Properties

Label 462.2.j.e.295.2
Level $462$
Weight $2$
Character 462.295
Analytic conductor $3.689$
Analytic rank $0$
Dimension $8$
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] = [462,2,Mod(169,462)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(462, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("462.169");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 462.j (of order \(5\), 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: \(3.68908857338\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.484000000.9
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + x^{6} + 16x^{4} + 66x^{2} + 121 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 295.2
Root \(-1.73855 + 1.26313i\) of defining polynomial
Character \(\chi\) \(=\) 462.295
Dual form 462.2.j.e.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.910415 + 2.80197i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.910415 + 2.80197i) q^{5} +(0.309017 + 0.951057i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +2.94617 q^{10} +(-3.06668 + 1.26313i) q^{11} +1.00000 q^{12} +(-0.164066 + 0.504942i) q^{13} +(-0.809017 + 0.587785i) q^{14} +(-2.38350 - 1.73171i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.26700 + 6.97709i) q^{17} +(-0.809017 - 0.587785i) q^{18} +(-4.35658 + 3.16524i) q^{19} +(0.910415 - 2.80197i) q^{20} +1.00000 q^{21} +(0.253650 + 3.30691i) q^{22} -0.710097 q^{23} +(0.309017 - 0.951057i) q^{24} +(-2.97709 + 2.16298i) q^{25} +(0.429529 + 0.312071i) q^{26} +(0.309017 + 0.951057i) q^{27} +(0.309017 + 0.951057i) q^{28} +(0.0769587 + 0.0559138i) q^{29} +(-2.38350 + 1.73171i) q^{30} +(-1.55784 + 4.79455i) q^{31} +1.00000 q^{32} +(1.73855 - 2.82444i) q^{33} +7.33615 q^{34} +(0.910415 - 2.80197i) q^{35} +(-0.809017 + 0.587785i) q^{36} +(1.85257 + 1.34597i) q^{37} +(1.66407 + 5.12147i) q^{38} +(-0.164066 - 0.504942i) q^{39} +(-2.38350 - 1.73171i) q^{40} +(1.88999 - 1.37315i) q^{41} +(0.309017 - 0.951057i) q^{42} -0.172587 q^{43} +(3.22344 + 0.780656i) q^{44} +2.94617 q^{45} +(-0.219432 + 0.675342i) q^{46} +(10.6981 - 7.77259i) q^{47} +(-0.809017 - 0.587785i) q^{48} +(0.309017 + 0.951057i) q^{49} +(1.13715 + 3.49978i) q^{50} +(-5.93507 - 4.31208i) q^{51} +(0.429529 - 0.312071i) q^{52} +(-1.22673 + 3.77550i) q^{53} +1.00000 q^{54} +(-6.33119 - 7.44277i) q^{55} +1.00000 q^{56} +(1.66407 - 5.12147i) q^{57} +(0.0769587 - 0.0559138i) q^{58} +(7.40815 + 5.38234i) q^{59} +(0.910415 + 2.80197i) q^{60} +(-2.37263 - 7.30221i) q^{61} +(4.07849 + 2.96320i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(0.309017 - 0.951057i) q^{64} -1.56420 q^{65} +(-2.14896 - 2.52626i) q^{66} -12.9240 q^{67} +(2.26700 - 6.97709i) q^{68} +(0.574481 - 0.417385i) q^{69} +(-2.38350 - 1.73171i) q^{70} +(2.74337 + 8.44322i) q^{71} +(0.309017 + 0.951057i) q^{72} +(-5.25919 - 3.82103i) q^{73} +(1.85257 - 1.34597i) q^{74} +(1.13715 - 3.49978i) q^{75} +5.38503 q^{76} +(3.22344 + 0.780656i) q^{77} -0.530927 q^{78} +(3.17836 - 9.78198i) q^{79} +(-2.38350 + 1.73171i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(-0.721910 - 2.22181i) q^{82} +(-4.54522 - 13.9887i) q^{83} +(-0.809017 - 0.587785i) q^{84} +(-17.4857 + 12.7041i) q^{85} +(-0.0533324 + 0.164140i) q^{86} -0.0951262 q^{87} +(1.73855 - 2.82444i) q^{88} +8.61947 q^{89} +(0.910415 - 2.80197i) q^{90} +(0.429529 - 0.312071i) q^{91} +(0.574481 + 0.417385i) q^{92} +(-1.55784 - 4.79455i) q^{93} +(-4.08629 - 12.5763i) q^{94} +(-12.8352 - 9.32532i) q^{95} +(-0.809017 + 0.587785i) q^{96} +(-0.280568 + 0.863499i) q^{97} +1.00000 q^{98} +(0.253650 + 3.30691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{2} - 2 q^{3} - 2 q^{4} + 4 q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} + 4 q^{10} + 8 q^{12} + 4 q^{13} - 2 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 2 q^{18} - 12 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{23} - 2 q^{24} + 4 q^{25} - 6 q^{26} - 2 q^{27} - 2 q^{28} - 4 q^{29} - 6 q^{30} - 14 q^{31} + 8 q^{32} + 12 q^{34} + 4 q^{35} - 2 q^{36} + 10 q^{37} + 8 q^{38} + 4 q^{39} - 6 q^{40} - 12 q^{41} - 2 q^{42} + 20 q^{43} + 4 q^{45} + 6 q^{46} + 28 q^{47} - 2 q^{48} - 2 q^{49} - 6 q^{50} + 2 q^{51} - 6 q^{52} + 2 q^{53} + 8 q^{54} + 4 q^{55} + 8 q^{56} + 8 q^{57} - 4 q^{58} + 4 q^{60} - 34 q^{61} + 6 q^{62} - 2 q^{63} - 2 q^{64} + 16 q^{65} - 24 q^{67} - 8 q^{68} - 4 q^{69} - 6 q^{70} - 2 q^{72} + 10 q^{74} - 6 q^{75} + 8 q^{76} + 4 q^{78} + 22 q^{79} - 6 q^{80} - 2 q^{81} - 2 q^{82} - 30 q^{83} - 2 q^{84} - 28 q^{85} + 36 q^{87} - 4 q^{89} + 4 q^{90} - 6 q^{91} - 4 q^{92} - 14 q^{93} - 22 q^{94} - 30 q^{95} - 2 q^{96} - 10 q^{97} + 8 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 0.951057i 0.218508 0.672499i
\(3\) −0.809017 + 0.587785i −0.467086 + 0.339358i
\(4\) −0.809017 0.587785i −0.404508 0.293893i
\(5\) 0.910415 + 2.80197i 0.407150 + 1.25308i 0.919087 + 0.394056i \(0.128928\pi\)
−0.511937 + 0.859023i \(0.671072\pi\)
\(6\) 0.309017 + 0.951057i 0.126156 + 0.388267i
\(7\) −0.809017 0.587785i −0.305780 0.222162i
\(8\) −0.809017 + 0.587785i −0.286031 + 0.207813i
\(9\) 0.309017 0.951057i 0.103006 0.317019i
\(10\) 2.94617 0.931659
\(11\) −3.06668 + 1.26313i −0.924638 + 0.380847i
\(12\) 1.00000 0.288675
\(13\) −0.164066 + 0.504942i −0.0455036 + 0.140046i −0.971227 0.238155i \(-0.923457\pi\)
0.925723 + 0.378201i \(0.123457\pi\)
\(14\) −0.809017 + 0.587785i −0.216219 + 0.157092i
\(15\) −2.38350 1.73171i −0.615416 0.447126i
\(16\) 0.309017 + 0.951057i 0.0772542 + 0.237764i
\(17\) 2.26700 + 6.97709i 0.549827 + 1.69219i 0.709227 + 0.704980i \(0.249044\pi\)
−0.159400 + 0.987214i \(0.550956\pi\)
\(18\) −0.809017 0.587785i −0.190687 0.138542i
\(19\) −4.35658 + 3.16524i −0.999468 + 0.726156i −0.961974 0.273141i \(-0.911937\pi\)
−0.0374940 + 0.999297i \(0.511937\pi\)
\(20\) 0.910415 2.80197i 0.203575 0.626539i
\(21\) 1.00000 0.218218
\(22\) 0.253650 + 3.30691i 0.0540785 + 0.705036i
\(23\) −0.710097 −0.148065 −0.0740327 0.997256i \(-0.523587\pi\)
−0.0740327 + 0.997256i \(0.523587\pi\)
\(24\) 0.309017 0.951057i 0.0630778 0.194134i
\(25\) −2.97709 + 2.16298i −0.595418 + 0.432597i
\(26\) 0.429529 + 0.312071i 0.0842376 + 0.0612022i
\(27\) 0.309017 + 0.951057i 0.0594703 + 0.183031i
\(28\) 0.309017 + 0.951057i 0.0583987 + 0.179733i
\(29\) 0.0769587 + 0.0559138i 0.0142909 + 0.0103829i 0.594908 0.803794i \(-0.297189\pi\)
−0.580617 + 0.814177i \(0.697189\pi\)
\(30\) −2.38350 + 1.73171i −0.435165 + 0.316166i
\(31\) −1.55784 + 4.79455i −0.279797 + 0.861127i 0.708113 + 0.706099i \(0.249547\pi\)
−0.987910 + 0.155028i \(0.950453\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.73855 2.82444i 0.302642 0.491672i
\(34\) 7.33615 1.25814
\(35\) 0.910415 2.80197i 0.153888 0.473619i
\(36\) −0.809017 + 0.587785i −0.134836 + 0.0979642i
\(37\) 1.85257 + 1.34597i 0.304561 + 0.221276i 0.729559 0.683918i \(-0.239725\pi\)
−0.424998 + 0.905194i \(0.639725\pi\)
\(38\) 1.66407 + 5.12147i 0.269947 + 0.830812i
\(39\) −0.164066 0.504942i −0.0262715 0.0808554i
\(40\) −2.38350 1.73171i −0.376864 0.273808i
\(41\) 1.88999 1.37315i 0.295166 0.214451i −0.430339 0.902667i \(-0.641606\pi\)
0.725505 + 0.688216i \(0.241606\pi\)
\(42\) 0.309017 0.951057i 0.0476824 0.146751i
\(43\) −0.172587 −0.0263193 −0.0131597 0.999913i \(-0.504189\pi\)
−0.0131597 + 0.999913i \(0.504189\pi\)
\(44\) 3.22344 + 0.780656i 0.485952 + 0.117688i
\(45\) 2.94617 0.439188
\(46\) −0.219432 + 0.675342i −0.0323535 + 0.0995738i
\(47\) 10.6981 7.77259i 1.56047 1.13375i 0.624850 0.780745i \(-0.285160\pi\)
0.935622 0.353004i \(-0.114840\pi\)
\(48\) −0.809017 0.587785i −0.116772 0.0848395i
\(49\) 0.309017 + 0.951057i 0.0441453 + 0.135865i
\(50\) 1.13715 + 3.49978i 0.160817 + 0.494944i
\(51\) −5.93507 4.31208i −0.831076 0.603812i
\(52\) 0.429529 0.312071i 0.0595650 0.0432765i
\(53\) −1.22673 + 3.77550i −0.168505 + 0.518604i −0.999277 0.0380076i \(-0.987899\pi\)
0.830773 + 0.556612i \(0.187899\pi\)
\(54\) 1.00000 0.136083
\(55\) −6.33119 7.44277i −0.853698 1.00358i
\(56\) 1.00000 0.133631
\(57\) 1.66407 5.12147i 0.220411 0.678355i
\(58\) 0.0769587 0.0559138i 0.0101052 0.00734184i
\(59\) 7.40815 + 5.38234i 0.964459 + 0.700721i 0.954182 0.299226i \(-0.0967286\pi\)
0.0102772 + 0.999947i \(0.496729\pi\)
\(60\) 0.910415 + 2.80197i 0.117534 + 0.361733i
\(61\) −2.37263 7.30221i −0.303784 0.934952i −0.980128 0.198366i \(-0.936437\pi\)
0.676344 0.736586i \(-0.263563\pi\)
\(62\) 4.07849 + 2.96320i 0.517969 + 0.376326i
\(63\) −0.809017 + 0.587785i −0.101927 + 0.0740540i
\(64\) 0.309017 0.951057i 0.0386271 0.118882i
\(65\) −1.56420 −0.194015
\(66\) −2.14896 2.52626i −0.264519 0.310961i
\(67\) −12.9240 −1.57891 −0.789457 0.613805i \(-0.789638\pi\)
−0.789457 + 0.613805i \(0.789638\pi\)
\(68\) 2.26700 6.97709i 0.274914 0.846097i
\(69\) 0.574481 0.417385i 0.0691593 0.0502472i
\(70\) −2.38350 1.73171i −0.284882 0.206979i
\(71\) 2.74337 + 8.44322i 0.325578 + 1.00203i 0.971179 + 0.238351i \(0.0766069\pi\)
−0.645601 + 0.763675i \(0.723393\pi\)
\(72\) 0.309017 + 0.951057i 0.0364180 + 0.112083i
\(73\) −5.25919 3.82103i −0.615542 0.447217i 0.235820 0.971797i \(-0.424223\pi\)
−0.851361 + 0.524580i \(0.824223\pi\)
\(74\) 1.85257 1.34597i 0.215357 0.156466i
\(75\) 1.13715 3.49978i 0.131307 0.404120i
\(76\) 5.38503 0.617705
\(77\) 3.22344 + 0.780656i 0.367345 + 0.0889640i
\(78\) −0.530927 −0.0601157
\(79\) 3.17836 9.78198i 0.357593 1.10056i −0.596898 0.802317i \(-0.703600\pi\)
0.954491 0.298241i \(-0.0963999\pi\)
\(80\) −2.38350 + 1.73171i −0.266483 + 0.193611i
\(81\) −0.809017 0.587785i −0.0898908 0.0653095i
\(82\) −0.721910 2.22181i −0.0797216 0.245358i
\(83\) −4.54522 13.9887i −0.498903 1.53546i −0.810785 0.585344i \(-0.800960\pi\)
0.311883 0.950121i \(-0.399040\pi\)
\(84\) −0.809017 0.587785i −0.0882710 0.0641326i
\(85\) −17.4857 + 12.7041i −1.89659 + 1.37795i
\(86\) −0.0533324 + 0.164140i −0.00575098 + 0.0176997i
\(87\) −0.0951262 −0.0101986
\(88\) 1.73855 2.82444i 0.185330 0.301086i
\(89\) 8.61947 0.913662 0.456831 0.889553i \(-0.348984\pi\)
0.456831 + 0.889553i \(0.348984\pi\)
\(90\) 0.910415 2.80197i 0.0959662 0.295354i
\(91\) 0.429529 0.312071i 0.0450269 0.0327139i
\(92\) 0.574481 + 0.417385i 0.0598937 + 0.0435153i
\(93\) −1.55784 4.79455i −0.161541 0.497172i
\(94\) −4.08629 12.5763i −0.421469 1.29715i
\(95\) −12.8352 9.32532i −1.31686 0.956758i
\(96\) −0.809017 + 0.587785i −0.0825700 + 0.0599906i
\(97\) −0.280568 + 0.863499i −0.0284874 + 0.0876751i −0.964289 0.264851i \(-0.914677\pi\)
0.935802 + 0.352526i \(0.114677\pi\)
\(98\) 1.00000 0.101015
\(99\) 0.253650 + 3.30691i 0.0254928 + 0.332357i
\(100\) 3.67989 0.367989
\(101\) −1.05938 + 3.26042i −0.105412 + 0.324424i −0.989827 0.142277i \(-0.954558\pi\)
0.884415 + 0.466701i \(0.154558\pi\)
\(102\) −5.93507 + 4.31208i −0.587660 + 0.426960i
\(103\) 0.146267 + 0.106269i 0.0144121 + 0.0104710i 0.594968 0.803749i \(-0.297165\pi\)
−0.580556 + 0.814220i \(0.697165\pi\)
\(104\) −0.164066 0.504942i −0.0160879 0.0495136i
\(105\) 0.910415 + 2.80197i 0.0888474 + 0.273444i
\(106\) 3.21163 + 2.33338i 0.311941 + 0.226638i
\(107\) −12.2107 + 8.87158i −1.18045 + 0.857648i −0.992222 0.124477i \(-0.960275\pi\)
−0.188229 + 0.982125i \(0.560275\pi\)
\(108\) 0.309017 0.951057i 0.0297352 0.0915155i
\(109\) 6.58783 0.630999 0.315500 0.948926i \(-0.397828\pi\)
0.315500 + 0.948926i \(0.397828\pi\)
\(110\) −9.03494 + 3.72138i −0.861447 + 0.354820i
\(111\) −2.28990 −0.217348
\(112\) 0.309017 0.951057i 0.0291994 0.0898664i
\(113\) 10.9168 7.93150i 1.02696 0.746132i 0.0592646 0.998242i \(-0.481124\pi\)
0.967699 + 0.252110i \(0.0811244\pi\)
\(114\) −4.35658 3.16524i −0.408031 0.296452i
\(115\) −0.646483 1.98967i −0.0602849 0.185538i
\(116\) −0.0293956 0.0904704i −0.00272931 0.00839996i
\(117\) 0.429529 + 0.312071i 0.0397100 + 0.0288510i
\(118\) 7.40815 5.38234i 0.681976 0.495484i
\(119\) 2.26700 6.97709i 0.207815 0.639589i
\(120\) 2.94617 0.268947
\(121\) 7.80902 7.74721i 0.709911 0.704292i
\(122\) −7.67800 −0.695133
\(123\) −0.721910 + 2.22181i −0.0650924 + 0.200334i
\(124\) 4.07849 2.96320i 0.366259 0.266103i
\(125\) 3.14648 + 2.28605i 0.281430 + 0.204471i
\(126\) 0.309017 + 0.951057i 0.0275294 + 0.0847268i
\(127\) 1.05640 + 3.25125i 0.0937399 + 0.288502i 0.986923 0.161191i \(-0.0515335\pi\)
−0.893183 + 0.449693i \(0.851533\pi\)
\(128\) −0.809017 0.587785i −0.0715077 0.0519534i
\(129\) 0.139626 0.101444i 0.0122934 0.00893167i
\(130\) −0.483364 + 1.48764i −0.0423938 + 0.130475i
\(131\) 4.82272 0.421363 0.210682 0.977555i \(-0.432432\pi\)
0.210682 + 0.977555i \(0.432432\pi\)
\(132\) −3.06668 + 1.26313i −0.266920 + 0.109941i
\(133\) 5.38503 0.466941
\(134\) −3.99373 + 12.2914i −0.345006 + 1.06182i
\(135\) −2.38350 + 1.73171i −0.205139 + 0.149042i
\(136\) −5.93507 4.31208i −0.508928 0.369758i
\(137\) 5.33390 + 16.4161i 0.455706 + 1.40252i 0.870304 + 0.492514i \(0.163922\pi\)
−0.414599 + 0.910004i \(0.636078\pi\)
\(138\) −0.219432 0.675342i −0.0186793 0.0574890i
\(139\) 14.1186 + 10.2578i 1.19753 + 0.870053i 0.994039 0.109024i \(-0.0347727\pi\)
0.203487 + 0.979078i \(0.434773\pi\)
\(140\) −2.38350 + 1.73171i −0.201442 + 0.146356i
\(141\) −4.08629 + 12.5763i −0.344128 + 1.05912i
\(142\) 8.87773 0.745002
\(143\) −0.134670 1.75573i −0.0112617 0.146821i
\(144\) 1.00000 0.0833333
\(145\) −0.0866043 + 0.266541i −0.00719209 + 0.0221350i
\(146\) −5.25919 + 3.82103i −0.435254 + 0.316230i
\(147\) −0.809017 0.587785i −0.0667266 0.0484797i
\(148\) −0.707619 2.17783i −0.0581659 0.179016i
\(149\) −3.12227 9.60936i −0.255786 0.787230i −0.993674 0.112306i \(-0.964176\pi\)
0.737887 0.674924i \(-0.235824\pi\)
\(150\) −2.97709 2.16298i −0.243079 0.176607i
\(151\) 3.05558 2.22001i 0.248660 0.180662i −0.456473 0.889737i \(-0.650887\pi\)
0.705133 + 0.709075i \(0.250887\pi\)
\(152\) 1.66407 5.12147i 0.134974 0.415406i
\(153\) 7.33615 0.593093
\(154\) 1.73855 2.82444i 0.140096 0.227600i
\(155\) −14.8525 −1.19298
\(156\) −0.164066 + 0.504942i −0.0131358 + 0.0404277i
\(157\) −17.7701 + 12.9107i −1.41821 + 1.03039i −0.426140 + 0.904657i \(0.640127\pi\)
−0.992065 + 0.125729i \(0.959873\pi\)
\(158\) −8.32105 6.04559i −0.661987 0.480962i
\(159\) −1.22673 3.77550i −0.0972863 0.299416i
\(160\) 0.910415 + 2.80197i 0.0719746 + 0.221515i
\(161\) 0.574481 + 0.417385i 0.0452754 + 0.0328945i
\(162\) −0.809017 + 0.587785i −0.0635624 + 0.0461808i
\(163\) 5.93056 18.2524i 0.464517 1.42964i −0.395072 0.918650i \(-0.629280\pi\)
0.859589 0.510986i \(-0.170720\pi\)
\(164\) −2.33615 −0.182423
\(165\) 9.49679 + 2.29994i 0.739324 + 0.179050i
\(166\) −14.7086 −1.14161
\(167\) 4.80604 14.7915i 0.371902 1.14460i −0.573643 0.819106i \(-0.694470\pi\)
0.945545 0.325492i \(-0.105530\pi\)
\(168\) −0.809017 + 0.587785i −0.0624170 + 0.0453486i
\(169\) 10.2892 + 7.47552i 0.791475 + 0.575040i
\(170\) 6.67894 + 20.5557i 0.512251 + 1.57655i
\(171\) 1.66407 + 5.12147i 0.127254 + 0.391648i
\(172\) 0.139626 + 0.101444i 0.0106464 + 0.00773506i
\(173\) −18.1275 + 13.1704i −1.37820 + 1.00132i −0.381159 + 0.924509i \(0.624475\pi\)
−0.997045 + 0.0768149i \(0.975525\pi\)
\(174\) −0.0293956 + 0.0904704i −0.00222847 + 0.00685854i
\(175\) 3.67989 0.278173
\(176\) −2.14896 2.52626i −0.161984 0.190424i
\(177\) −9.15698 −0.688281
\(178\) 2.66356 8.19760i 0.199642 0.614436i
\(179\) 14.8494 10.7887i 1.10989 0.806385i 0.127247 0.991871i \(-0.459386\pi\)
0.982647 + 0.185486i \(0.0593861\pi\)
\(180\) −2.38350 1.73171i −0.177655 0.129074i
\(181\) −1.02971 3.16911i −0.0765375 0.235558i 0.905467 0.424417i \(-0.139521\pi\)
−0.982004 + 0.188859i \(0.939521\pi\)
\(182\) −0.164066 0.504942i −0.0121613 0.0374288i
\(183\) 6.21163 + 4.51301i 0.459177 + 0.333611i
\(184\) 0.574481 0.417385i 0.0423513 0.0307700i
\(185\) −2.08476 + 6.41624i −0.153275 + 0.471731i
\(186\) −5.04129 −0.369645
\(187\) −15.7651 18.5330i −1.15286 1.35527i
\(188\) −13.2235 −0.964425
\(189\) 0.309017 0.951057i 0.0224777 0.0691792i
\(190\) −12.8352 + 9.32532i −0.931164 + 0.676530i
\(191\) 6.80888 + 4.94694i 0.492674 + 0.357948i 0.806212 0.591627i \(-0.201514\pi\)
−0.313538 + 0.949576i \(0.601514\pi\)
\(192\) 0.309017 + 0.951057i 0.0223014 + 0.0686366i
\(193\) −2.13408 6.56804i −0.153615 0.472778i 0.844403 0.535708i \(-0.179955\pi\)
−0.998018 + 0.0629306i \(0.979955\pi\)
\(194\) 0.734536 + 0.533672i 0.0527366 + 0.0383154i
\(195\) 1.26546 0.919413i 0.0906217 0.0658405i
\(196\) 0.309017 0.951057i 0.0220726 0.0679326i
\(197\) 10.5788 0.753708 0.376854 0.926273i \(-0.377006\pi\)
0.376854 + 0.926273i \(0.377006\pi\)
\(198\) 3.22344 + 0.780656i 0.229080 + 0.0554788i
\(199\) 16.7261 1.18568 0.592842 0.805319i \(-0.298006\pi\)
0.592842 + 0.805319i \(0.298006\pi\)
\(200\) 1.13715 3.49978i 0.0804085 0.247472i
\(201\) 10.4557 7.59652i 0.737489 0.535817i
\(202\) 2.77348 + 2.01505i 0.195142 + 0.141779i
\(203\) −0.0293956 0.0904704i −0.00206317 0.00634977i
\(204\) 2.26700 + 6.97709i 0.158721 + 0.488494i
\(205\) 5.56821 + 4.04554i 0.388901 + 0.282553i
\(206\) 0.146267 0.106269i 0.0101909 0.00740413i
\(207\) −0.219432 + 0.675342i −0.0152516 + 0.0469395i
\(208\) −0.530927 −0.0368132
\(209\) 9.36212 15.2097i 0.647591 1.05208i
\(210\) 2.94617 0.203305
\(211\) −3.81762 + 11.7494i −0.262816 + 0.808864i 0.729373 + 0.684117i \(0.239812\pi\)
−0.992189 + 0.124748i \(0.960188\pi\)
\(212\) 3.21163 2.33338i 0.220576 0.160258i
\(213\) −7.18223 5.21820i −0.492118 0.357545i
\(214\) 4.66407 + 14.3545i 0.318829 + 0.981255i
\(215\) −0.157126 0.483585i −0.0107159 0.0329802i
\(216\) −0.809017 0.587785i −0.0550466 0.0399937i
\(217\) 4.07849 2.96320i 0.276866 0.201155i
\(218\) 2.03575 6.26539i 0.137878 0.424346i
\(219\) 6.50072 0.439278
\(220\) 0.747296 + 9.74271i 0.0503827 + 0.656853i
\(221\) −3.89496 −0.262003
\(222\) −0.707619 + 2.17783i −0.0474923 + 0.146166i
\(223\) −10.7487 + 7.80938i −0.719786 + 0.522955i −0.886316 0.463081i \(-0.846744\pi\)
0.166530 + 0.986036i \(0.446744\pi\)
\(224\) −0.809017 0.587785i −0.0540547 0.0392731i
\(225\) 1.13715 + 3.49978i 0.0758099 + 0.233319i
\(226\) −4.16983 12.8334i −0.277373 0.853667i
\(227\) 12.1889 + 8.85578i 0.809008 + 0.587779i 0.913543 0.406742i \(-0.133335\pi\)
−0.104535 + 0.994521i \(0.533335\pi\)
\(228\) −4.35658 + 3.16524i −0.288522 + 0.209623i
\(229\) −2.59003 + 7.97129i −0.171154 + 0.526758i −0.999437 0.0335523i \(-0.989318\pi\)
0.828283 + 0.560310i \(0.189318\pi\)
\(230\) −2.09206 −0.137947
\(231\) −3.06668 + 1.26313i −0.201773 + 0.0831077i
\(232\) −0.0951262 −0.00624534
\(233\) −1.75627 + 5.40524i −0.115057 + 0.354109i −0.991959 0.126560i \(-0.959606\pi\)
0.876902 + 0.480669i \(0.159606\pi\)
\(234\) 0.429529 0.312071i 0.0280792 0.0204007i
\(235\) 31.5182 + 22.8993i 2.05602 + 1.49379i
\(236\) −2.82966 8.70881i −0.184195 0.566895i
\(237\) 3.17836 + 9.78198i 0.206456 + 0.635408i
\(238\) −5.93507 4.31208i −0.384713 0.279511i
\(239\) −20.0341 + 14.5556i −1.29590 + 0.941524i −0.999907 0.0136672i \(-0.995649\pi\)
−0.295990 + 0.955191i \(0.595649\pi\)
\(240\) 0.910415 2.80197i 0.0587670 0.180866i
\(241\) 8.91406 0.574205 0.287103 0.957900i \(-0.407308\pi\)
0.287103 + 0.957900i \(0.407308\pi\)
\(242\) −4.95492 9.82084i −0.318514 0.631307i
\(243\) 1.00000 0.0641500
\(244\) −2.37263 + 7.30221i −0.151892 + 0.467476i
\(245\) −2.38350 + 1.73171i −0.152276 + 0.110635i
\(246\) 1.88999 + 1.37315i 0.120501 + 0.0875491i
\(247\) −0.883498 2.71913i −0.0562156 0.173014i
\(248\) −1.55784 4.79455i −0.0989232 0.304454i
\(249\) 11.8995 + 8.64552i 0.754102 + 0.547888i
\(250\) 3.14648 2.28605i 0.199001 0.144583i
\(251\) 0.339359 1.04444i 0.0214202 0.0659245i −0.939775 0.341794i \(-0.888966\pi\)
0.961195 + 0.275869i \(0.0889656\pi\)
\(252\) 1.00000 0.0629941
\(253\) 2.17764 0.896943i 0.136907 0.0563903i
\(254\) 3.41857 0.214500
\(255\) 6.67894 20.5557i 0.418252 1.28725i
\(256\) −0.809017 + 0.587785i −0.0505636 + 0.0367366i
\(257\) 21.7922 + 15.8330i 1.35936 + 0.987635i 0.998485 + 0.0550211i \(0.0175226\pi\)
0.360877 + 0.932613i \(0.382477\pi\)
\(258\) −0.0533324 0.164140i −0.00332033 0.0102189i
\(259\) −0.707619 2.17783i −0.0439693 0.135324i
\(260\) 1.26546 + 0.919413i 0.0784807 + 0.0570196i
\(261\) 0.0769587 0.0559138i 0.00476362 0.00346097i
\(262\) 1.49030 4.58668i 0.0920713 0.283366i
\(263\) −25.0868 −1.54692 −0.773460 0.633846i \(-0.781475\pi\)
−0.773460 + 0.633846i \(0.781475\pi\)
\(264\) 0.253650 + 3.30691i 0.0156111 + 0.203526i
\(265\) −11.6957 −0.718459
\(266\) 1.66407 5.12147i 0.102030 0.314017i
\(267\) −6.97330 + 5.06640i −0.426759 + 0.310059i
\(268\) 10.4557 + 7.59652i 0.638685 + 0.464031i
\(269\) 8.17565 + 25.1621i 0.498478 + 1.53416i 0.811465 + 0.584401i \(0.198670\pi\)
−0.312987 + 0.949757i \(0.601330\pi\)
\(270\) 0.910415 + 2.80197i 0.0554061 + 0.170522i
\(271\) 21.2668 + 15.4513i 1.29187 + 0.938598i 0.999841 0.0178120i \(-0.00567004\pi\)
0.292028 + 0.956410i \(0.405670\pi\)
\(272\) −5.93507 + 4.31208i −0.359866 + 0.261458i
\(273\) −0.164066 + 0.504942i −0.00992970 + 0.0305605i
\(274\) 17.2609 1.04277
\(275\) 6.39766 10.3936i 0.385793 0.626759i
\(276\) −0.710097 −0.0427428
\(277\) 1.92101 5.91225i 0.115422 0.355233i −0.876613 0.481197i \(-0.840202\pi\)
0.992035 + 0.125964i \(0.0402023\pi\)
\(278\) 14.1186 10.2578i 0.846778 0.615221i
\(279\) 4.07849 + 2.96320i 0.244173 + 0.177402i
\(280\) 0.910415 + 2.80197i 0.0544077 + 0.167450i
\(281\) −9.51501 29.2842i −0.567618 1.74695i −0.660042 0.751229i \(-0.729462\pi\)
0.0924243 0.995720i \(-0.470538\pi\)
\(282\) 10.6981 + 7.77259i 0.637060 + 0.462851i
\(283\) 11.9872 8.70924i 0.712567 0.517711i −0.171433 0.985196i \(-0.554840\pi\)
0.884001 + 0.467485i \(0.154840\pi\)
\(284\) 2.74337 8.44322i 0.162789 0.501013i
\(285\) 15.8652 0.939772
\(286\) −1.71141 0.414471i −0.101198 0.0245082i
\(287\) −2.33615 −0.137899
\(288\) 0.309017 0.951057i 0.0182090 0.0560415i
\(289\) −29.7873 + 21.6417i −1.75219 + 1.27304i
\(290\) 0.226733 + 0.164731i 0.0133142 + 0.00967335i
\(291\) −0.280568 0.863499i −0.0164472 0.0506192i
\(292\) 2.00883 + 6.18255i 0.117558 + 0.361806i
\(293\) 10.0886 + 7.32982i 0.589385 + 0.428213i 0.842095 0.539329i \(-0.181322\pi\)
−0.252711 + 0.967542i \(0.581322\pi\)
\(294\) −0.809017 + 0.587785i −0.0471828 + 0.0342803i
\(295\) −8.33665 + 25.6576i −0.485379 + 1.49384i
\(296\) −2.28990 −0.133098
\(297\) −2.14896 2.52626i −0.124695 0.146588i
\(298\) −10.1039 −0.585302
\(299\) 0.116502 0.358558i 0.00673751 0.0207359i
\(300\) −2.97709 + 2.16298i −0.171882 + 0.124880i
\(301\) 0.139626 + 0.101444i 0.00804792 + 0.00584715i
\(302\) −1.16713 3.59205i −0.0671607 0.206699i
\(303\) −1.05938 3.26042i −0.0608596 0.187307i
\(304\) −4.35658 3.16524i −0.249867 0.181539i
\(305\) 18.3005 13.2961i 1.04788 0.761331i
\(306\) 2.26700 6.97709i 0.129595 0.398854i
\(307\) −25.1036 −1.43274 −0.716368 0.697722i \(-0.754197\pi\)
−0.716368 + 0.697722i \(0.754197\pi\)
\(308\) −2.14896 2.52626i −0.122448 0.143947i
\(309\) −0.180796 −0.0102851
\(310\) −4.58967 + 14.1255i −0.260676 + 0.802277i
\(311\) −17.1120 + 12.4326i −0.970331 + 0.704987i −0.955527 0.294903i \(-0.904712\pi\)
−0.0148042 + 0.999890i \(0.504712\pi\)
\(312\) 0.429529 + 0.312071i 0.0243173 + 0.0176675i
\(313\) 0.671869 + 2.06780i 0.0379763 + 0.116879i 0.968247 0.249994i \(-0.0804285\pi\)
−0.930271 + 0.366873i \(0.880429\pi\)
\(314\) 6.78756 + 20.8900i 0.383044 + 1.17889i
\(315\) −2.38350 1.73171i −0.134295 0.0975709i
\(316\) −8.32105 + 6.04559i −0.468095 + 0.340091i
\(317\) 0.784806 2.41538i 0.0440791 0.135661i −0.926595 0.376061i \(-0.877278\pi\)
0.970674 + 0.240399i \(0.0772784\pi\)
\(318\) −3.96979 −0.222615
\(319\) −0.306634 0.0742608i −0.0171682 0.00415781i
\(320\) 2.94617 0.164696
\(321\) 4.66407 14.3545i 0.260323 0.801191i
\(322\) 0.574481 0.417385i 0.0320146 0.0232599i
\(323\) −31.9605 23.2207i −1.77833 1.29203i
\(324\) 0.309017 + 0.951057i 0.0171676 + 0.0528365i
\(325\) −0.603743 1.85813i −0.0334896 0.103070i
\(326\) −15.5264 11.2806i −0.859928 0.624774i
\(327\) −5.32966 + 3.87223i −0.294731 + 0.214135i
\(328\) −0.721910 + 2.22181i −0.0398608 + 0.122679i
\(329\) −13.2235 −0.729036
\(330\) 5.12204 8.32126i 0.281959 0.458071i
\(331\) −13.6488 −0.750205 −0.375103 0.926983i \(-0.622393\pi\)
−0.375103 + 0.926983i \(0.622393\pi\)
\(332\) −4.54522 + 13.9887i −0.249451 + 0.767732i
\(333\) 1.85257 1.34597i 0.101520 0.0737588i
\(334\) −12.5824 9.14162i −0.688476 0.500207i
\(335\) −11.7662 36.2126i −0.642855 1.97850i
\(336\) 0.309017 + 0.951057i 0.0168583 + 0.0518844i
\(337\) −8.17230 5.93752i −0.445174 0.323438i 0.342514 0.939513i \(-0.388722\pi\)
−0.787687 + 0.616075i \(0.788722\pi\)
\(338\) 10.2892 7.47552i 0.559657 0.406615i
\(339\) −4.16983 + 12.8334i −0.226474 + 0.697016i
\(340\) 21.6135 1.17216
\(341\) −1.27873 16.6711i −0.0692469 0.902791i
\(342\) 5.38503 0.291189
\(343\) 0.309017 0.951057i 0.0166853 0.0513522i
\(344\) 0.139626 0.101444i 0.00752814 0.00546951i
\(345\) 1.69251 + 1.22968i 0.0911219 + 0.0662040i
\(346\) 6.92407 + 21.3101i 0.372240 + 1.14564i
\(347\) 9.97952 + 30.7138i 0.535729 + 1.64880i 0.742069 + 0.670323i \(0.233844\pi\)
−0.206341 + 0.978480i \(0.566156\pi\)
\(348\) 0.0769587 + 0.0559138i 0.00412542 + 0.00299729i
\(349\) 5.34893 3.88623i 0.286322 0.208025i −0.435348 0.900262i \(-0.643375\pi\)
0.721670 + 0.692237i \(0.243375\pi\)
\(350\) 1.13715 3.49978i 0.0607831 0.187071i
\(351\) −0.530927 −0.0283388
\(352\) −3.06668 + 1.26313i −0.163454 + 0.0673249i
\(353\) −19.4835 −1.03700 −0.518501 0.855077i \(-0.673510\pi\)
−0.518501 + 0.855077i \(0.673510\pi\)
\(354\) −2.82966 + 8.70881i −0.150395 + 0.462868i
\(355\) −21.1600 + 15.3737i −1.12306 + 0.815950i
\(356\) −6.97330 5.06640i −0.369584 0.268519i
\(357\) 2.26700 + 6.97709i 0.119982 + 0.369267i
\(358\) −5.67195 17.4565i −0.299772 0.922603i
\(359\) −7.95052 5.77639i −0.419613 0.304866i 0.357869 0.933772i \(-0.383503\pi\)
−0.777482 + 0.628905i \(0.783503\pi\)
\(360\) −2.38350 + 1.73171i −0.125621 + 0.0912693i
\(361\) 3.08972 9.50918i 0.162617 0.500483i
\(362\) −3.33220 −0.175137
\(363\) −1.76393 + 10.8576i −0.0925824 + 0.569879i
\(364\) −0.530927 −0.0278281
\(365\) 5.91835 18.2148i 0.309781 0.953407i
\(366\) 6.21163 4.51301i 0.324687 0.235899i
\(367\) 9.01168 + 6.54737i 0.470406 + 0.341770i 0.797599 0.603187i \(-0.206103\pi\)
−0.327194 + 0.944957i \(0.606103\pi\)
\(368\) −0.219432 0.675342i −0.0114387 0.0352047i
\(369\) −0.721910 2.22181i −0.0375811 0.115663i
\(370\) 5.45798 + 3.96545i 0.283747 + 0.206154i
\(371\) 3.21163 2.33338i 0.166739 0.121143i
\(372\) −1.55784 + 4.79455i −0.0807705 + 0.248586i
\(373\) −7.65347 −0.396281 −0.198141 0.980174i \(-0.563490\pi\)
−0.198141 + 0.980174i \(0.563490\pi\)
\(374\) −22.4976 + 9.26649i −1.16332 + 0.479159i
\(375\) −3.88927 −0.200841
\(376\) −4.08629 + 12.5763i −0.210735 + 0.648574i
\(377\) −0.0408595 + 0.0296861i −0.00210437 + 0.00152891i
\(378\) −0.809017 0.587785i −0.0416113 0.0302324i
\(379\) −2.17034 6.67961i −0.111483 0.343109i 0.879714 0.475502i \(-0.157734\pi\)
−0.991197 + 0.132394i \(0.957734\pi\)
\(380\) 4.90261 + 15.0887i 0.251499 + 0.774033i
\(381\) −2.76568 2.00938i −0.141690 0.102944i
\(382\) 6.80888 4.94694i 0.348373 0.253108i
\(383\) −8.79062 + 27.0548i −0.449180 + 1.38243i 0.428654 + 0.903469i \(0.358988\pi\)
−0.877834 + 0.478965i \(0.841012\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0.747296 + 9.74271i 0.0380857 + 0.496534i
\(386\) −6.90604 −0.351508
\(387\) −0.0533324 + 0.164140i −0.00271104 + 0.00834372i
\(388\) 0.734536 0.533672i 0.0372904 0.0270931i
\(389\) 5.18355 + 3.76607i 0.262816 + 0.190947i 0.711388 0.702800i \(-0.248067\pi\)
−0.448571 + 0.893747i \(0.648067\pi\)
\(390\) −0.483364 1.48764i −0.0244761 0.0753297i
\(391\) −1.60979 4.95441i −0.0814104 0.250555i
\(392\) −0.809017 0.587785i −0.0408615 0.0296876i
\(393\) −3.90167 + 2.83473i −0.196813 + 0.142993i
\(394\) 3.26903 10.0610i 0.164691 0.506868i
\(395\) 30.3024 1.52468
\(396\) 1.73855 2.82444i 0.0873652 0.141933i
\(397\) 30.7498 1.54329 0.771643 0.636056i \(-0.219435\pi\)
0.771643 + 0.636056i \(0.219435\pi\)
\(398\) 5.16866 15.9075i 0.259082 0.797371i
\(399\) −4.35658 + 3.16524i −0.218102 + 0.158460i
\(400\) −2.97709 2.16298i −0.148855 0.108149i
\(401\) 1.60374 + 4.93581i 0.0800871 + 0.246483i 0.983081 0.183170i \(-0.0586359\pi\)
−0.902994 + 0.429653i \(0.858636\pi\)
\(402\) −3.99373 12.2914i −0.199189 0.613041i
\(403\) −2.16538 1.57324i −0.107865 0.0783687i
\(404\) 2.77348 2.01505i 0.137986 0.100253i
\(405\) 0.910415 2.80197i 0.0452389 0.139231i
\(406\) −0.0951262 −0.00472103
\(407\) −7.38137 1.78763i −0.365881 0.0886093i
\(408\) 7.33615 0.363194
\(409\) 8.37043 25.7615i 0.413891 1.27383i −0.499348 0.866401i \(-0.666427\pi\)
0.913239 0.407424i \(-0.133573\pi\)
\(410\) 5.56821 4.04554i 0.274994 0.199795i
\(411\) −13.9643 10.1457i −0.688810 0.500450i
\(412\) −0.0558691 0.171947i −0.00275247 0.00847124i
\(413\) −2.82966 8.70881i −0.139239 0.428532i
\(414\) 0.574481 + 0.417385i 0.0282342 + 0.0205133i
\(415\) 35.0580 25.4711i 1.72093 1.25033i
\(416\) −0.164066 + 0.504942i −0.00804397 + 0.0247568i
\(417\) −17.4516 −0.854607
\(418\) −11.5722 13.6040i −0.566016 0.665391i
\(419\) −23.5391 −1.14996 −0.574980 0.818167i \(-0.694990\pi\)
−0.574980 + 0.818167i \(0.694990\pi\)
\(420\) 0.910415 2.80197i 0.0444237 0.136722i
\(421\) 6.84088 4.97019i 0.333404 0.242232i −0.408470 0.912772i \(-0.633937\pi\)
0.741874 + 0.670540i \(0.233937\pi\)
\(422\) 9.99466 + 7.26155i 0.486533 + 0.353487i
\(423\) −4.08629 12.5763i −0.198682 0.611482i
\(424\) −1.22673 3.77550i −0.0595754 0.183354i
\(425\) −21.8404 15.8680i −1.05941 0.769710i
\(426\) −7.18223 + 5.21820i −0.347980 + 0.252823i
\(427\) −2.37263 + 7.30221i −0.114820 + 0.353379i
\(428\) 15.0932 0.729559
\(429\) 1.14094 + 1.34126i 0.0550852 + 0.0647565i
\(430\) −0.508471 −0.0245206
\(431\) 9.86189 30.3518i 0.475031 1.46199i −0.370886 0.928679i \(-0.620946\pi\)
0.845916 0.533316i \(-0.179054\pi\)
\(432\) −0.809017 + 0.587785i −0.0389238 + 0.0282798i
\(433\) −32.6167 23.6974i −1.56746 1.13883i −0.929540 0.368721i \(-0.879796\pi\)
−0.637918 0.770104i \(-0.720204\pi\)
\(434\) −1.55784 4.79455i −0.0747789 0.230146i
\(435\) −0.0866043 0.266541i −0.00415236 0.0127796i
\(436\) −5.32966 3.87223i −0.255245 0.185446i
\(437\) 3.09359 2.24763i 0.147987 0.107519i
\(438\) 2.00883 6.18255i 0.0959857 0.295414i
\(439\) 30.2721 1.44481 0.722404 0.691471i \(-0.243037\pi\)
0.722404 + 0.691471i \(0.243037\pi\)
\(440\) 9.49679 + 2.29994i 0.452742 + 0.109645i
\(441\) 1.00000 0.0476190
\(442\) −1.20361 + 3.70433i −0.0572499 + 0.176197i
\(443\) −2.55179 + 1.85398i −0.121239 + 0.0880854i −0.646752 0.762700i \(-0.723873\pi\)
0.525513 + 0.850785i \(0.323873\pi\)
\(444\) 1.85257 + 1.34597i 0.0879191 + 0.0638770i
\(445\) 7.84730 + 24.1515i 0.371998 + 1.14489i
\(446\) 4.10564 + 12.6358i 0.194407 + 0.598325i
\(447\) 8.17421 + 5.93891i 0.386627 + 0.280901i
\(448\) −0.809017 + 0.587785i −0.0382225 + 0.0277702i
\(449\) 6.01127 18.5008i 0.283690 0.873107i −0.703099 0.711092i \(-0.748201\pi\)
0.986788 0.162015i \(-0.0517992\pi\)
\(450\) 3.67989 0.173472
\(451\) −4.06151 + 6.59831i −0.191249 + 0.310703i
\(452\) −13.4939 −0.634698
\(453\) −1.16713 + 3.59205i −0.0548365 + 0.168769i
\(454\) 12.1889 8.85578i 0.572055 0.415622i
\(455\) 1.26546 + 0.919413i 0.0593258 + 0.0431028i
\(456\) 1.66407 + 5.12147i 0.0779270 + 0.239835i
\(457\) −11.6848 35.9623i −0.546594 1.68224i −0.717170 0.696899i \(-0.754563\pi\)
0.170576 0.985345i \(-0.445437\pi\)
\(458\) 6.78078 + 4.92653i 0.316845 + 0.230202i
\(459\) −5.93507 + 4.31208i −0.277025 + 0.201271i
\(460\) −0.646483 + 1.98967i −0.0301424 + 0.0927689i
\(461\) 15.3852 0.716560 0.358280 0.933614i \(-0.383363\pi\)
0.358280 + 0.933614i \(0.383363\pi\)
\(462\) 0.253650 + 3.30691i 0.0118009 + 0.153851i
\(463\) 13.7538 0.639195 0.319597 0.947553i \(-0.396452\pi\)
0.319597 + 0.947553i \(0.396452\pi\)
\(464\) −0.0293956 + 0.0904704i −0.00136466 + 0.00419998i
\(465\) 12.0159 8.73007i 0.557224 0.404847i
\(466\) 4.59797 + 3.34062i 0.212997 + 0.154751i
\(467\) −5.88110 18.1002i −0.272145 0.837576i −0.989961 0.141343i \(-0.954858\pi\)
0.717816 0.696233i \(-0.245142\pi\)
\(468\) −0.164066 0.504942i −0.00758393 0.0233409i
\(469\) 10.4557 + 7.59652i 0.482800 + 0.350775i
\(470\) 31.5182 22.8993i 1.45383 1.05627i
\(471\) 6.78756 20.8900i 0.312754 0.962558i
\(472\) −9.15698 −0.421484
\(473\) 0.529270 0.218000i 0.0243359 0.0100236i
\(474\) 10.2854 0.472423
\(475\) 6.12358 18.8464i 0.280969 0.864733i
\(476\) −5.93507 + 4.31208i −0.272034 + 0.197644i
\(477\) 3.21163 + 2.33338i 0.147050 + 0.106838i
\(478\) 7.65233 + 23.5515i 0.350010 + 1.07722i
\(479\) 11.0503 + 34.0094i 0.504902 + 1.55393i 0.800936 + 0.598751i \(0.204336\pi\)
−0.296034 + 0.955177i \(0.595664\pi\)
\(480\) −2.38350 1.73171i −0.108791 0.0790415i
\(481\) −0.983580 + 0.714613i −0.0448474 + 0.0325835i
\(482\) 2.75460 8.47778i 0.125468 0.386152i
\(483\) −0.710097 −0.0323105
\(484\) −10.8713 + 1.67760i −0.494151 + 0.0762545i
\(485\) −2.67493 −0.121462
\(486\) 0.309017 0.951057i 0.0140173 0.0431408i
\(487\) 25.4489 18.4897i 1.15320 0.837848i 0.164295 0.986411i \(-0.447465\pi\)
0.988903 + 0.148564i \(0.0474650\pi\)
\(488\) 6.21163 + 4.51301i 0.281187 + 0.204294i
\(489\) 5.93056 + 18.2524i 0.268189 + 0.825401i
\(490\) 0.910415 + 2.80197i 0.0411284 + 0.126580i
\(491\) 18.8669 + 13.7076i 0.851453 + 0.618617i 0.925546 0.378634i \(-0.123606\pi\)
−0.0740931 + 0.997251i \(0.523606\pi\)
\(492\) 1.88999 1.37315i 0.0852071 0.0619066i
\(493\) −0.215651 + 0.663704i −0.00971241 + 0.0298917i
\(494\) −2.85906 −0.128635
\(495\) −9.03494 + 3.72138i −0.406090 + 0.167264i
\(496\) −5.04129 −0.226361
\(497\) 2.74337 8.44322i 0.123057 0.378730i
\(498\) 11.8995 8.64552i 0.533231 0.387415i
\(499\) −1.85774 1.34973i −0.0831640 0.0604222i 0.545426 0.838159i \(-0.316368\pi\)
−0.628590 + 0.777737i \(0.716368\pi\)
\(500\) −1.20185 3.69891i −0.0537483 0.165420i
\(501\) 4.80604 + 14.7915i 0.214718 + 0.660834i
\(502\) −0.888454 0.645499i −0.0396536 0.0288101i
\(503\) −24.9007 + 18.0914i −1.11027 + 0.806657i −0.982706 0.185174i \(-0.940715\pi\)
−0.127562 + 0.991831i \(0.540715\pi\)
\(504\) 0.309017 0.951057i 0.0137647 0.0423634i
\(505\) −10.1001 −0.449448
\(506\) −0.180116 2.34823i −0.00800715 0.104391i
\(507\) −12.7181 −0.564831
\(508\) 1.05640 3.25125i 0.0468700 0.144251i
\(509\) 11.0202 8.00665i 0.488462 0.354888i −0.316131 0.948716i \(-0.602384\pi\)
0.804592 + 0.593827i \(0.202384\pi\)
\(510\) −17.4857 12.7041i −0.774280 0.562547i
\(511\) 2.00883 + 6.18255i 0.0888655 + 0.273500i
\(512\) 0.309017 + 0.951057i 0.0136568 + 0.0420312i
\(513\) −4.35658 3.16524i −0.192348 0.139749i
\(514\) 21.7922 15.8330i 0.961214 0.698363i
\(515\) −0.164600 + 0.506585i −0.00725312 + 0.0223228i
\(516\) −0.172587 −0.00759774
\(517\) −22.9897 + 37.3490i −1.01109 + 1.64261i
\(518\) −2.28990 −0.100613
\(519\) 6.92407 21.3101i 0.303933 0.935409i
\(520\) 1.26546 0.919413i 0.0554942 0.0403189i
\(521\) −29.9244 21.7414i −1.31101 0.952507i −0.999998 0.00210172i \(-0.999331\pi\)
−0.311015 0.950405i \(-0.600669\pi\)
\(522\) −0.0293956 0.0904704i −0.00128661 0.00395978i
\(523\) 5.09391 + 15.6774i 0.222741 + 0.685526i 0.998513 + 0.0545129i \(0.0173606\pi\)
−0.775772 + 0.631013i \(0.782639\pi\)
\(524\) −3.90167 2.83473i −0.170445 0.123836i
\(525\) −2.97709 + 2.16298i −0.129931 + 0.0944004i
\(526\) −7.75225 + 23.8590i −0.338014 + 1.04030i
\(527\) −36.9837 −1.61103
\(528\) 3.22344 + 0.780656i 0.140282 + 0.0339737i
\(529\) −22.4958 −0.978077
\(530\) −3.61416 + 11.1232i −0.156989 + 0.483162i
\(531\) 7.40815 5.38234i 0.321486 0.233574i
\(532\) −4.35658 3.16524i −0.188882 0.137231i
\(533\) 0.383282 + 1.17962i 0.0166018 + 0.0510950i
\(534\) 2.66356 + 8.19760i 0.115264 + 0.354745i
\(535\) −35.9747 26.1371i −1.55532 1.13001i
\(536\) 10.4557 7.59652i 0.451618 0.328120i
\(537\) −5.67195 + 17.4565i −0.244763 + 0.753302i
\(538\) 26.4570 1.14064
\(539\) −2.14896 2.52626i −0.0925623 0.108814i
\(540\) 2.94617 0.126783
\(541\) −5.18878 + 15.9694i −0.223083 + 0.686579i 0.775397 + 0.631473i \(0.217550\pi\)
−0.998481 + 0.0551056i \(0.982450\pi\)
\(542\) 21.2668 15.4513i 0.913489 0.663689i
\(543\) 2.69581 + 1.95862i 0.115688 + 0.0840523i
\(544\) 2.26700 + 6.97709i 0.0971966 + 0.299140i
\(545\) 5.99766 + 18.4589i 0.256911 + 0.790692i
\(546\) 0.429529 + 0.312071i 0.0183821 + 0.0133554i
\(547\) 20.0494 14.5668i 0.857252 0.622830i −0.0698841 0.997555i \(-0.522263\pi\)
0.927136 + 0.374725i \(0.122263\pi\)
\(548\) 5.33390 16.4161i 0.227853 0.701259i
\(549\) −7.67800 −0.327689
\(550\) −7.90794 9.29634i −0.337196 0.396397i
\(551\) −0.512257 −0.0218229
\(552\) −0.219432 + 0.675342i −0.00933965 + 0.0287445i
\(553\) −8.32105 + 6.04559i −0.353847 + 0.257085i
\(554\) −5.02926 3.65397i −0.213673 0.155242i
\(555\) −2.08476 6.41624i −0.0884932 0.272354i
\(556\) −5.39283 16.5974i −0.228707 0.703888i
\(557\) −32.9856 23.9654i −1.39764 1.01545i −0.994977 0.100100i \(-0.968084\pi\)
−0.402666 0.915347i \(-0.631916\pi\)
\(558\) 4.07849 2.96320i 0.172656 0.125442i
\(559\) 0.0283156 0.0871466i 0.00119762 0.00368591i
\(560\) 2.94617 0.124498
\(561\) 23.6477 + 5.72701i 0.998405 + 0.241794i
\(562\) −30.7912 −1.29885
\(563\) 0.600872 1.84929i 0.0253237 0.0779384i −0.937596 0.347727i \(-0.886954\pi\)
0.962920 + 0.269788i \(0.0869537\pi\)
\(564\) 10.6981 7.77259i 0.450469 0.327285i
\(565\) 32.1626 + 23.3675i 1.35309 + 0.983078i
\(566\) −4.57872 14.0918i −0.192458 0.592324i
\(567\) 0.309017 + 0.951057i 0.0129775 + 0.0399406i
\(568\) −7.18223 5.21820i −0.301360 0.218951i
\(569\) −16.5945 + 12.0566i −0.695679 + 0.505440i −0.878522 0.477702i \(-0.841470\pi\)
0.182843 + 0.983142i \(0.441470\pi\)
\(570\) 4.90261 15.0887i 0.205348 0.631996i
\(571\) −21.1757 −0.886173 −0.443087 0.896479i \(-0.646117\pi\)
−0.443087 + 0.896479i \(0.646117\pi\)
\(572\) −0.923041 + 1.49957i −0.0385943 + 0.0627002i
\(573\) −8.41624 −0.351594
\(574\) −0.721910 + 2.22181i −0.0301319 + 0.0927366i
\(575\) 2.11402 1.53593i 0.0881609 0.0640526i
\(576\) −0.809017 0.587785i −0.0337090 0.0244911i
\(577\) −12.8383 39.5124i −0.534467 1.64492i −0.744797 0.667291i \(-0.767454\pi\)
0.210329 0.977631i \(-0.432546\pi\)
\(578\) 11.3777 + 35.0170i 0.473251 + 1.45652i
\(579\) 5.58711 + 4.05927i 0.232192 + 0.168698i
\(580\) 0.226733 0.164731i 0.00941457 0.00684009i
\(581\) −4.54522 + 13.9887i −0.188567 + 0.580351i
\(582\) −0.907937 −0.0376352
\(583\) −1.00694 13.1277i −0.0417032 0.543696i
\(584\) 6.50072 0.269002
\(585\) −0.483364 + 1.48764i −0.0199846 + 0.0615064i
\(586\) 10.0886 7.32982i 0.416758 0.302792i
\(587\) 28.2965 + 20.5586i 1.16792 + 0.848543i 0.990758 0.135638i \(-0.0433085\pi\)
0.177162 + 0.984182i \(0.443309\pi\)
\(588\) 0.309017 + 0.951057i 0.0127436 + 0.0392209i
\(589\) −8.38904 25.8188i −0.345664 1.06385i
\(590\) 21.8256 + 15.8573i 0.898547 + 0.652833i
\(591\) −8.55843 + 6.21806i −0.352047 + 0.255777i
\(592\) −0.707619 + 2.17783i −0.0290830 + 0.0895081i
\(593\) −23.3437 −0.958611 −0.479306 0.877648i \(-0.659111\pi\)
−0.479306 + 0.877648i \(0.659111\pi\)
\(594\) −3.06668 + 1.26313i −0.125827 + 0.0518268i
\(595\) 21.6135 0.886068
\(596\) −3.12227 + 9.60936i −0.127893 + 0.393615i
\(597\) −13.5317 + 9.83138i −0.553817 + 0.402371i
\(598\) −0.305007 0.221601i −0.0124727 0.00906193i
\(599\) −2.28291 7.02608i −0.0932773 0.287078i 0.893524 0.449016i \(-0.148225\pi\)
−0.986801 + 0.161938i \(0.948225\pi\)
\(600\) 1.13715 + 3.49978i 0.0464239 + 0.142878i
\(601\) 18.7178 + 13.5993i 0.763517 + 0.554728i 0.899987 0.435917i \(-0.143576\pi\)
−0.136470 + 0.990644i \(0.543576\pi\)
\(602\) 0.139626 0.101444i 0.00569074 0.00413456i
\(603\) −3.99373 + 12.2914i −0.162637 + 0.500546i
\(604\) −3.77691 −0.153680
\(605\) 28.8169 + 14.8275i 1.17157 + 0.602822i
\(606\) −3.42821 −0.139262
\(607\) 2.36650 7.28334i 0.0960533 0.295622i −0.891473 0.453073i \(-0.850328\pi\)
0.987527 + 0.157451i \(0.0503277\pi\)
\(608\) −4.35658 + 3.16524i −0.176683 + 0.128367i
\(609\) 0.0769587 + 0.0559138i 0.00311852 + 0.00226574i
\(610\) −6.99016 21.5135i −0.283023 0.871056i
\(611\) 2.16952 + 6.67711i 0.0877696 + 0.270127i
\(612\) −5.93507 4.31208i −0.239911 0.174306i
\(613\) −15.0507 + 10.9350i −0.607892 + 0.441659i −0.848671 0.528921i \(-0.822597\pi\)
0.240780 + 0.970580i \(0.422597\pi\)
\(614\) −7.75743 + 23.8749i −0.313064 + 0.963513i
\(615\) −6.88268 −0.277537
\(616\) −3.06668 + 1.26313i −0.123560 + 0.0508929i
\(617\) 2.11892 0.0853044 0.0426522 0.999090i \(-0.486419\pi\)
0.0426522 + 0.999090i \(0.486419\pi\)
\(618\) −0.0558691 + 0.171947i −0.00224738 + 0.00691674i
\(619\) 7.68317 5.58215i 0.308813 0.224365i −0.422574 0.906328i \(-0.638873\pi\)
0.731387 + 0.681963i \(0.238873\pi\)
\(620\) 12.0159 + 8.73007i 0.482570 + 0.350608i
\(621\) −0.219432 0.675342i −0.00880550 0.0271006i
\(622\) 6.53619 + 20.1163i 0.262078 + 0.806592i
\(623\) −6.97330 5.06640i −0.279379 0.202981i
\(624\) 0.429529 0.312071i 0.0171949 0.0124928i
\(625\) −9.22659 + 28.3965i −0.369063 + 1.13586i
\(626\) 2.17421 0.0868991
\(627\) 1.36592 + 17.8078i 0.0545494 + 0.711176i
\(628\) 21.9650 0.876499
\(629\) −5.19120 + 15.9769i −0.206987 + 0.637039i
\(630\) −2.38350 + 1.73171i −0.0949608 + 0.0689931i
\(631\) 34.6162 + 25.1501i 1.37805 + 1.00121i 0.997059 + 0.0766316i \(0.0244165\pi\)
0.380989 + 0.924579i \(0.375583\pi\)
\(632\) 3.17836 + 9.78198i 0.126428 + 0.389106i
\(633\) −3.81762 11.7494i −0.151737 0.466998i
\(634\) −2.05465 1.49279i −0.0816005 0.0592862i
\(635\) −8.14815 + 5.91998i −0.323349 + 0.234927i
\(636\) −1.22673 + 3.77550i −0.0486431 + 0.149708i
\(637\) −0.530927 −0.0210361
\(638\) −0.165381 + 0.268678i −0.00654750 + 0.0106371i
\(639\) 8.87773 0.351198
\(640\) 0.910415 2.80197i 0.0359873 0.110758i
\(641\) 17.7615 12.9045i 0.701539 0.509698i −0.178894 0.983868i \(-0.557252\pi\)
0.880433 + 0.474171i \(0.157252\pi\)
\(642\) −12.2107 8.87158i −0.481917 0.350133i
\(643\) −6.03449 18.5723i −0.237977 0.732418i −0.996713 0.0810194i \(-0.974182\pi\)
0.758735 0.651399i \(-0.225818\pi\)
\(644\) −0.219432 0.675342i −0.00864683 0.0266122i
\(645\) 0.411362 + 0.298872i 0.0161973 + 0.0117681i
\(646\) −31.9605 + 23.2207i −1.25747 + 0.913606i
\(647\) −9.68683 + 29.8130i −0.380828 + 1.17207i 0.558633 + 0.829415i \(0.311326\pi\)
−0.939461 + 0.342655i \(0.888674\pi\)
\(648\) 1.00000 0.0392837
\(649\) −29.5170 7.14845i −1.15864 0.280601i
\(650\) −1.95375 −0.0766325
\(651\) −1.55784 + 4.79455i −0.0610567 + 0.187913i
\(652\) −15.5264 + 11.2806i −0.608061 + 0.441782i
\(653\) 16.0480 + 11.6596i 0.628007 + 0.456273i 0.855709 0.517457i \(-0.173121\pi\)
−0.227702 + 0.973731i \(0.573121\pi\)
\(654\) 2.03575 + 6.26539i 0.0796041 + 0.244996i
\(655\) 4.39068 + 13.5131i 0.171558 + 0.528001i
\(656\) 1.88999 + 1.37315i 0.0737915 + 0.0536127i
\(657\) −5.25919 + 3.82103i −0.205181 + 0.149072i
\(658\) −4.08629 + 12.5763i −0.159300 + 0.490276i
\(659\) 37.3020 1.45308 0.726539 0.687125i \(-0.241128\pi\)
0.726539 + 0.687125i \(0.241128\pi\)
\(660\) −6.33119 7.44277i −0.246441 0.289709i
\(661\) 5.41129 0.210475 0.105237 0.994447i \(-0.466440\pi\)
0.105237 + 0.994447i \(0.466440\pi\)
\(662\) −4.21771 + 12.9808i −0.163926 + 0.504512i
\(663\) 3.15109 2.28940i 0.122378 0.0889130i
\(664\) 11.8995 + 8.64552i 0.461792 + 0.335511i
\(665\) 4.90261 + 15.0887i 0.190115 + 0.585114i
\(666\) −0.707619 2.17783i −0.0274197 0.0843891i
\(667\) −0.0546481 0.0397042i −0.00211598 0.00153735i
\(668\) −12.5824 + 9.14162i −0.486826 + 0.353700i
\(669\) 4.10564 12.6358i 0.158733 0.488530i
\(670\) −38.0762 −1.47101
\(671\) 16.4997 + 19.3966i 0.636964 + 0.748797i
\(672\) 1.00000 0.0385758
\(673\) 14.9180 45.9129i 0.575047 1.76981i −0.0609714 0.998140i \(-0.519420\pi\)
0.636019 0.771674i \(-0.280580\pi\)
\(674\) −8.17230 + 5.93752i −0.314785 + 0.228705i
\(675\) −2.97709 2.16298i −0.114588 0.0832533i
\(676\) −3.93011 12.0956i −0.151158 0.465217i
\(677\) 9.07104 + 27.9178i 0.348629 + 1.07297i 0.959612 + 0.281325i \(0.0907740\pi\)
−0.610984 + 0.791643i \(0.709226\pi\)
\(678\) 10.9168 + 7.93150i 0.419256 + 0.304607i
\(679\) 0.734536 0.533672i 0.0281889 0.0204804i
\(680\) 6.67894 20.5557i 0.256126 0.788274i
\(681\) −15.0664 −0.577344
\(682\) −16.2503 3.93551i −0.622256 0.150699i
\(683\) 24.9058 0.952992 0.476496 0.879177i \(-0.341907\pi\)
0.476496 + 0.879177i \(0.341907\pi\)
\(684\) 1.66407 5.12147i 0.0636271 0.195824i
\(685\) −41.1412 + 29.8909i −1.57193 + 1.14207i
\(686\) −0.809017 0.587785i −0.0308884 0.0224417i
\(687\) −2.59003 7.97129i −0.0988158 0.304124i
\(688\) −0.0533324 0.164140i −0.00203328 0.00625779i
\(689\) −1.70514 1.23886i −0.0649607 0.0471967i
\(690\) 1.69251 1.22968i 0.0644329 0.0468133i
\(691\) 10.5427 32.4470i 0.401063 1.23434i −0.523076 0.852286i \(-0.675216\pi\)
0.924139 0.382057i \(-0.124784\pi\)
\(692\) 22.4068 0.851777
\(693\) 1.73855 2.82444i 0.0660419 0.107292i
\(694\) 32.2944 1.22588
\(695\) −15.8882 + 48.8988i −0.602673 + 1.85484i
\(696\) 0.0769587 0.0559138i 0.00291711 0.00211941i
\(697\) 13.8652 + 10.0737i 0.525183 + 0.381567i
\(698\) −2.04311 6.28804i −0.0773328 0.238006i
\(699\) −1.75627 5.40524i −0.0664282 0.204445i
\(700\) −2.97709 2.16298i −0.112524 0.0817531i
\(701\) 11.4354 8.30832i 0.431910 0.313801i −0.350502 0.936562i \(-0.613989\pi\)
0.782412 + 0.622761i \(0.213989\pi\)
\(702\) −0.164066 + 0.504942i −0.00619225 + 0.0190578i
\(703\) −12.3312 −0.465080
\(704\) 0.253650 + 3.30691i 0.00955981 + 0.124634i
\(705\) −38.9587 −1.46727
\(706\) −6.02073 + 18.5299i −0.226593 + 0.697382i
\(707\) 2.77348 2.01505i 0.104308 0.0757839i
\(708\) 7.40815 + 5.38234i 0.278415 + 0.202281i
\(709\) 5.58255 + 17.1813i 0.209657 + 0.645258i 0.999490 + 0.0319360i \(0.0101673\pi\)
−0.789833 + 0.613322i \(0.789833\pi\)
\(710\) 8.08242 + 24.8751i 0.303328 + 0.933547i
\(711\) −8.32105 6.04559i −0.312064 0.226727i
\(712\) −6.97330 + 5.06640i −0.261335 + 0.189871i
\(713\) 1.10622 3.40460i 0.0414283 0.127503i
\(714\) 7.33615 0.274549
\(715\) 4.79689 1.97578i 0.179394 0.0738901i
\(716\) −18.3548 −0.685952
\(717\) 7.65233 23.5515i 0.285782 0.879546i
\(718\) −7.95052 + 5.77639i −0.296711 + 0.215573i
\(719\) 16.4996 + 11.9877i 0.615333 + 0.447065i 0.851288 0.524699i \(-0.175822\pi\)
−0.235955 + 0.971764i \(0.575822\pi\)
\(720\) 0.910415 + 2.80197i 0.0339292 + 0.104423i
\(721\) −0.0558691 0.171947i −0.00208067 0.00640365i
\(722\) −8.08899 5.87699i −0.301041 0.218719i
\(723\) −7.21163 + 5.23955i −0.268203 + 0.194861i
\(724\) −1.02971 + 3.16911i −0.0382687 + 0.117779i
\(725\) −0.350054 −0.0130007
\(726\) 9.78115 + 5.03280i 0.363013 + 0.186785i
\(727\) 17.3725 0.644310 0.322155 0.946687i \(-0.395593\pi\)
0.322155 + 0.946687i \(0.395593\pi\)
\(728\) −0.164066 + 0.504942i −0.00608067 + 0.0187144i
\(729\) −0.809017 + 0.587785i −0.0299636 + 0.0217698i
\(730\) −15.4944 11.2574i −0.573475 0.416654i
\(731\) −0.391255 1.20416i −0.0144711 0.0445374i
\(732\) −2.37263 7.30221i −0.0876950 0.269897i
\(733\) −18.7389 13.6146i −0.692138 0.502867i 0.185225 0.982696i \(-0.440699\pi\)
−0.877362 + 0.479829i \(0.840699\pi\)
\(734\) 9.01168 6.54737i 0.332627 0.241668i
\(735\) 0.910415 2.80197i 0.0335812 0.103352i
\(736\) −0.710097 −0.0261745
\(737\) 39.6337 16.3246i 1.45992 0.601326i
\(738\) −2.33615 −0.0859949
\(739\) −12.6532 + 38.9425i −0.465455 + 1.43252i 0.392953 + 0.919558i \(0.371453\pi\)
−0.858409 + 0.512966i \(0.828547\pi\)
\(740\) 5.45798 3.96545i 0.200639 0.145773i
\(741\) 2.31303 + 1.68051i 0.0849712 + 0.0617352i
\(742\) −1.22673 3.77550i −0.0450348 0.138603i
\(743\) 2.14756 + 6.60952i 0.0787864 + 0.242480i 0.982690 0.185256i \(-0.0593114\pi\)
−0.903904 + 0.427736i \(0.859311\pi\)
\(744\) 4.07849 + 2.96320i 0.149525 + 0.108636i
\(745\) 24.0826 17.4970i 0.882318 0.641041i
\(746\) −2.36505 + 7.27888i −0.0865907 + 0.266499i
\(747\) −14.7086 −0.538161
\(748\) 1.86082 + 24.2600i 0.0680382 + 0.887033i
\(749\) 15.0932 0.551495
\(750\) −1.20185 + 3.69891i −0.0438853 + 0.135065i
\(751\) 14.0636 10.2178i 0.513188 0.372853i −0.300844 0.953674i \(-0.597268\pi\)
0.814032 + 0.580821i \(0.197268\pi\)
\(752\) 10.6981 + 7.77259i 0.390118 + 0.283437i
\(753\) 0.339359 + 1.04444i 0.0123669 + 0.0380615i
\(754\) 0.0156069 + 0.0480332i 0.000568371 + 0.00174926i
\(755\) 9.00225 + 6.54052i 0.327625 + 0.238034i
\(756\) −0.809017 + 0.587785i −0.0294237 + 0.0213775i
\(757\) 7.10161 21.8565i 0.258113 0.794389i −0.735088 0.677972i \(-0.762859\pi\)
0.993200 0.116417i \(-0.0371409\pi\)
\(758\) −7.02336 −0.255100
\(759\) −1.23454 + 2.00563i −0.0448108 + 0.0727996i
\(760\) 15.8652 0.575491
\(761\) 1.88927 5.81457i 0.0684859 0.210778i −0.910956 0.412503i \(-0.864655\pi\)
0.979442 + 0.201725i \(0.0646547\pi\)
\(762\) −2.76568 + 2.00938i −0.100190 + 0.0727923i
\(763\) −5.32966 3.87223i −0.192947 0.140184i
\(764\) −2.60076 8.00432i −0.0940923 0.289586i
\(765\) 6.67894 + 20.5557i 0.241478 + 0.743192i
\(766\) 23.0141 + 16.7208i 0.831535 + 0.604145i
\(767\) −3.93319 + 2.85763i −0.142019 + 0.103183i
\(768\) 0.309017 0.951057i 0.0111507 0.0343183i
\(769\) −13.5706 −0.489369 −0.244684 0.969603i \(-0.578684\pi\)
−0.244684 + 0.969603i \(0.578684\pi\)
\(770\) 9.49679 + 2.29994i 0.342241 + 0.0828841i
\(771\) −26.9367 −0.970101
\(772\) −2.13408 + 6.56804i −0.0768074 + 0.236389i
\(773\) −15.3040 + 11.1190i −0.550448 + 0.399924i −0.827951 0.560801i \(-0.810493\pi\)
0.277502 + 0.960725i \(0.410493\pi\)
\(774\) 0.139626 + 0.101444i 0.00501876 + 0.00364634i
\(775\) −5.73269 17.6434i −0.205924 0.633770i
\(776\) −0.280568 0.863499i −0.0100718 0.0309978i
\(777\) 1.85257 + 1.34597i 0.0664606 + 0.0482864i
\(778\) 5.18355 3.76607i 0.185839 0.135020i
\(779\) −3.88751 + 11.9645i −0.139284 + 0.428673i
\(780\) −1.56420 −0.0560073
\(781\) −19.0779 22.4274i −0.682661 0.802516i
\(782\) −5.20938 −0.186287
\(783\) −0.0293956 + 0.0904704i −0.00105051 + 0.00323315i
\(784\) −0.809017 + 0.587785i −0.0288935 + 0.0209923i
\(785\) −52.3535 38.0371i −1.86858 1.35760i
\(786\) 1.49030 + 4.58668i 0.0531574 + 0.163602i
\(787\) −6.79260 20.9055i −0.242130 0.745199i −0.996095 0.0882851i \(-0.971861\pi\)
0.753965 0.656914i \(-0.228139\pi\)
\(788\) −8.55843 6.21806i −0.304881 0.221509i
\(789\) 20.2957 14.7457i 0.722545 0.524959i
\(790\) 9.36396 28.8193i 0.333155 1.02535i
\(791\) −13.4939 −0.479787
\(792\) −2.14896 2.52626i −0.0763600 0.0897666i
\(793\) 4.07646 0.144759
\(794\) 9.50220 29.2448i 0.337220 1.03786i
\(795\) 9.46199 6.87454i 0.335582 0.243815i
\(796\) −13.5317 9.83138i −0.479619 0.348464i
\(797\) 3.73330 + 11.4899i 0.132240 + 0.406994i 0.995151 0.0983632i \(-0.0313607\pi\)
−0.862910 + 0.505357i \(0.831361\pi\)
\(798\) 1.66407 + 5.12147i 0.0589073 + 0.181298i
\(799\) 78.4825 + 57.0209i 2.77651 + 2.01725i
\(800\) −2.97709 + 2.16298i −0.105256 + 0.0764730i
\(801\) 2.66356 8.19760i 0.0941124 0.289648i
\(802\) 5.18982 0.183259
\(803\) 20.9547 + 5.07482i 0.739475 + 0.179087i
\(804\) −12.9240 −0.455793
\(805\) −0.646483 + 1.98967i −0.0227855 + 0.0701267i
\(806\) −2.16538 + 1.57324i −0.0762723 + 0.0554151i
\(807\) −21.4041 15.5510i −0.753461 0.547422i
\(808\) −1.05938 3.26042i −0.0372687 0.114701i
\(809\) −1.28660 3.95976i −0.0452346 0.139218i 0.925888 0.377797i \(-0.123318\pi\)
−0.971123 + 0.238579i \(0.923318\pi\)
\(810\) −2.38350 1.73171i −0.0837476 0.0608462i
\(811\) 11.4988 8.35439i 0.403778 0.293362i −0.367300 0.930103i \(-0.619718\pi\)
0.771078 + 0.636740i \(0.219718\pi\)
\(812\) −0.0293956 + 0.0904704i −0.00103158 + 0.00317489i
\(813\) −26.2873 −0.921935
\(814\) −3.98110 + 6.46769i −0.139538 + 0.226692i
\(815\) 56.5419 1.98058
\(816\) 2.26700 6.97709i 0.0793607 0.244247i
\(817\) 0.751891 0.546281i 0.0263053 0.0191119i
\(818\) −21.9141 15.9215i −0.766207 0.556682i
\(819\) −0.164066 0.504942i −0.00573291 0.0176441i
\(820\) −2.12687 6.54582i −0.0742734 0.228590i
\(821\) 20.6905 + 15.0325i 0.722102 + 0.524638i 0.887055 0.461663i \(-0.152747\pi\)
−0.164953 + 0.986301i \(0.552747\pi\)
\(822\) −13.9643 + 10.1457i −0.487062 + 0.353871i
\(823\) −5.80093 + 17.8534i −0.202208 + 0.622332i 0.797609 + 0.603175i \(0.206098\pi\)
−0.999816 + 0.0191565i \(0.993902\pi\)
\(824\) −0.180796 −0.00629833
\(825\) 0.933405 + 12.1691i 0.0324970 + 0.423672i
\(826\) −9.15698 −0.318612
\(827\) −0.0920121 + 0.283184i −0.00319957 + 0.00984728i −0.952644 0.304089i \(-0.901648\pi\)
0.949444 + 0.313936i \(0.101648\pi\)
\(828\) 0.574481 0.417385i 0.0199646 0.0145051i
\(829\) 9.47190 + 6.88174i 0.328973 + 0.239013i 0.739995 0.672613i \(-0.234828\pi\)
−0.411022 + 0.911625i \(0.634828\pi\)
\(830\) −13.3910 41.2131i −0.464807 1.43053i
\(831\) 1.92101 + 5.91225i 0.0666390 + 0.205094i
\(832\) 0.429529 + 0.312071i 0.0148912 + 0.0108191i
\(833\) −5.93507 + 4.31208i −0.205638 + 0.149405i
\(834\) −5.39283 + 16.5974i −0.186739 + 0.574722i
\(835\) 45.8207 1.58569
\(836\) −16.5141 + 6.80198i −0.571154 + 0.235251i
\(837\) −5.04129 −0.174253
\(838\) −7.27399 + 22.3870i −0.251276 + 0.773347i
\(839\) −37.9109 + 27.5438i −1.30883 + 0.950919i −1.00000 0.000198649i \(-0.999937\pi\)
−0.308828 + 0.951118i \(0.599937\pi\)
\(840\) −2.38350 1.73171i −0.0822385 0.0597498i
\(841\) −8.95870 27.5720i −0.308921 0.950760i
\(842\) −2.61298 8.04193i −0.0900493 0.277143i
\(843\) 24.9106 + 18.0986i 0.857967 + 0.623350i
\(844\) 9.99466 7.26155i 0.344030 0.249953i
\(845\) −11.5788 + 35.6358i −0.398322 + 1.22591i
\(846\) −13.2235 −0.454634
\(847\) −10.8713 + 1.67760i −0.373543 + 0.0576430i
\(848\) −3.96979 −0.136323
\(849\) −4.57872 + 14.0918i −0.157141 + 0.483631i
\(850\) −21.8404 + 15.8680i −0.749119 + 0.544267i
\(851\) −1.31550 0.955770i −0.0450949 0.0327634i
\(852\) 2.74337 + 8.44322i 0.0939863 + 0.289260i
\(853\) −10.6555 32.7944i −0.364839 1.12286i −0.950082 0.312000i \(-0.899001\pi\)
0.585243 0.810858i \(-0.300999\pi\)
\(854\) 6.21163 + 4.51301i 0.212558 + 0.154432i
\(855\) −12.8352 + 9.32532i −0.438955 + 0.318919i
\(856\) 4.66407 14.3545i 0.159414 0.490627i
\(857\) 25.3446 0.865755 0.432878 0.901453i \(-0.357498\pi\)
0.432878 + 0.901453i \(0.357498\pi\)
\(858\) 1.62818 0.670629i 0.0555852 0.0228949i
\(859\) 2.18125 0.0744234 0.0372117 0.999307i \(-0.488152\pi\)
0.0372117 + 0.999307i \(0.488152\pi\)
\(860\) −0.157126 + 0.483585i −0.00535796 + 0.0164901i
\(861\) 1.88999 1.37315i 0.0644105 0.0467970i
\(862\) −25.8188 18.7584i −0.879391 0.638915i
\(863\) −10.6820 32.8758i −0.363620 1.11911i −0.950841 0.309680i \(-0.899778\pi\)
0.587221 0.809427i \(-0.300222\pi\)
\(864\) 0.309017 + 0.951057i 0.0105130 + 0.0323556i
\(865\) −53.4065 38.8021i −1.81587 1.31931i
\(866\) −32.6167 + 23.6974i −1.10836 + 0.805271i
\(867\) 11.3777 35.0170i 0.386408 1.18924i
\(868\) −5.04129 −0.171113
\(869\) 2.60889 + 34.0128i 0.0885006 + 1.15381i
\(870\) −0.280257 −0.00950161
\(871\) 2.12038 6.52585i 0.0718463 0.221120i
\(872\) −5.32966 + 3.87223i −0.180485 + 0.131130i
\(873\) 0.734536 + 0.533672i 0.0248603 + 0.0180621i
\(874\) −1.18165 3.63674i −0.0399698 0.123015i
\(875\) −1.20185 3.69891i −0.0406299 0.125046i
\(876\) −5.25919 3.82103i −0.177692 0.129101i
\(877\) 23.6161 17.1581i 0.797460 0.579389i −0.112708 0.993628i \(-0.535952\pi\)
0.910168 + 0.414239i \(0.135952\pi\)
\(878\) 9.35459 28.7905i 0.315702 0.971631i
\(879\) −12.4702 −0.420611
\(880\) 5.12204 8.32126i 0.172664 0.280510i
\(881\) 34.0184 1.14611 0.573054 0.819518i \(-0.305759\pi\)
0.573054 + 0.819518i \(0.305759\pi\)
\(882\) 0.309017 0.951057i 0.0104051 0.0320237i
\(883\) 28.3721 20.6135i 0.954797 0.693701i 0.00286069 0.999996i \(-0.499089\pi\)
0.951937 + 0.306295i \(0.0990894\pi\)
\(884\) 3.15109 + 2.28940i 0.105983 + 0.0770009i
\(885\) −8.33665 25.6576i −0.280234 0.862470i
\(886\) 0.974697 + 2.99981i 0.0327456 + 0.100781i
\(887\) 7.46505 + 5.42368i 0.250652 + 0.182109i 0.706016 0.708196i \(-0.250491\pi\)
−0.455364 + 0.890305i \(0.650491\pi\)
\(888\) 1.85257 1.34597i 0.0621682 0.0451678i
\(889\) 1.05640 3.25125i 0.0354304 0.109043i
\(890\) 25.3944 0.851222
\(891\) 3.22344 + 0.780656i 0.107989 + 0.0261530i
\(892\) 13.2861 0.444852
\(893\) −22.0048 + 67.7238i −0.736363 + 2.26629i
\(894\) 8.17421 5.93891i 0.273387 0.198627i
\(895\) 43.7487 + 31.7853i 1.46236 + 1.06246i
\(896\) 0.309017 + 0.951057i 0.0103235 + 0.0317726i
\(897\) 0.116502 + 0.358558i 0.00388990 + 0.0119719i
\(898\) −15.7377 11.4341i −0.525175 0.381562i
\(899\) −0.387971 + 0.281878i −0.0129396 + 0.00940114i
\(900\) 1.13715 3.49978i 0.0379049 0.116659i
\(901\) −29.1230 −0.970227
\(902\) 5.02030 + 5.90171i 0.167158 + 0.196506i
\(903\) −0.172587 −0.00574335
\(904\) −4.16983 + 12.8334i −0.138687 + 0.426834i
\(905\) 7.94229 5.77041i 0.264011 0.191815i
\(906\) 3.05558 + 2.22001i 0.101515 + 0.0737549i
\(907\) −8.25897 25.4185i −0.274235 0.844007i −0.989421 0.145073i \(-0.953658\pi\)
0.715186 0.698934i \(-0.246342\pi\)
\(908\) −4.65576 14.3290i −0.154507 0.475523i
\(909\) 2.77348 + 2.01505i 0.0919906 + 0.0668351i
\(910\) 1.26546 0.919413i 0.0419497 0.0304782i
\(911\) 17.2785 53.1778i 0.572463 1.76186i −0.0721959 0.997390i \(-0.523001\pi\)
0.644659 0.764470i \(-0.276999\pi\)
\(912\) 5.38503 0.178316
\(913\) 31.6083 + 37.1578i 1.04608 + 1.22974i
\(914\) −37.8130 −1.25074
\(915\) −6.99016 + 21.5135i −0.231088 + 0.711215i
\(916\) 6.78078 4.92653i 0.224043 0.162777i
\(917\) −3.90167 2.83473i −0.128844 0.0936109i
\(918\) 2.26700 + 6.97709i 0.0748220 + 0.230278i
\(919\) 0.116888 + 0.359744i 0.00385578 + 0.0118669i 0.952966 0.303078i \(-0.0980141\pi\)
−0.949110 + 0.314944i \(0.898014\pi\)
\(920\) 1.69251 + 1.22968i 0.0558006 + 0.0405415i
\(921\) 20.3092 14.7555i 0.669212 0.486211i
\(922\) 4.75429 14.6322i 0.156574 0.481885i
\(923\) −4.71343 −0.155144
\(924\) 3.22344 + 0.780656i 0.106043 + 0.0256817i
\(925\) −8.42659 −0.277064
\(926\) 4.25017 13.0807i 0.139669 0.429857i
\(927\) 0.146267 0.106269i 0.00480404 0.00349034i
\(928\) 0.0769587 + 0.0559138i 0.00252629 + 0.00183546i
\(929\) 14.6478 + 45.0813i 0.480578 + 1.47907i 0.838284 + 0.545234i \(0.183559\pi\)
−0.357706 + 0.933834i \(0.616441\pi\)
\(930\) −4.58967 14.1255i −0.150501 0.463195i
\(931\) −4.35658 3.16524i −0.142781 0.103737i
\(932\) 4.59797 3.34062i 0.150612 0.109426i
\(933\) 6.53619 20.1163i 0.213985 0.658579i
\(934\) −19.0316 −0.622734
\(935\) 37.5761 61.0460i 1.22887 1.99642i
\(936\) −0.530927 −0.0173539
\(937\) −8.65356 + 26.6329i −0.282699 + 0.870059i 0.704379 + 0.709824i \(0.251225\pi\)
−0.987079 + 0.160236i \(0.948775\pi\)
\(938\) 10.4557 7.59652i 0.341391 0.248035i
\(939\) −1.75898 1.27797i −0.0574020 0.0417050i
\(940\) −12.0389 37.0519i −0.392665 1.20850i
\(941\) −3.04399 9.36845i −0.0992313 0.305403i 0.889102 0.457709i \(-0.151330\pi\)
−0.988333 + 0.152307i \(0.951330\pi\)
\(942\) −17.7701 12.9107i −0.578980 0.420653i
\(943\) −1.34207 + 0.975073i −0.0437039 + 0.0317527i
\(944\) −2.82966 + 8.70881i −0.0920977 + 0.283447i
\(945\) 2.94617 0.0958388
\(946\) −0.0437769 0.570731i −0.00142331 0.0185561i
\(947\) 6.83921 0.222244 0.111122 0.993807i \(-0.464555\pi\)
0.111122 + 0.993807i \(0.464555\pi\)
\(948\) 3.17836 9.78198i 0.103228 0.317704i
\(949\) 2.79225 2.02869i 0.0906402 0.0658540i
\(950\) −16.0317 11.6477i −0.520138 0.377902i
\(951\) 0.784806 + 2.41538i 0.0254491 + 0.0783242i
\(952\) 2.26700 + 6.97709i 0.0734737 + 0.226129i
\(953\) −48.9900 35.5933i −1.58694 1.15298i −0.908146 0.418653i \(-0.862502\pi\)
−0.678795 0.734328i \(-0.737498\pi\)
\(954\) 3.21163 2.33338i 0.103980 0.0755461i
\(955\) −7.66227 + 23.5821i −0.247945 + 0.763097i
\(956\) 24.7635 0.800908
\(957\) 0.291721 0.120156i 0.00943001 0.00388411i
\(958\) 35.7596 1.15534
\(959\) 5.33390 16.4161i 0.172241 0.530102i
\(960\) −2.38350 + 1.73171i −0.0769271 + 0.0558908i
\(961\) 4.51867 + 3.28301i 0.145764 + 0.105903i
\(962\) 0.375694 + 1.15627i 0.0121129 + 0.0372796i
\(963\) 4.66407 + 14.3545i 0.150297 + 0.462568i
\(964\) −7.21163 5.23955i −0.232271 0.168755i
\(965\) 16.4605 11.9593i 0.529883 0.384983i
\(966\) −0.219432 + 0.675342i −0.00706011 + 0.0217288i
\(967\) −34.1168 −1.09712 −0.548560 0.836111i \(-0.684824\pi\)
−0.548560 + 0.836111i \(0.684824\pi\)
\(968\) −1.76393 + 10.8576i −0.0566949 + 0.348978i
\(969\) 39.5054 1.26910
\(970\) −0.826599 + 2.54401i −0.0265405 + 0.0816833i
\(971\) −7.63458 + 5.54684i −0.245005 + 0.178007i −0.703510 0.710685i \(-0.748385\pi\)
0.458505 + 0.888692i \(0.348385\pi\)
\(972\) −0.809017 0.587785i −0.0259492 0.0188532i
\(973\) −5.39283 16.5974i −0.172886 0.532089i
\(974\) −9.72060 29.9169i −0.311468 0.958600i
\(975\) 1.58062 + 1.14839i 0.0506203 + 0.0367778i
\(976\) 6.21163 4.51301i 0.198829 0.144458i
\(977\) 16.9493 52.1646i 0.542256 1.66889i −0.185169 0.982707i \(-0.559283\pi\)
0.727426 0.686187i \(-0.240717\pi\)
\(978\) 19.1917 0.613683
\(979\) −26.4331 + 10.8875i −0.844807 + 0.347966i
\(980\) 2.94617 0.0941118
\(981\) 2.03575 6.26539i 0.0649965 0.200039i
\(982\) 18.8669 13.7076i 0.602068 0.437428i
\(983\) −21.1135 15.3399i −0.673417 0.489266i 0.197750 0.980252i \(-0.436636\pi\)
−0.871167 + 0.490986i \(0.836636\pi\)
\(984\) −0.721910 2.22181i −0.0230137 0.0708287i
\(985\) 9.63110 + 29.6415i 0.306872 + 0.944456i
\(986\) 0.564580 + 0.410192i 0.0179799 + 0.0130632i
\(987\) 10.6981 7.77259i 0.340523 0.247404i
\(988\) −0.883498 + 2.71913i −0.0281078 + 0.0865069i
\(989\) 0.122554 0.00389698
\(990\) 0.747296 + 9.74271i 0.0237506 + 0.309644i
\(991\) −16.8285 −0.534574 −0.267287 0.963617i \(-0.586127\pi\)
−0.267287 + 0.963617i \(0.586127\pi\)
\(992\) −1.55784 + 4.79455i −0.0494616 + 0.152227i
\(993\) 11.0421 8.02256i 0.350411 0.254588i
\(994\) −7.18223 5.21820i −0.227807 0.165511i
\(995\) 15.2277 + 46.8661i 0.482751 + 1.48576i
\(996\) −4.54522 13.9887i −0.144021 0.443250i
\(997\) −11.1209 8.07979i −0.352202 0.255890i 0.397590 0.917563i \(-0.369847\pi\)
−0.749792 + 0.661673i \(0.769847\pi\)
\(998\) −1.85774 + 1.34973i −0.0588058 + 0.0427249i
\(999\) −0.707619 + 2.17783i −0.0223881 + 0.0689034i
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 462.2.j.e.295.2 8
11.4 even 5 5082.2.a.cf.1.4 4
11.5 even 5 inner 462.2.j.e.379.2 yes 8
11.7 odd 10 5082.2.a.ca.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
462.2.j.e.295.2 8 1.1 even 1 trivial
462.2.j.e.379.2 yes 8 11.5 even 5 inner
5082.2.a.ca.1.4 4 11.7 odd 10
5082.2.a.cf.1.4 4 11.4 even 5