) −6.21957 4.35499i −0.220447 0.154358i
\(797\) 29.5496 10.7552i 1.04670 0.380968i 0.239284 0.970950i \(-0.423087\pi\)
0.807416 + 0.589982i \(0.200865\pi\)
\(798\) 5.58523 0.488645i 0.197715 0.0172978i
\(799\) 0.903790 + 10.3304i 0.0319738 + 0.365462i
\(800\) −4.78239 1.45902i −0.169083 0.0515843i
\(801\) −32.0488 68.7289i −1.13239 2.42842i
\(802\) −6.70325 + 4.69367i −0.236700 + 0.165739i
\(803\) 0.972814 0.260665i 0.0343298 0.00919865i
\(804\) −19.3421 33.5014i −0.682142 1.18150i
\(805\) 0.000570212 0.00936845i 2.00973e−5 0.000330194i
\(806\) −2.62264 + 0.702735i −0.0923786 + 0.0247528i
\(807\) −93.8122 8.20750i −3.30235 0.288918i
\(808\) 19.6379i 0.690860i
\(809\) 0.181877 2.07886i 0.00639444 0.0730888i −0.992327 0.123641i \(-0.960543\pi\)
0.998721 + 0.0505527i \(0.0160983\pi\)
\(810\) −12.3176 + 0.326200i −0.432796 + 0.0114615i
\(811\) −2.89640 16.4263i −0.101706 0.576805i −0.992485 0.122368i \(-0.960951\pi\)
0.890779 0.454438i \(-0.150160\pi\)
\(812\) 1.74998 + 0.308568i 0.0614122 + 0.0108286i
\(813\) −32.7557 + 32.7557i −1.14879 + 1.14879i
\(814\) 2.29858 + 0.538975i 0.0805652 + 0.0188911i
\(815\) 5.35518 + 13.5831i 0.187584 + 0.475796i
\(816\) −6.01506 + 4.21179i −0.210569 + 0.147442i
\(817\) −34.5177 + 49.2964i −1.20762 + 1.72466i
\(818\) 17.5656 8.19099i 0.614168 0.286391i
\(819\) −2.05109 0.179447i −0.0716707 0.00627038i
\(820\) −7.58326 19.2345i −0.264819 0.671698i
\(821\) 19.5952 16.4423i 0.683877 0.573841i −0.233260 0.972415i \(-0.574939\pi\)
0.917136 + 0.398574i \(0.130495\pi\)
\(822\) 53.1994 + 30.7147i 1.85554 + 1.07130i
\(823\) 33.1342 + 15.4507i 1.15498 + 0.538578i 0.903206 0.429207i \(-0.141207\pi\)
0.251778 + 0.967785i \(0.418985\pi\)
\(824\) 1.57751 0.910774i 0.0549550 0.0317283i
\(825\) −3.01193 + 4.82647i −0.104862 + 0.168036i
\(826\) 0.520800 2.95360i 0.0181209 0.102769i
\(827\) 8.23112 22.6148i 0.286224 0.786394i −0.710362 0.703836i \(-0.751469\pi\)
0.996586 0.0825580i \(-0.0263090\pi\)
\(828\) 0.0649540 0.0375012i 0.00225731 0.00130326i
\(829\) 18.9503 1.65794i 0.658173 0.0575826i 0.246823 0.969060i \(-0.420613\pi\)
0.411349 + 0.911478i \(0.365058\pi\)
\(830\) 16.4004 + 32.8698i 0.569267 + 1.14093i
\(831\) 18.5030 39.6798i 0.641863 1.37648i
\(832\) −0.204155 1.15782i −0.00707781 0.0401402i
\(833\) 3.00209 + 17.0257i 0.104016 + 0.589905i
\(834\) 6.46471 13.8636i 0.223855 0.480058i
\(835\) 4.77029 14.2710i 0.165083 0.493867i
\(836\) 2.36209 0.206656i 0.0816945 0.00714734i
\(837\) 15.2088 8.78083i 0.525695 0.303510i
\(838\) −3.63214 + 9.97922i −0.125470 + 0.344726i
\(839\) −2.46131 + 13.9588i −0.0849739 + 0.481911i 0.912388 + 0.409326i \(0.134236\pi\)
−0.997362 + 0.0725853i \(0.976875\pi\)
\(840\) 2.02971 + 0.302727i 0.0700316 + 0.0104451i
\(841\) −2.78716 + 1.60917i −0.0961089 + 0.0554885i
\(842\) −15.6048 7.27662i −0.537776 0.250769i
\(843\) −36.3096 20.9634i −1.25057 0.722017i
\(844\) −16.1812 + 13.5776i −0.556979 + 0.467361i
\(845\) 24.1677 9.52818i 0.831393 0.327779i
\(846\) 23.0705 + 2.01841i 0.793180 + 0.0693942i
\(847\) 3.07829 1.43543i 0.105771 0.0493219i
\(848\) 2.65889 3.79729i 0.0913067 0.130399i
\(849\) −57.0439 + 39.9426i −1.95774 + 1.37083i
\(850\) −8.54688 9.15453i −0.293156 0.313998i
\(851\) 0.0446528 0.0682461i 0.00153068 0.00233945i
\(852\) −0.0606090 + 0.0606090i −0.00207643 + 0.00207643i
\(853\) −11.1525 1.96649i −0.381856 0.0673314i −0.0205743 0.999788i \(-0.506549\pi\)
−0.361281 + 0.932457i \(0.617661\pi\)
\(854\) −0.307603 1.74451i −0.0105260 0.0596958i
\(855\) −52.5838 + 55.4446i −1.79833 + 1.89617i
\(856\) 0.760767 8.69560i 0.0260025 0.297210i
\(857\) 43.3102i 1.47945i 0.672911 + 0.739724i \(0.265044\pi\)
−0.672911 + 0.739724i \(0.734956\pi\)
\(858\) −1.33264 0.116591i −0.0454955 0.00398034i
\(859\) 40.6201 10.8841i 1.38594 0.371362i 0.512665 0.858589i \(-0.328658\pi\)
0.873275 + 0.487227i \(0.161992\pi\)
\(860\) −16.4933 + 14.6008i −0.562417 + 0.497882i
\(861\) 4.24293 + 7.34896i 0.144599 + 0.250452i
\(862\) −26.6953 + 7.15298i −0.909245 + 0.243632i
\(863\) −3.95436 + 2.76887i −0.134608 + 0.0942536i −0.638941 0.769256i \(-0.720627\pi\)
0.504333 + 0.863509i \(0.331738\pi\)
\(864\) 3.21373 + 6.89186i 0.109333 + 0.234466i
\(865\) −26.7401 + 3.05468i −0.909192 + 0.103862i
\(866\) 2.65713 + 30.3712i 0.0902930 + 1.03205i
\(867\) 31.3236 2.74046i 1.06380 0.0930708i
\(868\) −0.679392 + 0.247279i −0.0230601 + 0.00839318i
\(869\) 3.68470 + 2.58006i 0.124995 + 0.0875225i
\(870\) −31.7190 + 19.4504i −1.07538 + 0.659430i
\(871\) 14.0605 + 6.55653i 0.476423 + 0.222160i
\(872\) −1.65700 18.9396i −0.0561132 0.641377i
\(873\) 35.9896 + 30.1989i 1.21806 + 1.02208i
\(874\) 0.0211994 0.0791171i 0.000717079 0.00267617i
\(875\) −0.0274326 + 3.50003i −0.000927390 + 0.118323i
\(876\) 7.49122 + 1.32090i 0.253105 + 0.0446292i
\(877\) 3.20794 + 11.9722i 0.108324 + 0.404272i 0.998701 0.0509523i \(-0.0162257\pi\)
−0.890377 + 0.455225i \(0.849559\pi\)
\(878\) −32.3995 8.68143i −1.09343 0.292984i
\(879\) 2.89003 1.05189i 0.0974784 0.0354792i
\(880\) 0.858398 + 0.128028i 0.0289366 + 0.00431584i
\(881\) 21.4035 + 25.5077i 0.721103 + 0.859378i 0.994738 0.102456i \(-0.0326702\pi\)
−0.273634 + 0.961834i \(0.588226\pi\)
\(882\) 38.6095 1.30005
\(883\) 24.3253 + 28.9898i 0.818612 + 0.975583i 0.999969 0.00783376i \(-0.00249359\pi\)
−0.181358 + 0.983417i \(0.558049\pi\)
\(884\) 1.00721 2.76729i 0.0338762 0.0930740i
\(885\) 32.8282 + 53.5352i 1.10351 + 1.79957i
\(886\) 7.07043 + 10.0976i 0.237536 + 0.339236i
\(887\) −21.7314 21.7314i −0.729668 0.729668i 0.240886 0.970553i \(-0.422562\pi\)
−0.970553 + 0.240886i \(0.922562\pi\)
\(888\) 14.0140 + 11.0265i 0.470280 + 0.370026i
\(889\) 1.15588i 0.0387668i
\(890\) −25.2826 16.7234i −0.847473 0.560569i
\(891\) 2.10633 0.371403i 0.0705647 0.0124425i
\(892\) 1.56764 + 3.36181i 0.0524884 + 0.112562i
\(893\) 19.3739 16.2567i 0.648324 0.544008i
\(894\) 41.7884 + 41.7884i 1.39761 + 1.39761i
\(895\) −3.62251 12.2161i −0.121087 0.408338i
\(896\) −0.0810263 0.302394i −0.00270690 0.0101023i
\(897\) −0.0195295 + 0.0418811i −0.000652071 + 0.00139837i
\(898\) 5.09397 19.0109i 0.169988 0.634404i
\(899\) 6.55431 11.3524i 0.218598 0.378623i
\(900\) −23.4484 + 15.2474i −0.781614 + 0.508245i
\(901\) 10.5236 4.90723i 0.350591 0.163483i
\(902\) 1.79440 + 3.10800i 0.0597471 + 0.103485i
\(903\) 5.81131 6.92566i 0.193388 0.230471i
\(904\) −2.51365 + 2.99565i −0.0836028 + 0.0996339i
\(905\) 3.78097 3.34712i 0.125684 0.111262i
\(906\) 11.7522 16.7839i 0.390441 0.557608i
\(907\) 16.0494 2.82994i 0.532911 0.0939666i 0.0992843 0.995059i \(-0.468345\pi\)
0.433627 + 0.901092i \(0.357234\pi\)
\(908\) −1.47009 4.03904i −0.0487867 0.134040i
\(909\) −84.1530 70.6127i −2.79118 2.34208i
\(910\) −0.736431 + 0.367443i −0.0244124 + 0.0121806i
\(911\) −36.1815 9.69479i −1.19875 0.321203i −0.396408 0.918074i \(-0.629744\pi\)
−0.802337 + 0.596871i \(0.796410\pi\)
\(912\) 16.8288 + 6.12518i 0.557257 + 0.202825i
\(913\) −3.65727 5.22313i −0.121038 0.172860i
\(914\) 2.99267 + 1.72782i 0.0989886 + 0.0571511i
\(915\) 29.0349 + 23.0813i 0.959863 + 0.763045i
\(916\) 3.45266 + 9.48610i 0.114079 + 0.313429i
\(917\) −1.00462 + 1.74005i −0.0331755 + 0.0574616i
\(918\) −1.66010 + 18.9751i −0.0547916 + 0.626270i
\(919\) 37.5287 37.5287i 1.23796 1.23796i 0.277122 0.960835i \(-0.410619\pi\)
0.960835 0.277122i \(-0.0893806\pi\)
\(920\) 0.0142977 0.0263517i 0.000471382 0.000868791i
\(921\) 36.0991 + 13.1390i 1.18951 + 0.432945i
\(922\) 15.4426 + 10.8130i 0.508574 + 0.356107i
\(923\) 0.00596920 0.0338530i 0.000196479 0.00111429i
\(924\) −0.356211 −0.0117185
\(925\) −15.2815 + 26.2959i −0.502453 + 0.864604i
\(926\) 21.4869 0.706102
\(927\) 1.76942 10.0349i 0.0581153 0.329588i
\(928\) 4.64960 + 3.25569i 0.152631 + 0.106873i
\(929\) −0.693541 0.252428i −0.0227543 0.00828190i 0.330618 0.943765i \(-0.392743\pi\)
−0.353372 + 0.935483i \(0.614965\pi\)
\(930\) 7.21959 13.3062i 0.236740 0.436329i
\(931\) 29.8147 29.8147i 0.977136 0.977136i
\(932\) −1.81799 + 20.7797i −0.0595502 + 0.680662i
\(933\) 19.5456 33.8540i 0.639894 1.10833i
\(934\) −5.56284 15.2838i −0.182022 0.500100i
\(935\) 1.70173 + 1.35280i 0.0556526 + 0.0442412i
\(936\) −5.69561 3.28836i −0.186167 0.107484i
\(937\) 2.60279 + 3.71717i 0.0850294 + 0.121435i 0.859413 0.511281i \(-0.170829\pi\)
−0.774384 + 0.632716i \(0.781940\pi\)
\(938\) 3.88196 + 1.41292i 0.126751 + 0.0461334i
\(939\) −98.7217 26.4524i −3.22166 0.863241i
\(940\) 8.28333 4.13298i 0.270172 0.134803i
\(941\) 15.4524 + 12.9661i 0.503735 + 0.422684i 0.858918 0.512113i \(-0.171137\pi\)
−0.355183 + 0.934797i \(0.615581\pi\)
\(942\) −5.58832 15.3538i −0.182077 0.500254i
\(943\) 0.122089 0.0215276i 0.00397576 0.000701034i
\(944\) 5.49493 7.84757i 0.178845 0.255417i
\(945\) 3.98582 3.52846i 0.129659 0.114781i
\(946\) 2.45770 2.92897i 0.0799068 0.0952292i
\(947\) 14.5384 17.3262i 0.472436 0.563027i −0.476225 0.879324i \(-0.657995\pi\)
0.948660 + 0.316297i \(0.102440\pi\)
\(948\) 16.9873 + 29.4228i 0.551721 + 0.955609i
\(949\) −2.76484 + 1.28927i −0.0897506 + 0.0418514i
\(950\) −6.33296 + 29.8813i −0.205468 + 0.969478i
\(951\) 29.9346 51.8483i 0.970696 1.68130i
\(952\) 0.202957 0.757447i 0.00657788 0.0245490i
\(953\) −22.1961 + 47.5998i −0.719003 + 1.54191i 0.116969 + 0.993136i \(0.462682\pi\)
−0.835972 + 0.548772i \(0.815095\pi\)
\(954\) −6.71158 25.0480i −0.217296 0.810958i
\(955\) 12.6686 + 42.7220i 0.409946 + 1.38245i
\(956\) −3.37413 3.37413i −0.109127 0.109127i
\(957\) 4.94747 4.15142i 0.159929 0.134196i
\(958\) 9.06742 + 19.4451i 0.292955 + 0.628244i
\(959\) −6.46042 + 1.13915i −0.208618 + 0.0367850i
\(960\) 5.46731 + 3.61640i 0.176457 + 0.116719i
\(961\) 25.6665i 0.827952i
\(962\) −7.14027 0.398753i −0.230212 0.0128563i
\(963\) −34.5271 34.5271i −1.11262 1.11262i
\(964\) 7.30711 + 10.4356i 0.235346 + 0.336109i
\(965\) −4.06247 6.62495i −0.130776 0.213265i
\(966\) −0.00420856 + 0.0115629i −0.000135408 + 0.000372031i
\(967\) 6.64702 + 7.92162i 0.213754 + 0.254742i 0.862258 0.506469i \(-0.169050\pi\)
−0.648504 + 0.761211i \(0.724605\pi\)
\(968\) 10.8494 0.348711
\(969\) 28.8346 + 34.3637i 0.926300 + 1.10392i
\(970\) 18.5743 + 2.77031i 0.596383 + 0.0889494i
\(971\) 28.6871 10.4413i 0.920614 0.335076i 0.162131 0.986769i \(-0.448163\pi\)
0.758483 + 0.651693i \(0.225941\pi\)
\(972\) −6.43170 1.72337i −0.206297 0.0552771i
\(973\) 0.422795 + 1.57789i 0.0135542 + 0.0505849i
\(974\) −8.80983 1.55341i −0.282285 0.0497745i
\(975\) 6.44607 15.9818i 0.206439 0.511828i
\(976\) 1.46449 5.46556i 0.0468773 0.174948i
\(977\) 14.1432 + 11.8676i 0.452482 + 0.379678i 0.840356 0.542035i \(-0.182346\pi\)
−0.387874 + 0.921712i \(0.626790\pi\)
\(978\) −1.66832 19.0690i −0.0533471 0.609760i
\(979\) 4.76871 + 2.22369i 0.152409 + 0.0710693i
\(980\) 13.1567 8.06779i 0.420275 0.257716i
\(981\) −87.1187 61.0012i −2.78149 1.94762i
\(982\) 1.46543 0.533374i 0.0467639 0.0170207i
\(983\) 52.4973 4.59292i 1.67440 0.146491i 0.789967 0.613150i \(-0.210098\pi\)
0.884438 + 0.466658i \(0.154542\pi\)
\(984\) 2.36245 + 27.0029i 0.0753120 + 0.860820i
\(985\) −35.8314 + 4.09322i −1.14168 + 0.130421i
\(986\) 6.00867 + 12.8856i 0.191355 + 0.410362i
\(987\) −3.11232 + 2.17927i −0.0990662 + 0.0693669i
\(988\) −6.93753 + 1.85890i −0.220712 + 0.0591396i
\(989\) −0.0660399 0.114384i −0.00209995 0.00363721i
\(990\) 3.63520 3.21807i 0.115534 0.102277i
\(991\) −27.3306 + 7.32322i −0.868186 + 0.232630i −0.665303 0.746573i \(-0.731698\pi\)
−0.202883 + 0.979203i \(0.565031\pi\)
\(992\) −2.30064 0.201280i −0.0730455 0.00639065i
\(993\) 70.0945i 2.22438i
\(994\) 0.000797777 0.00911863i 2.53039e−5 0.000289225i
\(995\) −11.6831 + 12.3187i −0.370378 + 0.390529i
\(996\) −8.36280 47.4278i −0.264985 1.50281i
\(997\) −35.4257 6.24650i −1.12194 0.197829i −0.418249 0.908333i \(-0.637356\pi\)
−0.703693 + 0.710504i \(0.748467\pi\)
\(998\) 8.93431 8.93431i 0.282811 0.282811i
\(999\) 45.2772 9.46187i 1.43251 0.299360i
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 370.2.ba.a.283.9 yes 108
5.2 odd 4 370.2.bd.a.357.9 yes 108
37.17 odd 36 370.2.bd.a.313.9 yes 108
185.17 even 36 inner 370.2.ba.a.17.9 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.ba.a.17.9 108 185.17 even 36 inner
370.2.ba.a.283.9 yes 108 1.1 even 1 trivial
370.2.bd.a.313.9 yes 108 37.17 odd 36
370.2.bd.a.357.9 yes 108 5.2 odd 4