Properties

Label 187.2.g.e.103.2
Level $187$
Weight $2$
Character 187.103
Analytic conductor $1.493$
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] = [187,2,Mod(69,187)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(187, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("187.69");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 187 = 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 187.g (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: \(1.49320251780\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 103.2
Root \(-0.227943 - 0.701538i\) of defining polynomial
Character \(\chi\) \(=\) 187.103
Dual form 187.2.g.e.69.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.965584 + 0.701538i) q^{2} +(0.418926 - 1.28932i) q^{3} +(-0.177837 - 0.547326i) q^{4} +(-0.131180 + 0.0953077i) q^{5} +(1.30902 - 0.951057i) q^{6} +(0.0598032 + 0.184055i) q^{7} +(0.949894 - 2.92347i) q^{8} +(0.940197 + 0.683093i) q^{9} +O(q^{10})\) \(q+(0.965584 + 0.701538i) q^{2} +(0.418926 - 1.28932i) q^{3} +(-0.177837 - 0.547326i) q^{4} +(-0.131180 + 0.0953077i) q^{5} +(1.30902 - 0.951057i) q^{6} +(0.0598032 + 0.184055i) q^{7} +(0.949894 - 2.92347i) q^{8} +(0.940197 + 0.683093i) q^{9} -0.193527 q^{10} +(3.04508 + 1.31433i) q^{11} -0.780181 q^{12} +(-3.25587 - 2.36553i) q^{13} +(-0.0713767 + 0.219675i) q^{14} +(0.0679277 + 0.209060i) q^{15} +(2.03696 - 1.47994i) q^{16} +(0.809017 - 0.587785i) q^{17} +(0.428623 + 1.31917i) q^{18} +(-1.80344 + 5.55041i) q^{19} +(0.0754931 + 0.0548489i) q^{20} +0.262360 q^{21} +(2.01823 + 3.40534i) q^{22} -9.42270 q^{23} +(-3.37136 - 2.44944i) q^{24} +(-1.53696 + 4.73028i) q^{25} +(-1.48431 - 4.56824i) q^{26} +(4.56489 - 3.31659i) q^{27} +(0.0901031 - 0.0654637i) q^{28} +(2.45589 + 7.55844i) q^{29} +(-0.0810736 + 0.249519i) q^{30} +(0.530300 + 0.385285i) q^{31} -3.14275 q^{32} +(2.97026 - 3.37549i) q^{33} +1.19353 q^{34} +(-0.0253869 - 0.0184446i) q^{35} +(0.206673 - 0.636074i) q^{36} +(0.983405 + 3.02661i) q^{37} +(-5.63519 + 4.09420i) q^{38} +(-4.41391 + 3.20689i) q^{39} +(0.154023 + 0.474033i) q^{40} +(-1.71982 + 5.29306i) q^{41} +(0.253330 + 0.184055i) q^{42} +3.95431 q^{43} +(0.177837 - 1.90039i) q^{44} -0.188439 q^{45} +(-9.09840 - 6.61038i) q^{46} +(3.86192 - 11.8858i) q^{47} +(-1.05478 - 3.24628i) q^{48} +(5.63282 - 4.09248i) q^{49} +(-4.80253 + 3.48924i) q^{50} +(-0.418926 - 1.28932i) q^{51} +(-0.715702 + 2.20271i) q^{52} +(-4.43675 - 3.22349i) q^{53} +6.73450 q^{54} +(-0.524719 + 0.117807i) q^{55} +0.594887 q^{56} +(6.40076 + 4.65042i) q^{57} +(-2.93117 + 9.02121i) q^{58} +(-4.10047 - 12.6199i) q^{59} +(0.102344 - 0.0743573i) q^{60} +(-1.62706 + 1.18213i) q^{61} +(0.241757 + 0.744051i) q^{62} +(-0.0695001 + 0.213899i) q^{63} +(-7.10851 - 5.16464i) q^{64} +0.652559 q^{65} +(5.23607 - 1.17557i) q^{66} -5.26745 q^{67} +(-0.465584 - 0.338266i) q^{68} +(-3.94742 + 12.1489i) q^{69} +(-0.0115735 - 0.0356197i) q^{70} +(6.55987 - 4.76602i) q^{71} +(2.89009 - 2.09977i) q^{72} +(1.56482 + 4.81603i) q^{73} +(-1.17372 + 3.61234i) q^{74} +(5.45498 + 3.96328i) q^{75} +3.35860 q^{76} +(-0.0598032 + 0.639065i) q^{77} -6.51175 q^{78} +(3.07246 + 2.23227i) q^{79} +(-0.126159 + 0.388276i) q^{80} +(-1.28643 - 3.95922i) q^{81} +(-5.37391 + 3.90437i) q^{82} +(4.62549 - 3.36062i) q^{83} +(-0.0466573 - 0.143596i) q^{84} +(-0.0501062 + 0.154211i) q^{85} +(3.81822 + 2.77410i) q^{86} +10.7741 q^{87} +(6.73491 - 7.65375i) q^{88} -7.62131 q^{89} +(-0.181954 - 0.132197i) q^{90} +(0.240677 - 0.740727i) q^{91} +(1.67571 + 5.15729i) q^{92} +(0.718914 - 0.522322i) q^{93} +(12.0673 - 8.76743i) q^{94} +(-0.292422 - 0.899983i) q^{95} +(-1.31658 + 4.05202i) q^{96} +(8.18202 + 5.94459i) q^{97} +8.30999 q^{98} +(1.96517 + 3.31580i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - q^{2} + 3 q^{3} + 5 q^{4} - 3 q^{5} + 6 q^{6} + 3 q^{7} + 6 q^{8} + 5 q^{9} + 12 q^{10} + 2 q^{11} + 2 q^{12} + 3 q^{13} - 10 q^{15} + 7 q^{16} + 2 q^{17} + 4 q^{18} - 5 q^{19} - 4 q^{20} + 6 q^{21} - 9 q^{22} - 24 q^{23} - 7 q^{24} - 3 q^{25} - 19 q^{26} + 3 q^{27} + 16 q^{28} + 10 q^{29} - q^{30} + 17 q^{31} - 24 q^{32} - 8 q^{33} - 4 q^{34} + 6 q^{35} - q^{36} - 13 q^{37} - 38 q^{38} - 11 q^{39} + 15 q^{40} - 22 q^{41} - 9 q^{42} + 8 q^{43} - 5 q^{44} - 24 q^{45} - 20 q^{46} + 9 q^{47} + 13 q^{48} + q^{49} - q^{50} - 3 q^{51} - 18 q^{52} - 23 q^{53} + 22 q^{54} - 12 q^{55} + 2 q^{56} + 16 q^{57} - 6 q^{58} - 35 q^{59} - q^{60} - 19 q^{61} - 6 q^{62} - 4 q^{63} + 8 q^{64} + 10 q^{65} + 24 q^{66} - 10 q^{67} + 5 q^{68} + 12 q^{69} + 3 q^{70} - 5 q^{71} + 19 q^{72} + 39 q^{73} - 7 q^{74} + 6 q^{75} + 32 q^{76} - 3 q^{77} + 6 q^{78} - 3 q^{79} + 21 q^{80} + 7 q^{81} - 5 q^{82} + 29 q^{83} + 8 q^{84} - 2 q^{85} - 14 q^{86} + 32 q^{87} + 9 q^{88} + 40 q^{89} + 9 q^{90} + 21 q^{91} + 12 q^{92} - 14 q^{93} + 40 q^{94} + 23 q^{95} - 12 q^{96} - 5 q^{97} + 30 q^{98} + 20 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).

\(n\) \(35\) \(122\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965584 + 0.701538i 0.682771 + 0.496062i 0.874276 0.485430i \(-0.161337\pi\)
−0.191505 + 0.981492i \(0.561337\pi\)
\(3\) 0.418926 1.28932i 0.241867 0.744391i −0.754269 0.656566i \(-0.772008\pi\)
0.996136 0.0878250i \(-0.0279916\pi\)
\(4\) −0.177837 0.547326i −0.0889186 0.273663i
\(5\) −0.131180 + 0.0953077i −0.0586654 + 0.0426229i −0.616731 0.787174i \(-0.711544\pi\)
0.558066 + 0.829797i \(0.311544\pi\)
\(6\) 1.30902 0.951057i 0.534404 0.388267i
\(7\) 0.0598032 + 0.184055i 0.0226035 + 0.0695663i 0.961722 0.274027i \(-0.0883558\pi\)
−0.939119 + 0.343593i \(0.888356\pi\)
\(8\) 0.949894 2.92347i 0.335838 1.03360i
\(9\) 0.940197 + 0.683093i 0.313399 + 0.227698i
\(10\) −0.193527 −0.0611986
\(11\) 3.04508 + 1.31433i 0.918128 + 0.396285i
\(12\) −0.780181 −0.225219
\(13\) −3.25587 2.36553i −0.903017 0.656080i 0.0362221 0.999344i \(-0.488468\pi\)
−0.939239 + 0.343263i \(0.888468\pi\)
\(14\) −0.0713767 + 0.219675i −0.0190762 + 0.0587106i
\(15\) 0.0679277 + 0.209060i 0.0175389 + 0.0539791i
\(16\) 2.03696 1.47994i 0.509240 0.369985i
\(17\) 0.809017 0.587785i 0.196215 0.142559i
\(18\) 0.428623 + 1.31917i 0.101027 + 0.310931i
\(19\) −1.80344 + 5.55041i −0.413737 + 1.27335i 0.499639 + 0.866234i \(0.333466\pi\)
−0.913376 + 0.407117i \(0.866534\pi\)
\(20\) 0.0754931 + 0.0548489i 0.0168808 + 0.0122646i
\(21\) 0.262360 0.0572516
\(22\) 2.01823 + 3.40534i 0.430289 + 0.726020i
\(23\) −9.42270 −1.96477 −0.982384 0.186873i \(-0.940165\pi\)
−0.982384 + 0.186873i \(0.940165\pi\)
\(24\) −3.37136 2.44944i −0.688177 0.499990i
\(25\) −1.53696 + 4.73028i −0.307392 + 0.946056i
\(26\) −1.48431 4.56824i −0.291097 0.895905i
\(27\) 4.56489 3.31659i 0.878514 0.638278i
\(28\) 0.0901031 0.0654637i 0.0170279 0.0123715i
\(29\) 2.45589 + 7.55844i 0.456047 + 1.40357i 0.869902 + 0.493225i \(0.164182\pi\)
−0.413855 + 0.910343i \(0.635818\pi\)
\(30\) −0.0810736 + 0.249519i −0.0148019 + 0.0455557i
\(31\) 0.530300 + 0.385285i 0.0952447 + 0.0691993i 0.634388 0.773014i \(-0.281252\pi\)
−0.539144 + 0.842214i \(0.681252\pi\)
\(32\) −3.14275 −0.555566
\(33\) 2.97026 3.37549i 0.517056 0.587598i
\(34\) 1.19353 0.204688
\(35\) −0.0253869 0.0184446i −0.00429116 0.00311771i
\(36\) 0.206673 0.636074i 0.0344455 0.106012i
\(37\) 0.983405 + 3.02661i 0.161671 + 0.497572i 0.998776 0.0494710i \(-0.0157535\pi\)
−0.837105 + 0.547043i \(0.815754\pi\)
\(38\) −5.63519 + 4.09420i −0.914148 + 0.664168i
\(39\) −4.41391 + 3.20689i −0.706790 + 0.513513i
\(40\) 0.154023 + 0.474033i 0.0243531 + 0.0749512i
\(41\) −1.71982 + 5.29306i −0.268591 + 0.826637i 0.722254 + 0.691628i \(0.243106\pi\)
−0.990844 + 0.135009i \(0.956894\pi\)
\(42\) 0.253330 + 0.184055i 0.0390897 + 0.0284003i
\(43\) 3.95431 0.603027 0.301514 0.953462i \(-0.402508\pi\)
0.301514 + 0.953462i \(0.402508\pi\)
\(44\) 0.177837 1.90039i 0.0268100 0.286495i
\(45\) −0.188439 −0.0280908
\(46\) −9.09840 6.61038i −1.34149 0.974647i
\(47\) 3.86192 11.8858i 0.563319 1.73372i −0.109574 0.993979i \(-0.534949\pi\)
0.672893 0.739740i \(-0.265051\pi\)
\(48\) −1.05478 3.24628i −0.152245 0.468561i
\(49\) 5.63282 4.09248i 0.804688 0.584640i
\(50\) −4.80253 + 3.48924i −0.679181 + 0.493454i
\(51\) −0.418926 1.28932i −0.0586614 0.180541i
\(52\) −0.715702 + 2.20271i −0.0992501 + 0.305460i
\(53\) −4.43675 3.22349i −0.609434 0.442780i 0.239781 0.970827i \(-0.422924\pi\)
−0.849215 + 0.528047i \(0.822924\pi\)
\(54\) 6.73450 0.916449
\(55\) −0.524719 + 0.117807i −0.0707531 + 0.0158851i
\(56\) 0.594887 0.0794951
\(57\) 6.40076 + 4.65042i 0.847801 + 0.615964i
\(58\) −2.93117 + 9.02121i −0.384881 + 1.18454i
\(59\) −4.10047 12.6199i −0.533835 1.64298i −0.746152 0.665775i \(-0.768101\pi\)
0.212317 0.977201i \(-0.431899\pi\)
\(60\) 0.102344 0.0743573i 0.0132126 0.00959949i
\(61\) −1.62706 + 1.18213i −0.208324 + 0.151356i −0.687055 0.726605i \(-0.741097\pi\)
0.478731 + 0.877962i \(0.341097\pi\)
\(62\) 0.241757 + 0.744051i 0.0307031 + 0.0944945i
\(63\) −0.0695001 + 0.213899i −0.00875619 + 0.0269488i
\(64\) −7.10851 5.16464i −0.888564 0.645580i
\(65\) 0.652559 0.0809399
\(66\) 5.23607 1.17557i 0.644515 0.144703i
\(67\) −5.26745 −0.643521 −0.321761 0.946821i \(-0.604275\pi\)
−0.321761 + 0.946821i \(0.604275\pi\)
\(68\) −0.465584 0.338266i −0.0564603 0.0410208i
\(69\) −3.94742 + 12.1489i −0.475213 + 1.46256i
\(70\) −0.0115735 0.0356197i −0.00138330 0.00425736i
\(71\) 6.55987 4.76602i 0.778513 0.565623i −0.126019 0.992028i \(-0.540220\pi\)
0.904532 + 0.426405i \(0.140220\pi\)
\(72\) 2.89009 2.09977i 0.340600 0.247461i
\(73\) 1.56482 + 4.81603i 0.183149 + 0.563674i 0.999912 0.0132995i \(-0.00423350\pi\)
−0.816763 + 0.576974i \(0.804233\pi\)
\(74\) −1.17372 + 3.61234i −0.136442 + 0.419926i
\(75\) 5.45498 + 3.96328i 0.629887 + 0.457640i
\(76\) 3.35860 0.385258
\(77\) −0.0598032 + 0.639065i −0.00681520 + 0.0728282i
\(78\) −6.51175 −0.737310
\(79\) 3.07246 + 2.23227i 0.345678 + 0.251150i 0.747054 0.664764i \(-0.231468\pi\)
−0.401375 + 0.915914i \(0.631468\pi\)
\(80\) −0.126159 + 0.388276i −0.0141050 + 0.0434106i
\(81\) −1.28643 3.95922i −0.142937 0.439914i
\(82\) −5.37391 + 3.90437i −0.593449 + 0.431166i
\(83\) 4.62549 3.36062i 0.507714 0.368876i −0.304242 0.952595i \(-0.598403\pi\)
0.811956 + 0.583719i \(0.198403\pi\)
\(84\) −0.0466573 0.143596i −0.00509073 0.0156677i
\(85\) −0.0501062 + 0.154211i −0.00543479 + 0.0167265i
\(86\) 3.81822 + 2.77410i 0.411729 + 0.299139i
\(87\) 10.7741 1.15511
\(88\) 6.73491 7.65375i 0.717944 0.815892i
\(89\) −7.62131 −0.807858 −0.403929 0.914790i \(-0.632356\pi\)
−0.403929 + 0.914790i \(0.632356\pi\)
\(90\) −0.181954 0.132197i −0.0191796 0.0139348i
\(91\) 0.240677 0.740727i 0.0252298 0.0776493i
\(92\) 1.67571 + 5.15729i 0.174704 + 0.537685i
\(93\) 0.718914 0.522322i 0.0745479 0.0541622i
\(94\) 12.0673 8.76743i 1.24465 0.904291i
\(95\) −0.292422 0.899983i −0.0300019 0.0923363i
\(96\) −1.31658 + 4.05202i −0.134373 + 0.413558i
\(97\) 8.18202 + 5.94459i 0.830758 + 0.603581i 0.919774 0.392449i \(-0.128372\pi\)
−0.0890155 + 0.996030i \(0.528372\pi\)
\(98\) 8.30999 0.839436
\(99\) 1.96517 + 3.31580i 0.197507 + 0.333251i
\(100\) 2.86233 0.286233
\(101\) −8.66566 6.29597i −0.862266 0.626473i 0.0662347 0.997804i \(-0.478901\pi\)
−0.928500 + 0.371331i \(0.878901\pi\)
\(102\) 0.500000 1.53884i 0.0495074 0.152368i
\(103\) −1.33283 4.10203i −0.131328 0.404185i 0.863673 0.504053i \(-0.168158\pi\)
−0.995001 + 0.0998672i \(0.968158\pi\)
\(104\) −10.0083 + 7.27146i −0.981395 + 0.713025i
\(105\) −0.0344163 + 0.0250049i −0.00335869 + 0.00244023i
\(106\) −2.02265 6.22509i −0.196458 0.604634i
\(107\) −6.18293 + 19.0291i −0.597726 + 1.83961i −0.0570654 + 0.998370i \(0.518174\pi\)
−0.540661 + 0.841241i \(0.681826\pi\)
\(108\) −2.62706 1.90867i −0.252789 0.183662i
\(109\) −2.95543 −0.283079 −0.141540 0.989933i \(-0.545205\pi\)
−0.141540 + 0.989933i \(0.545205\pi\)
\(110\) −0.589306 0.254358i −0.0561882 0.0242521i
\(111\) 4.31425 0.409491
\(112\) 0.394207 + 0.286408i 0.0372491 + 0.0270630i
\(113\) 3.08123 9.48305i 0.289858 0.892091i −0.695043 0.718969i \(-0.744614\pi\)
0.984900 0.173122i \(-0.0553855\pi\)
\(114\) 2.91802 + 8.98075i 0.273298 + 0.841124i
\(115\) 1.23607 0.898056i 0.115264 0.0837441i
\(116\) 3.70019 2.68834i 0.343554 0.249606i
\(117\) −1.44529 4.44813i −0.133617 0.411230i
\(118\) 4.89402 15.0622i 0.450531 1.38659i
\(119\) 0.156567 + 0.113752i 0.0143524 + 0.0104277i
\(120\) 0.675706 0.0616832
\(121\) 7.54508 + 8.00448i 0.685917 + 0.727680i
\(122\) −2.40038 −0.217320
\(123\) 6.10398 + 4.43480i 0.550378 + 0.399873i
\(124\) 0.116570 0.358765i 0.0104683 0.0322181i
\(125\) −0.499745 1.53806i −0.0446986 0.137568i
\(126\) −0.217166 + 0.157781i −0.0193467 + 0.0140562i
\(127\) 13.6400 9.91007i 1.21036 0.879376i 0.215095 0.976593i \(-0.430994\pi\)
0.995263 + 0.0972169i \(0.0309940\pi\)
\(128\) −1.29835 3.99591i −0.114759 0.353191i
\(129\) 1.65657 5.09839i 0.145853 0.448888i
\(130\) 0.630100 + 0.457794i 0.0552634 + 0.0401512i
\(131\) −9.93575 −0.868090 −0.434045 0.900891i \(-0.642914\pi\)
−0.434045 + 0.900891i \(0.642914\pi\)
\(132\) −2.37572 1.02541i −0.206780 0.0892508i
\(133\) −1.12943 −0.0979342
\(134\) −5.08616 3.69531i −0.439377 0.319226i
\(135\) −0.282725 + 0.870139i −0.0243331 + 0.0748896i
\(136\) −0.949894 2.92347i −0.0814527 0.250686i
\(137\) −8.00673 + 5.81723i −0.684061 + 0.496999i −0.874702 0.484660i \(-0.838943\pi\)
0.190642 + 0.981660i \(0.438943\pi\)
\(138\) −12.3345 + 8.96152i −1.04998 + 0.762855i
\(139\) −3.59579 11.0667i −0.304991 0.938666i −0.979681 0.200564i \(-0.935722\pi\)
0.674689 0.738102i \(-0.264278\pi\)
\(140\) −0.00558051 + 0.0171750i −0.000471639 + 0.00145156i
\(141\) −13.7067 9.95853i −1.15432 0.838659i
\(142\) 9.67765 0.812130
\(143\) −6.80533 11.4825i −0.569090 0.960217i
\(144\) 2.92608 0.243840
\(145\) −1.04254 0.757450i −0.0865783 0.0629028i
\(146\) −1.86766 + 5.74807i −0.154569 + 0.475713i
\(147\) −2.91679 8.97697i −0.240573 0.740408i
\(148\) 1.48166 1.07649i 0.121792 0.0884867i
\(149\) 3.29800 2.39614i 0.270183 0.196299i −0.444441 0.895808i \(-0.646598\pi\)
0.714624 + 0.699509i \(0.246598\pi\)
\(150\) 2.48685 + 7.65375i 0.203051 + 0.624926i
\(151\) −1.63956 + 5.04604i −0.133425 + 0.410641i −0.995342 0.0964092i \(-0.969264\pi\)
0.861916 + 0.507051i \(0.169264\pi\)
\(152\) 14.5134 + 10.5446i 1.17719 + 0.855279i
\(153\) 1.16215 0.0939540
\(154\) −0.506073 + 0.575116i −0.0407805 + 0.0463442i
\(155\) −0.106285 −0.00853704
\(156\) 2.54017 + 1.84554i 0.203377 + 0.147762i
\(157\) −5.93518 + 18.2666i −0.473679 + 1.45783i 0.374053 + 0.927407i \(0.377968\pi\)
−0.847732 + 0.530425i \(0.822032\pi\)
\(158\) 1.40069 + 4.31089i 0.111433 + 0.342956i
\(159\) −6.01479 + 4.37000i −0.477003 + 0.346563i
\(160\) 0.412266 0.299529i 0.0325925 0.0236798i
\(161\) −0.563507 1.73430i −0.0444106 0.136682i
\(162\) 1.53539 4.72544i 0.120631 0.371266i
\(163\) 0.317142 + 0.230417i 0.0248404 + 0.0180476i 0.600136 0.799898i \(-0.295113\pi\)
−0.575296 + 0.817945i \(0.695113\pi\)
\(164\) 3.20288 0.250103
\(165\) −0.0679277 + 0.725885i −0.00528817 + 0.0565101i
\(166\) 6.82390 0.529637
\(167\) −15.1024 10.9725i −1.16866 0.849081i −0.177812 0.984065i \(-0.556902\pi\)
−0.990848 + 0.134984i \(0.956902\pi\)
\(168\) 0.249214 0.767001i 0.0192273 0.0591754i
\(169\) 0.987759 + 3.04001i 0.0759815 + 0.233847i
\(170\) −0.156567 + 0.113752i −0.0120081 + 0.00872441i
\(171\) −5.48703 + 3.98656i −0.419604 + 0.304860i
\(172\) −0.703224 2.16430i −0.0536203 0.165026i
\(173\) 2.12484 6.53959i 0.161549 0.497196i −0.837217 0.546871i \(-0.815819\pi\)
0.998765 + 0.0496755i \(0.0158187\pi\)
\(174\) 10.4033 + 7.55844i 0.788672 + 0.573004i
\(175\) −0.962547 −0.0727617
\(176\) 8.14784 1.82930i 0.614167 0.137889i
\(177\) −17.9890 −1.35213
\(178\) −7.35902 5.34664i −0.551581 0.400747i
\(179\) −0.833736 + 2.56598i −0.0623164 + 0.191790i −0.977368 0.211547i \(-0.932150\pi\)
0.915051 + 0.403337i \(0.132150\pi\)
\(180\) 0.0335114 + 0.103138i 0.00249780 + 0.00768742i
\(181\) −5.57006 + 4.04688i −0.414019 + 0.300803i −0.775227 0.631683i \(-0.782365\pi\)
0.361208 + 0.932485i \(0.382365\pi\)
\(182\) 0.752041 0.546390i 0.0557450 0.0405011i
\(183\) 0.842528 + 2.59304i 0.0622815 + 0.191683i
\(184\) −8.95056 + 27.5470i −0.659844 + 2.03079i
\(185\) −0.417462 0.303304i −0.0306924 0.0222994i
\(186\) 1.06060 0.0777670
\(187\) 3.23607 0.726543i 0.236645 0.0531301i
\(188\) −7.19219 −0.524545
\(189\) 0.883430 + 0.641850i 0.0642601 + 0.0466877i
\(190\) 0.349014 1.07415i 0.0253201 0.0779273i
\(191\) −4.30145 13.2385i −0.311242 0.957905i −0.977274 0.211981i \(-0.932008\pi\)
0.666032 0.745924i \(-0.267992\pi\)
\(192\) −9.63683 + 7.00156i −0.695478 + 0.505294i
\(193\) −9.43360 + 6.85391i −0.679046 + 0.493356i −0.873041 0.487647i \(-0.837855\pi\)
0.193995 + 0.981002i \(0.437855\pi\)
\(194\) 3.73007 + 11.4800i 0.267804 + 0.824215i
\(195\) 0.273374 0.841359i 0.0195767 0.0602509i
\(196\) −3.24165 2.35520i −0.231546 0.168228i
\(197\) 1.52179 0.108423 0.0542116 0.998529i \(-0.482735\pi\)
0.0542116 + 0.998529i \(0.482735\pi\)
\(198\) −0.428623 + 4.58033i −0.0304609 + 0.325510i
\(199\) 10.2278 0.725032 0.362516 0.931978i \(-0.381918\pi\)
0.362516 + 0.931978i \(0.381918\pi\)
\(200\) 12.3689 + 8.98652i 0.874612 + 0.635443i
\(201\) −2.20667 + 6.79144i −0.155647 + 0.479031i
\(202\) −3.95056 12.1586i −0.277961 0.855475i
\(203\) −1.24430 + 0.904037i −0.0873328 + 0.0634510i
\(204\) −0.631180 + 0.458579i −0.0441914 + 0.0321070i
\(205\) −0.278864 0.858255i −0.0194767 0.0599431i
\(206\) 1.59077 4.89589i 0.110834 0.341113i
\(207\) −8.85919 6.43658i −0.615756 0.447373i
\(208\) −10.1329 −0.702592
\(209\) −12.7867 + 14.5312i −0.884473 + 1.00514i
\(210\) −0.0507737 −0.00350372
\(211\) 16.3639 + 11.8891i 1.12654 + 0.818477i 0.985187 0.171483i \(-0.0548558\pi\)
0.141350 + 0.989960i \(0.454856\pi\)
\(212\) −0.975281 + 3.00161i −0.0669825 + 0.206151i
\(213\) −3.39684 10.4544i −0.232748 0.716324i
\(214\) −19.3198 + 14.0366i −1.32067 + 0.959524i
\(215\) −0.518726 + 0.376877i −0.0353768 + 0.0257028i
\(216\) −5.35979 16.4957i −0.364688 1.12239i
\(217\) −0.0392002 + 0.120646i −0.00266108 + 0.00818997i
\(218\) −2.85372 2.07335i −0.193278 0.140425i
\(219\) 6.86497 0.463892
\(220\) 0.157793 + 0.266242i 0.0106384 + 0.0179501i
\(221\) −4.02448 −0.270716
\(222\) 4.16577 + 3.02661i 0.279588 + 0.203133i
\(223\) 4.90619 15.0997i 0.328543 1.01115i −0.641273 0.767313i \(-0.721593\pi\)
0.969816 0.243838i \(-0.0784067\pi\)
\(224\) −0.187947 0.578440i −0.0125577 0.0386487i
\(225\) −4.67626 + 3.39751i −0.311751 + 0.226500i
\(226\) 9.62791 6.99508i 0.640439 0.465306i
\(227\) −2.25465 6.93909i −0.149646 0.460564i 0.847933 0.530103i \(-0.177847\pi\)
−0.997579 + 0.0695398i \(0.977847\pi\)
\(228\) 1.40701 4.33032i 0.0931813 0.286783i
\(229\) 7.61047 + 5.52933i 0.502914 + 0.365388i 0.810129 0.586252i \(-0.199397\pi\)
−0.307215 + 0.951640i \(0.599397\pi\)
\(230\) 1.82355 0.120241
\(231\) 0.798908 + 0.344827i 0.0525643 + 0.0226879i
\(232\) 24.4297 1.60389
\(233\) 9.55830 + 6.94451i 0.626185 + 0.454950i 0.855076 0.518502i \(-0.173510\pi\)
−0.228892 + 0.973452i \(0.573510\pi\)
\(234\) 1.72499 5.30896i 0.112766 0.347058i
\(235\) 0.626200 + 1.92725i 0.0408488 + 0.125720i
\(236\) −6.17801 + 4.48859i −0.402154 + 0.292182i
\(237\) 4.16525 3.02623i 0.270562 0.196575i
\(238\) 0.0713767 + 0.219675i 0.00462666 + 0.0142394i
\(239\) 4.24389 13.0613i 0.274514 0.844868i −0.714833 0.699295i \(-0.753497\pi\)
0.989347 0.145573i \(-0.0465026\pi\)
\(240\) 0.447762 + 0.325318i 0.0289029 + 0.0209992i
\(241\) −12.8523 −0.827889 −0.413944 0.910302i \(-0.635849\pi\)
−0.413944 + 0.910302i \(0.635849\pi\)
\(242\) 1.66997 + 13.0222i 0.107350 + 0.837096i
\(243\) 11.2839 0.723863
\(244\) 0.936364 + 0.680308i 0.0599445 + 0.0435523i
\(245\) −0.348867 + 1.07370i −0.0222883 + 0.0685963i
\(246\) 2.78273 + 8.56435i 0.177420 + 0.546043i
\(247\) 19.0014 13.8053i 1.20903 0.878413i
\(248\) 1.63010 1.18434i 0.103511 0.0752055i
\(249\) −2.39518 7.37160i −0.151788 0.467156i
\(250\) 0.596459 1.83571i 0.0377234 0.116101i
\(251\) −2.63743 1.91620i −0.166473 0.120950i 0.501429 0.865199i \(-0.332808\pi\)
−0.667902 + 0.744249i \(0.732808\pi\)
\(252\) 0.129432 0.00815348
\(253\) −28.6929 12.3845i −1.80391 0.778608i
\(254\) 20.1229 1.26262
\(255\) 0.177837 + 0.129206i 0.0111366 + 0.00809121i
\(256\) −3.88081 + 11.9439i −0.242550 + 0.746493i
\(257\) 0.374589 + 1.15287i 0.0233662 + 0.0719138i 0.962060 0.272839i \(-0.0879627\pi\)
−0.938693 + 0.344753i \(0.887963\pi\)
\(258\) 5.17626 3.76078i 0.322260 0.234136i
\(259\) −0.498253 + 0.362002i −0.0309599 + 0.0224937i
\(260\) −0.116049 0.357163i −0.00719706 0.0221503i
\(261\) −2.85410 + 8.78402i −0.176664 + 0.543717i
\(262\) −9.59379 6.97030i −0.592707 0.430627i
\(263\) 16.9095 1.04268 0.521342 0.853348i \(-0.325432\pi\)
0.521342 + 0.853348i \(0.325432\pi\)
\(264\) −7.04672 11.8898i −0.433696 0.731768i
\(265\) 0.889235 0.0546253
\(266\) −1.09056 0.792339i −0.0668666 0.0485814i
\(267\) −3.19277 + 9.82633i −0.195394 + 0.601362i
\(268\) 0.936748 + 2.88301i 0.0572210 + 0.176108i
\(269\) 19.1430 13.9082i 1.16717 0.847998i 0.176502 0.984300i \(-0.443522\pi\)
0.990667 + 0.136302i \(0.0435219\pi\)
\(270\) −0.883430 + 0.641850i −0.0537638 + 0.0390617i
\(271\) 3.61845 + 11.1364i 0.219805 + 0.676490i 0.998777 + 0.0494321i \(0.0157411\pi\)
−0.778973 + 0.627058i \(0.784259\pi\)
\(272\) 0.778050 2.39459i 0.0471762 0.145193i
\(273\) −0.854210 0.620620i −0.0516992 0.0375616i
\(274\) −11.8122 −0.713599
\(275\) −10.8973 + 12.3840i −0.657133 + 0.746785i
\(276\) 7.35141 0.442503
\(277\) −9.96048 7.23671i −0.598467 0.434812i 0.246867 0.969049i \(-0.420599\pi\)
−0.845335 + 0.534237i \(0.820599\pi\)
\(278\) 4.29167 13.2084i 0.257398 0.792188i
\(279\) 0.235401 + 0.724488i 0.0140931 + 0.0433740i
\(280\) −0.0780372 + 0.0566973i −0.00466361 + 0.00338831i
\(281\) 19.7509 14.3499i 1.17824 0.856043i 0.186270 0.982499i \(-0.440360\pi\)
0.991972 + 0.126455i \(0.0403599\pi\)
\(282\) −6.24872 19.2316i −0.372106 1.14522i
\(283\) 9.66561 29.7477i 0.574561 1.76832i −0.0631079 0.998007i \(-0.520101\pi\)
0.637669 0.770311i \(-0.279899\pi\)
\(284\) −3.77516 2.74281i −0.224015 0.162756i
\(285\) −1.28287 −0.0759908
\(286\) 1.48431 15.8615i 0.0877691 0.937912i
\(287\) −1.07707 −0.0635772
\(288\) −2.95481 2.14679i −0.174114 0.126501i
\(289\) 0.309017 0.951057i 0.0181775 0.0559445i
\(290\) −0.475281 1.46276i −0.0279094 0.0858964i
\(291\) 11.0922 8.05892i 0.650234 0.472422i
\(292\) 2.35766 1.71294i 0.137972 0.100242i
\(293\) 5.27501 + 16.2348i 0.308170 + 0.948448i 0.978475 + 0.206363i \(0.0661629\pi\)
−0.670306 + 0.742085i \(0.733837\pi\)
\(294\) 3.48127 10.7143i 0.203032 0.624868i
\(295\) 1.74068 + 1.26468i 0.101346 + 0.0736323i
\(296\) 9.78234 0.568587
\(297\) 18.2596 4.09953i 1.05953 0.237879i
\(298\) 4.86548 0.281850
\(299\) 30.6791 + 22.2897i 1.77422 + 1.28905i
\(300\) 1.19911 3.69047i 0.0692305 0.213070i
\(301\) 0.236480 + 0.727812i 0.0136305 + 0.0419504i
\(302\) −5.12312 + 3.72217i −0.294803 + 0.214187i
\(303\) −11.7478 + 8.53529i −0.674894 + 0.490340i
\(304\) 4.54073 + 13.9749i 0.260429 + 0.801517i
\(305\) 0.100772 0.310143i 0.00577017 0.0177588i
\(306\) 1.12215 + 0.815290i 0.0641491 + 0.0466070i
\(307\) −11.4475 −0.653343 −0.326672 0.945138i \(-0.605927\pi\)
−0.326672 + 0.945138i \(0.605927\pi\)
\(308\) 0.360412 0.0809176i 0.0205364 0.00461071i
\(309\) −5.84720 −0.332636
\(310\) −0.102627 0.0745632i −0.00582884 0.00423490i
\(311\) 1.45087 4.46530i 0.0822710 0.253204i −0.901457 0.432869i \(-0.857501\pi\)
0.983728 + 0.179665i \(0.0575013\pi\)
\(312\) 5.18251 + 15.9501i 0.293402 + 0.902999i
\(313\) 22.8655 16.6128i 1.29243 0.939009i 0.292583 0.956240i \(-0.405485\pi\)
0.999852 + 0.0172312i \(0.00548515\pi\)
\(314\) −18.5456 + 13.4742i −1.04659 + 0.760392i
\(315\) −0.0112692 0.0346832i −0.000634950 0.00195417i
\(316\) 0.675384 2.07862i 0.0379933 0.116931i
\(317\) −4.01371 2.91613i −0.225432 0.163786i 0.469336 0.883019i \(-0.344493\pi\)
−0.694769 + 0.719233i \(0.744493\pi\)
\(318\) −8.87350 −0.497601
\(319\) −2.45589 + 26.2439i −0.137503 + 1.46938i
\(320\) 1.42472 0.0796445
\(321\) 21.9444 + 15.9436i 1.22482 + 0.889884i
\(322\) 0.672561 2.06993i 0.0374804 0.115353i
\(323\) 1.80344 + 5.55041i 0.100346 + 0.308833i
\(324\) −1.93821 + 1.40819i −0.107678 + 0.0782330i
\(325\) 16.1938 11.7655i 0.898269 0.652630i
\(326\) 0.144581 + 0.444974i 0.00800758 + 0.0246448i
\(327\) −1.23811 + 3.81051i −0.0684676 + 0.210722i
\(328\) 13.8405 + 10.0557i 0.764212 + 0.555232i
\(329\) 2.41859 0.133341
\(330\) −0.574826 + 0.653249i −0.0316431 + 0.0359602i
\(331\) −30.4124 −1.67161 −0.835807 0.549023i \(-0.815000\pi\)
−0.835807 + 0.549023i \(0.815000\pi\)
\(332\) −2.66194 1.93401i −0.146093 0.106143i
\(333\) −1.14286 + 3.51737i −0.0626284 + 0.192750i
\(334\) −6.88499 21.1898i −0.376730 1.15946i
\(335\) 0.690983 0.502029i 0.0377524 0.0274287i
\(336\) 0.534416 0.388276i 0.0291548 0.0211822i
\(337\) 9.03897 + 27.8191i 0.492384 + 1.51540i 0.820994 + 0.570937i \(0.193420\pi\)
−0.328610 + 0.944466i \(0.606580\pi\)
\(338\) −1.17892 + 3.62833i −0.0641246 + 0.197355i
\(339\) −10.9359 7.94540i −0.593957 0.431535i
\(340\) 0.0933146 0.00506069
\(341\) 1.10842 + 1.87021i 0.0600241 + 0.101278i
\(342\) −8.09491 −0.437722
\(343\) 2.18607 + 1.58827i 0.118037 + 0.0857587i
\(344\) 3.75618 11.5603i 0.202520 0.623291i
\(345\) −0.640063 1.96991i −0.0344598 0.106056i
\(346\) 6.63948 4.82386i 0.356941 0.259333i
\(347\) −12.0906 + 8.78434i −0.649057 + 0.471568i −0.862950 0.505289i \(-0.831386\pi\)
0.213893 + 0.976857i \(0.431386\pi\)
\(348\) −1.91604 5.89695i −0.102710 0.316110i
\(349\) −8.45100 + 26.0095i −0.452372 + 1.39226i 0.421822 + 0.906679i \(0.361391\pi\)
−0.874193 + 0.485578i \(0.838609\pi\)
\(350\) −0.929420 0.675263i −0.0496796 0.0360943i
\(351\) −22.7082 −1.21207
\(352\) −9.56995 4.13061i −0.510080 0.220162i
\(353\) 22.6070 1.20325 0.601625 0.798779i \(-0.294520\pi\)
0.601625 + 0.798779i \(0.294520\pi\)
\(354\) −17.3699 12.6199i −0.923198 0.670742i
\(355\) −0.406284 + 1.25041i −0.0215633 + 0.0663650i
\(356\) 1.35535 + 4.17135i 0.0718335 + 0.221081i
\(357\) 0.212253 0.154211i 0.0112336 0.00816172i
\(358\) −2.60517 + 1.89277i −0.137688 + 0.100036i
\(359\) 6.91693 + 21.2881i 0.365062 + 1.12354i 0.949943 + 0.312425i \(0.101141\pi\)
−0.584881 + 0.811119i \(0.698859\pi\)
\(360\) −0.178997 + 0.550896i −0.00943397 + 0.0290348i
\(361\) −12.1833 8.85169i −0.641227 0.465879i
\(362\) −8.21740 −0.431897
\(363\) 13.4812 6.37476i 0.707579 0.334588i
\(364\) −0.448221 −0.0234931
\(365\) −0.664279 0.482627i −0.0347699 0.0252618i
\(366\) −1.00558 + 3.09486i −0.0525625 + 0.161771i
\(367\) 6.03505 + 18.5740i 0.315027 + 0.969554i 0.975743 + 0.218918i \(0.0702528\pi\)
−0.660716 + 0.750636i \(0.729747\pi\)
\(368\) −19.1937 + 13.9450i −1.00054 + 0.726934i
\(369\) −5.23262 + 3.80172i −0.272399 + 0.197910i
\(370\) −0.190316 0.585731i −0.00989403 0.0304507i
\(371\) 0.327968 1.00938i 0.0170272 0.0524045i
\(372\) −0.413730 0.300592i −0.0214509 0.0155850i
\(373\) −22.9224 −1.18688 −0.593439 0.804879i \(-0.702230\pi\)
−0.593439 + 0.804879i \(0.702230\pi\)
\(374\) 3.63439 + 1.56869i 0.187930 + 0.0811148i
\(375\) −2.19241 −0.113215
\(376\) −31.0793 22.5804i −1.60279 1.16450i
\(377\) 9.88367 30.4188i 0.509035 1.56665i
\(378\) 0.402744 + 1.23952i 0.0207149 + 0.0637540i
\(379\) −3.90257 + 2.83538i −0.200462 + 0.145644i −0.683488 0.729962i \(-0.739538\pi\)
0.483026 + 0.875606i \(0.339538\pi\)
\(380\) −0.440581 + 0.320101i −0.0226013 + 0.0164208i
\(381\) −7.06311 21.7380i −0.361854 1.11367i
\(382\) 5.13390 15.8005i 0.262673 0.808425i
\(383\) −8.66176 6.29314i −0.442595 0.321564i 0.344070 0.938944i \(-0.388194\pi\)
−0.786665 + 0.617380i \(0.788194\pi\)
\(384\) −5.69592 −0.290669
\(385\) −0.0530628 0.0895321i −0.00270433 0.00456298i
\(386\) −13.9172 −0.708367
\(387\) 3.71783 + 2.70116i 0.188988 + 0.137308i
\(388\) 1.79856 5.53540i 0.0913081 0.281018i
\(389\) 8.73254 + 26.8760i 0.442757 + 1.36267i 0.884925 + 0.465734i \(0.154210\pi\)
−0.442167 + 0.896933i \(0.645790\pi\)
\(390\) 0.854210 0.620620i 0.0432546 0.0314263i
\(391\) −7.62312 + 5.53852i −0.385518 + 0.280095i
\(392\) −6.61368 20.3548i −0.334041 1.02807i
\(393\) −4.16235 + 12.8104i −0.209963 + 0.646198i
\(394\) 1.46942 + 1.06759i 0.0740281 + 0.0537846i
\(395\) −0.615797 −0.0309841
\(396\) 1.46535 1.66526i 0.0736364 0.0836826i
\(397\) −24.3949 −1.22435 −0.612174 0.790723i \(-0.709705\pi\)
−0.612174 + 0.790723i \(0.709705\pi\)
\(398\) 9.87583 + 7.17521i 0.495031 + 0.359661i
\(399\) −0.473149 + 1.45620i −0.0236871 + 0.0729013i
\(400\) 3.86979 + 11.9100i 0.193490 + 0.595500i
\(401\) 7.17889 5.21577i 0.358497 0.260463i −0.393928 0.919141i \(-0.628884\pi\)
0.752425 + 0.658678i \(0.228884\pi\)
\(402\) −6.89518 + 5.00964i −0.343900 + 0.249858i
\(403\) −0.815185 2.50888i −0.0406073 0.124976i
\(404\) −1.90488 + 5.86260i −0.0947711 + 0.291675i
\(405\) 0.546098 + 0.396763i 0.0271358 + 0.0197153i
\(406\) −1.83569 −0.0911039
\(407\) −0.983405 + 10.5088i −0.0487456 + 0.520902i
\(408\) −4.16724 −0.206309
\(409\) 11.3921 + 8.27688i 0.563305 + 0.409265i 0.832667 0.553774i \(-0.186813\pi\)
−0.269362 + 0.963039i \(0.586813\pi\)
\(410\) 0.332832 1.02435i 0.0164374 0.0505890i
\(411\) 4.14606 + 12.7602i 0.204510 + 0.629417i
\(412\) −2.00812 + 1.45899i −0.0989332 + 0.0718792i
\(413\) 2.07754 1.50942i 0.102229 0.0742739i
\(414\) −4.03879 12.4301i −0.198496 0.610907i
\(415\) −0.286479 + 0.881690i −0.0140627 + 0.0432805i
\(416\) 10.2324 + 7.43428i 0.501685 + 0.364496i
\(417\) −15.7749 −0.772502
\(418\) −22.5408 + 5.06071i −1.10250 + 0.247528i
\(419\) 15.2681 0.745895 0.372948 0.927852i \(-0.378347\pi\)
0.372948 + 0.927852i \(0.378347\pi\)
\(420\) 0.0198063 + 0.0143902i 0.000966451 + 0.000702168i
\(421\) −9.34298 + 28.7547i −0.455349 + 1.40142i 0.415376 + 0.909650i \(0.363650\pi\)
−0.870725 + 0.491770i \(0.836350\pi\)
\(422\) 7.46008 + 22.9598i 0.363151 + 1.11766i
\(423\) 11.7501 8.53692i 0.571307 0.415079i
\(424\) −13.6382 + 9.90874i −0.662330 + 0.481211i
\(425\) 1.53696 + 4.73028i 0.0745535 + 0.229452i
\(426\) 4.05422 12.4776i 0.196428 0.604542i
\(427\) −0.314881 0.228774i −0.0152382 0.0110712i
\(428\) 11.5147 0.556583
\(429\) −17.6556 + 3.96393i −0.852421 + 0.191381i
\(430\) −0.765267 −0.0369044
\(431\) 1.97304 + 1.43350i 0.0950380 + 0.0690492i 0.634289 0.773096i \(-0.281293\pi\)
−0.539251 + 0.842145i \(0.681293\pi\)
\(432\) 4.39016 13.5115i 0.211222 0.650073i
\(433\) 0.811652 + 2.49801i 0.0390055 + 0.120047i 0.968663 0.248378i \(-0.0798974\pi\)
−0.929658 + 0.368424i \(0.879897\pi\)
\(434\) −0.122489 + 0.0889932i −0.00587964 + 0.00427181i
\(435\) −1.41335 + 1.02686i −0.0677647 + 0.0492340i
\(436\) 0.525586 + 1.61759i 0.0251710 + 0.0774684i
\(437\) 16.9932 52.2998i 0.812897 2.50184i
\(438\) 6.62870 + 4.81603i 0.316732 + 0.230119i
\(439\) −12.5835 −0.600580 −0.300290 0.953848i \(-0.597083\pi\)
−0.300290 + 0.953848i \(0.597083\pi\)
\(440\) −0.154023 + 1.64591i −0.00734274 + 0.0784655i
\(441\) 8.09150 0.385310
\(442\) −3.88597 2.82333i −0.184837 0.134292i
\(443\) 4.79004 14.7422i 0.227581 0.700424i −0.770438 0.637515i \(-0.779962\pi\)
0.998019 0.0629086i \(-0.0200377\pi\)
\(444\) −0.767234 2.36130i −0.0364113 0.112063i
\(445\) 0.999763 0.726370i 0.0473933 0.0344332i
\(446\) 15.3304 11.1382i 0.725913 0.527407i
\(447\) −1.70778 5.25600i −0.0807751 0.248600i
\(448\) 0.525467 1.61722i 0.0248260 0.0764065i
\(449\) −7.06502 5.13304i −0.333419 0.242243i 0.408461 0.912776i \(-0.366066\pi\)
−0.741880 + 0.670533i \(0.766066\pi\)
\(450\) −6.89880 −0.325213
\(451\) −12.1938 + 13.8574i −0.574184 + 0.652520i
\(452\) −5.73828 −0.269906
\(453\) 5.81913 + 4.22784i 0.273406 + 0.198641i
\(454\) 2.69098 8.28199i 0.126294 0.388693i
\(455\) 0.0390251 + 0.120107i 0.00182952 + 0.00563069i
\(456\) 19.6754 14.2950i 0.921386 0.669426i
\(457\) 11.6029 8.43000i 0.542761 0.394339i −0.282348 0.959312i \(-0.591113\pi\)
0.825109 + 0.564973i \(0.191113\pi\)
\(458\) 3.46951 + 10.6781i 0.162120 + 0.498953i
\(459\) 1.74363 5.36635i 0.0813858 0.250480i
\(460\) −0.711349 0.516825i −0.0331668 0.0240971i
\(461\) 4.91419 0.228877 0.114438 0.993430i \(-0.463493\pi\)
0.114438 + 0.993430i \(0.463493\pi\)
\(462\) 0.529503 + 0.893423i 0.0246347 + 0.0415658i
\(463\) 21.2802 0.988975 0.494488 0.869185i \(-0.335356\pi\)
0.494488 + 0.869185i \(0.335356\pi\)
\(464\) 16.1886 + 11.7617i 0.751536 + 0.546023i
\(465\) −0.0445257 + 0.137036i −0.00206483 + 0.00635490i
\(466\) 4.35750 + 13.4110i 0.201857 + 0.621253i
\(467\) −9.76965 + 7.09806i −0.452085 + 0.328459i −0.790419 0.612567i \(-0.790137\pi\)
0.338333 + 0.941026i \(0.390137\pi\)
\(468\) −2.17755 + 1.58209i −0.100657 + 0.0731319i
\(469\) −0.315010 0.969501i −0.0145458 0.0447674i
\(470\) −0.747387 + 2.30022i −0.0344744 + 0.106101i
\(471\) 21.0651 + 15.3047i 0.970630 + 0.705204i
\(472\) −40.7891 −1.87747
\(473\) 12.0412 + 5.19727i 0.553656 + 0.238971i
\(474\) 6.14491 0.282245
\(475\) −23.4832 17.0615i −1.07748 0.782836i
\(476\) 0.0344163 0.105922i 0.00157747 0.00485495i
\(477\) −1.96948 6.06142i −0.0901761 0.277533i
\(478\) 13.2609 9.63457i 0.606537 0.440675i
\(479\) −13.3865 + 9.72583i −0.611643 + 0.444384i −0.849992 0.526795i \(-0.823394\pi\)
0.238350 + 0.971179i \(0.423394\pi\)
\(480\) −0.213480 0.657024i −0.00974399 0.0299889i
\(481\) 3.95770 12.1805i 0.180455 0.555385i
\(482\) −12.4100 9.01637i −0.565258 0.410684i
\(483\) −2.47214 −0.112486
\(484\) 3.03927 5.55312i 0.138149 0.252414i
\(485\) −1.63988 −0.0744632
\(486\) 10.8956 + 7.91609i 0.494233 + 0.359081i
\(487\) −4.75130 + 14.6230i −0.215302 + 0.662632i 0.783830 + 0.620976i \(0.213263\pi\)
−0.999132 + 0.0416562i \(0.986737\pi\)
\(488\) 1.91039 + 5.87957i 0.0864793 + 0.266156i
\(489\) 0.429941 0.312370i 0.0194426 0.0141259i
\(490\) −1.09010 + 0.792006i −0.0492458 + 0.0357792i
\(491\) 1.04788 + 3.22506i 0.0472903 + 0.145545i 0.971913 0.235339i \(-0.0756199\pi\)
−0.924623 + 0.380883i \(0.875620\pi\)
\(492\) 1.34177 4.12954i 0.0604917 0.186174i
\(493\) 6.42960 + 4.67137i 0.289574 + 0.210388i
\(494\) 28.0324 1.26124
\(495\) −0.573813 0.247671i −0.0257910 0.0111320i
\(496\) 1.65040 0.0741051
\(497\) 1.26951 + 0.922355i 0.0569454 + 0.0413733i
\(498\) 2.85871 8.79821i 0.128102 0.394257i
\(499\) −2.09092 6.43518i −0.0936023 0.288078i 0.893285 0.449492i \(-0.148395\pi\)
−0.986887 + 0.161413i \(0.948395\pi\)
\(500\) −0.752946 + 0.547047i −0.0336728 + 0.0244647i
\(501\) −20.4740 + 14.8752i −0.914709 + 0.664575i
\(502\) −1.20237 3.70051i −0.0536643 0.165162i
\(503\) 4.32755 13.3188i 0.192956 0.593857i −0.807039 0.590499i \(-0.798931\pi\)
0.999994 0.00335815i \(-0.00106893\pi\)
\(504\) 0.559311 + 0.406363i 0.0249137 + 0.0181009i
\(505\) 1.73682 0.0772873
\(506\) −19.0172 32.0874i −0.845418 1.42646i
\(507\) 4.33335 0.192451
\(508\) −7.84975 5.70318i −0.348276 0.253038i
\(509\) 2.68860 8.27465i 0.119170 0.366767i −0.873624 0.486602i \(-0.838236\pi\)
0.992794 + 0.119834i \(0.0382363\pi\)
\(510\) 0.0810736 + 0.249519i 0.00359000 + 0.0110489i
\(511\) −0.792835 + 0.576028i −0.0350729 + 0.0254820i
\(512\) −18.9246 + 13.7495i −0.836356 + 0.607648i
\(513\) 10.1759 + 31.3183i 0.449278 + 1.38273i
\(514\) −0.447082 + 1.37598i −0.0197199 + 0.0606917i
\(515\) 0.565796 + 0.411075i 0.0249320 + 0.0181141i
\(516\) −3.08508 −0.135813
\(517\) 27.3817 31.1174i 1.20425 1.36854i
\(518\) −0.735062 −0.0322968
\(519\) −7.54149 5.47921i −0.331035 0.240511i
\(520\) 0.619861 1.90774i 0.0271827 0.0836598i
\(521\) 1.90675 + 5.86838i 0.0835363 + 0.257098i 0.984097 0.177632i \(-0.0568437\pi\)
−0.900561 + 0.434730i \(0.856844\pi\)
\(522\) −8.91820 + 6.47945i −0.390339 + 0.283598i
\(523\) −12.9303 + 9.39443i −0.565404 + 0.410790i −0.833433 0.552621i \(-0.813628\pi\)
0.268029 + 0.963411i \(0.413628\pi\)
\(524\) 1.76694 + 5.43810i 0.0771893 + 0.237564i
\(525\) −0.403236 + 1.24103i −0.0175987 + 0.0541632i
\(526\) 16.3275 + 11.8626i 0.711914 + 0.517236i
\(527\) 0.655487 0.0285535
\(528\) 1.05478 11.2715i 0.0459035 0.490531i
\(529\) 65.7872 2.86031
\(530\) 0.858631 + 0.623832i 0.0372965 + 0.0270975i
\(531\) 4.76535 14.6662i 0.206798 0.636460i
\(532\) 0.200855 + 0.618168i 0.00870817 + 0.0268010i
\(533\) 18.1204 13.1652i 0.784882 0.570250i
\(534\) −9.97643 + 7.24830i −0.431722 + 0.313665i
\(535\) −1.00254 3.08551i −0.0433438 0.133398i
\(536\) −5.00352 + 15.3992i −0.216119 + 0.665146i
\(537\) 2.95910 + 2.14991i 0.127695 + 0.0927755i
\(538\) 28.2413 1.21757
\(539\) 22.5313 5.05859i 0.970491 0.217889i
\(540\) 0.526529 0.0226582
\(541\) −23.5254 17.0922i −1.01144 0.734853i −0.0469276 0.998898i \(-0.514943\pi\)
−0.964510 + 0.264046i \(0.914943\pi\)
\(542\) −4.31871 + 13.2916i −0.185505 + 0.570925i
\(543\) 2.88430 + 8.87695i 0.123777 + 0.380946i
\(544\) −2.54254 + 1.84726i −0.109011 + 0.0792008i
\(545\) 0.387693 0.281676i 0.0166070 0.0120657i
\(546\) −0.389423 1.19852i −0.0166658 0.0512920i
\(547\) −5.51632 + 16.9775i −0.235861 + 0.725904i 0.761145 + 0.648581i \(0.224637\pi\)
−0.997006 + 0.0773232i \(0.975363\pi\)
\(548\) 4.60782 + 3.34777i 0.196836 + 0.143010i
\(549\) −2.33727 −0.0997520
\(550\) −19.2101 + 4.31294i −0.819123 + 0.183904i
\(551\) −46.3815 −1.97592
\(552\) 31.7673 + 23.0803i 1.35211 + 0.982364i
\(553\) −0.227118 + 0.698998i −0.00965806 + 0.0297244i
\(554\) −4.54085 13.9753i −0.192922 0.593754i
\(555\) −0.565943 + 0.411182i −0.0240229 + 0.0174537i
\(556\) −5.41764 + 3.93614i −0.229759 + 0.166930i
\(557\) −1.02231 3.14634i −0.0433166 0.133315i 0.927059 0.374915i \(-0.122328\pi\)
−0.970376 + 0.241600i \(0.922328\pi\)
\(558\) −0.280957 + 0.864696i −0.0118939 + 0.0366055i
\(559\) −12.8748 9.35405i −0.544544 0.395634i
\(560\) −0.0790089 −0.00333874
\(561\) 0.418926 4.47670i 0.0176871 0.189007i
\(562\) 29.1382 1.22912
\(563\) −28.2281 20.5089i −1.18967 0.864348i −0.196444 0.980515i \(-0.562939\pi\)
−0.993230 + 0.116167i \(0.962939\pi\)
\(564\) −3.01300 + 9.27306i −0.126870 + 0.390466i
\(565\) 0.499613 + 1.53765i 0.0210189 + 0.0646895i
\(566\) 30.2021 21.9431i 1.26949 0.922337i
\(567\) 0.651783 0.473548i 0.0273723 0.0198871i
\(568\) −7.70216 23.7048i −0.323176 0.994632i
\(569\) 2.73160 8.40699i 0.114515 0.352440i −0.877331 0.479886i \(-0.840678\pi\)
0.991845 + 0.127446i \(0.0406781\pi\)
\(570\) −1.23872 0.899983i −0.0518843 0.0376961i
\(571\) 8.27184 0.346166 0.173083 0.984907i \(-0.444627\pi\)
0.173083 + 0.984907i \(0.444627\pi\)
\(572\) −5.07445 + 5.76676i −0.212173 + 0.241120i
\(573\) −18.8707 −0.788335
\(574\) −1.04000 0.755602i −0.0434086 0.0315382i
\(575\) 14.4823 44.5720i 0.603954 1.85878i
\(576\) −3.15547 9.71155i −0.131478 0.404648i
\(577\) 8.67364 6.30177i 0.361088 0.262346i −0.392418 0.919787i \(-0.628361\pi\)
0.753506 + 0.657441i \(0.228361\pi\)
\(578\) 0.965584 0.701538i 0.0401630 0.0291801i
\(579\) 4.88492 + 15.0342i 0.203010 + 0.624802i
\(580\) −0.229170 + 0.705313i −0.00951577 + 0.0292865i
\(581\) 0.895158 + 0.650370i 0.0371374 + 0.0269819i
\(582\) 16.3640 0.678311
\(583\) −9.27356 15.6471i −0.384071 0.648038i
\(584\) 15.5660 0.644124
\(585\) 0.613533 + 0.445758i 0.0253665 + 0.0184298i
\(586\) −6.29587 + 19.3767i −0.260080 + 0.800444i
\(587\) −0.646664 1.99023i −0.0266907 0.0821455i 0.936824 0.349801i \(-0.113751\pi\)
−0.963515 + 0.267656i \(0.913751\pi\)
\(588\) −4.39462 + 3.19288i −0.181231 + 0.131672i
\(589\) −3.09485 + 2.24854i −0.127521 + 0.0926496i
\(590\) 0.793552 + 2.44230i 0.0326700 + 0.100548i
\(591\) 0.637518 1.96208i 0.0262240 0.0807092i
\(592\) 6.48235 + 4.70971i 0.266423 + 0.193568i
\(593\) −12.9481 −0.531713 −0.265857 0.964013i \(-0.585655\pi\)
−0.265857 + 0.964013i \(0.585655\pi\)
\(594\) 20.5071 + 8.85133i 0.841417 + 0.363175i
\(595\) −0.0313799 −0.00128645
\(596\) −1.89798 1.37896i −0.0777442 0.0564845i
\(597\) 4.28471 13.1870i 0.175362 0.539707i
\(598\) 13.9862 + 43.0451i 0.571938 + 1.76025i
\(599\) −22.6478 + 16.4546i −0.925366 + 0.672318i −0.944854 0.327492i \(-0.893796\pi\)
0.0194879 + 0.999810i \(0.493796\pi\)
\(600\) 16.7682 12.1828i 0.684558 0.497361i
\(601\) 9.03084 + 27.7941i 0.368375 + 1.13374i 0.947840 + 0.318746i \(0.103262\pi\)
−0.579465 + 0.814997i \(0.696738\pi\)
\(602\) −0.282246 + 0.868663i −0.0115035 + 0.0354041i
\(603\) −4.95244 3.59816i −0.201679 0.146528i
\(604\) 3.05341 0.124241
\(605\) −1.75265 0.330921i −0.0712554 0.0134539i
\(606\) −17.3313 −0.704037
\(607\) −4.10293 2.98095i −0.166533 0.120993i 0.501397 0.865217i \(-0.332820\pi\)
−0.667930 + 0.744224i \(0.732820\pi\)
\(608\) 5.66776 17.4436i 0.229858 0.707430i
\(609\) 0.644326 + 1.98303i 0.0261094 + 0.0803565i
\(610\) 0.314881 0.228774i 0.0127492 0.00926280i
\(611\) −40.6901 + 29.5631i −1.64615 + 1.19599i
\(612\) −0.206673 0.636074i −0.00835426 0.0257118i
\(613\) 9.08422 27.9583i 0.366908 1.12923i −0.581869 0.813282i \(-0.697679\pi\)
0.948778 0.315945i \(-0.102321\pi\)
\(614\) −11.0535 8.03085i −0.446084 0.324099i
\(615\) −1.22339 −0.0493319
\(616\) 1.81148 + 0.781876i 0.0729867 + 0.0315027i
\(617\) 9.43628 0.379890 0.189945 0.981795i \(-0.439169\pi\)
0.189945 + 0.981795i \(0.439169\pi\)
\(618\) −5.64596 4.10203i −0.227114 0.165008i
\(619\) −4.45662 + 13.7161i −0.179127 + 0.551295i −0.999798 0.0201054i \(-0.993600\pi\)
0.820671 + 0.571401i \(0.193600\pi\)
\(620\) 0.0189015 + 0.0581728i 0.000759102 + 0.00233628i
\(621\) −43.0136 + 31.2512i −1.72608 + 1.25407i
\(622\) 4.53351 3.29379i 0.181777 0.132069i
\(623\) −0.455779 1.40274i −0.0182604 0.0561997i
\(624\) −4.24495 + 13.0646i −0.169934 + 0.523003i
\(625\) −19.9069 14.4632i −0.796277 0.578529i
\(626\) 33.7330 1.34824
\(627\) 13.3787 + 22.5736i 0.534293 + 0.901504i
\(628\) 11.0533 0.441074
\(629\) 2.57459 + 1.87055i 0.102656 + 0.0745836i
\(630\) 0.0134501 0.0413953i 0.000535867 0.00164923i
\(631\) −0.717367 2.20783i −0.0285579 0.0878923i 0.935762 0.352633i \(-0.114714\pi\)
−0.964320 + 0.264741i \(0.914714\pi\)
\(632\) 9.44449 6.86182i 0.375682 0.272949i
\(633\) 22.1841 16.1177i 0.881739 0.640621i
\(634\) −1.82980 5.63153i −0.0726704 0.223657i
\(635\) −0.844792 + 2.60000i −0.0335245 + 0.103178i
\(636\) 3.46147 + 2.51490i 0.137256 + 0.0997224i
\(637\) −28.0206 −1.11022
\(638\) −20.7825 + 23.6178i −0.822786 + 0.935039i
\(639\) 9.42321 0.372776
\(640\) 0.551158 + 0.400440i 0.0217864 + 0.0158288i
\(641\) 5.76116 17.7310i 0.227552 0.700333i −0.770470 0.637476i \(-0.779979\pi\)
0.998023 0.0628576i \(-0.0200214\pi\)
\(642\) 10.0042 + 30.7897i 0.394834 + 1.21517i
\(643\) 8.67780 6.30479i 0.342219 0.248637i −0.403379 0.915033i \(-0.632164\pi\)
0.745597 + 0.666397i \(0.232164\pi\)
\(644\) −0.849014 + 0.616845i −0.0334558 + 0.0243071i
\(645\) 0.268608 + 0.826689i 0.0105764 + 0.0325509i
\(646\) −2.15245 + 6.62456i −0.0846870 + 0.260640i
\(647\) 31.6155 + 22.9700i 1.24293 + 0.903043i 0.997790 0.0664445i \(-0.0211655\pi\)
0.245142 + 0.969487i \(0.421166\pi\)
\(648\) −12.7966 −0.502700
\(649\) 4.10047 43.8182i 0.160957 1.72001i
\(650\) 23.8904 0.937057
\(651\) 0.139129 + 0.101083i 0.00545291 + 0.00396177i
\(652\) 0.0697137 0.214557i 0.00273020 0.00840269i
\(653\) 12.9360 + 39.8130i 0.506226 + 1.55800i 0.798700 + 0.601729i \(0.205521\pi\)
−0.292474 + 0.956273i \(0.594479\pi\)
\(654\) −3.86871 + 2.81078i −0.151279 + 0.109910i
\(655\) 1.30337 0.946953i 0.0509269 0.0370005i
\(656\) 4.33020 + 13.3270i 0.169066 + 0.520331i
\(657\) −1.81856 + 5.59694i −0.0709486 + 0.218357i
\(658\) 2.33535 + 1.69673i 0.0910416 + 0.0661456i
\(659\) 36.1384 1.40775 0.703875 0.710323i \(-0.251451\pi\)
0.703875 + 0.710323i \(0.251451\pi\)
\(660\) 0.409376 0.0919107i 0.0159349 0.00357762i
\(661\) 13.4795 0.524292 0.262146 0.965028i \(-0.415570\pi\)
0.262146 + 0.965028i \(0.415570\pi\)
\(662\) −29.3657 21.3354i −1.14133 0.829224i
\(663\) −1.68596 + 5.18886i −0.0654773 + 0.201518i
\(664\) −5.43094 16.7147i −0.210761 0.648657i
\(665\) 0.148159 0.107644i 0.00574535 0.00417424i
\(666\) −3.57109 + 2.59455i −0.138377 + 0.100537i
\(667\) −23.1411 71.2209i −0.896026 2.75768i
\(668\) −3.31979 + 10.2173i −0.128447 + 0.395318i
\(669\) −17.4131 12.6513i −0.673228 0.489129i
\(670\) 1.01939 0.0393826
\(671\) −6.50825 + 1.46119i −0.251248 + 0.0564088i
\(672\) −0.824532 −0.0318070
\(673\) −6.24193 4.53503i −0.240609 0.174813i 0.460946 0.887428i \(-0.347510\pi\)
−0.701554 + 0.712616i \(0.747510\pi\)
\(674\) −10.7883 + 33.2028i −0.415548 + 1.27893i
\(675\) 8.67232 + 26.6907i 0.333798 + 1.02732i
\(676\) 1.48822 1.08125i 0.0572391 0.0415867i
\(677\) 10.0936 7.33340i 0.387927 0.281845i −0.376679 0.926344i \(-0.622934\pi\)
0.764605 + 0.644499i \(0.222934\pi\)
\(678\) −4.98554 15.3439i −0.191468 0.589279i
\(679\) −0.604821 + 1.86145i −0.0232109 + 0.0714358i
\(680\) 0.403236 + 0.292968i 0.0154634 + 0.0112348i
\(681\) −9.89126 −0.379034
\(682\) −0.241757 + 2.58345i −0.00925734 + 0.0989252i
\(683\) −43.4165 −1.66129 −0.830644 0.556804i \(-0.812027\pi\)
−0.830644 + 0.556804i \(0.812027\pi\)
\(684\) 3.15775 + 2.29424i 0.120739 + 0.0877224i
\(685\) 0.495894 1.52621i 0.0189472 0.0583133i
\(686\) 0.996600 + 3.06722i 0.0380504 + 0.117107i
\(687\) 10.3173 7.49597i 0.393630 0.285989i
\(688\) 8.05478 5.85214i 0.307086 0.223111i
\(689\) 6.82024 + 20.9905i 0.259830 + 0.799676i
\(690\) 0.763932 2.35114i 0.0290824 0.0895064i
\(691\) 27.8819 + 20.2574i 1.06068 + 0.770628i 0.974214 0.225627i \(-0.0724432\pi\)
0.0864642 + 0.996255i \(0.472443\pi\)
\(692\) −3.95717 −0.150429
\(693\) −0.492767 + 0.559995i −0.0187187 + 0.0212725i
\(694\) −17.8370 −0.677084
\(695\) 1.52644 + 1.10902i 0.0579011 + 0.0420676i
\(696\) 10.2343 31.4978i 0.387929 1.19392i
\(697\) 1.71982 + 5.29306i 0.0651428 + 0.200489i
\(698\) −26.4068 + 19.1857i −0.999512 + 0.726188i
\(699\) 12.9579 9.41449i 0.490114 0.356089i
\(700\) 0.171177 + 0.526828i 0.00646987 + 0.0199122i
\(701\) 14.0478 43.2346i 0.530577 1.63295i −0.222439 0.974947i \(-0.571402\pi\)
0.753016 0.658002i \(-0.228598\pi\)
\(702\) −21.9267 15.9307i −0.827569 0.601264i
\(703\) −18.5724 −0.700472
\(704\) −14.8580 25.0697i −0.559982 0.944849i
\(705\) 2.74717 0.103465
\(706\) 21.8290 + 15.8597i 0.821544 + 0.596886i
\(707\) 0.640572 1.97148i 0.0240912 0.0741451i
\(708\) 3.19911 + 9.84584i 0.120230 + 0.370029i
\(709\) 22.7758 16.5476i 0.855364 0.621458i −0.0712560 0.997458i \(-0.522701\pi\)
0.926620 + 0.376000i \(0.122701\pi\)
\(710\) −1.26951 + 0.922355i −0.0476440 + 0.0346154i
\(711\) 1.36387 + 4.19755i 0.0511490 + 0.157420i
\(712\) −7.23944 + 22.2807i −0.271309 + 0.835004i
\(713\) −4.99686 3.63043i −0.187134 0.135961i
\(714\) 0.313133 0.0117187
\(715\) 1.98710 + 0.857676i 0.0743132 + 0.0320753i
\(716\) 1.55270 0.0580270
\(717\) −15.0624 10.9435i −0.562516 0.408692i
\(718\) −8.25554 + 25.4079i −0.308094 + 0.948216i
\(719\) −9.08453 27.9593i −0.338796 1.04271i −0.964822 0.262904i \(-0.915320\pi\)
0.626026 0.779802i \(-0.284680\pi\)
\(720\) −0.383843 + 0.278878i −0.0143050 + 0.0103932i
\(721\) 0.675293 0.490629i 0.0251492 0.0182720i
\(722\) −5.55421 17.0941i −0.206706 0.636177i
\(723\) −5.38416 + 16.5708i −0.200239 + 0.616273i
\(724\) 3.20553 + 2.32895i 0.119133 + 0.0865549i
\(725\) −39.5281 −1.46804
\(726\) 17.4894 + 3.30220i 0.649091 + 0.122556i
\(727\) −36.7713 −1.36377 −0.681886 0.731459i \(-0.738840\pi\)
−0.681886 + 0.731459i \(0.738840\pi\)
\(728\) −1.93688 1.40722i −0.0717854 0.0521552i
\(729\) 8.58642 26.4263i 0.318015 0.978751i
\(730\) −0.302836 0.932033i −0.0112085 0.0344961i
\(731\) 3.19911 2.32429i 0.118323 0.0859669i
\(732\) 1.26940 0.922276i 0.0469185 0.0340883i
\(733\) 10.2674 + 31.5997i 0.379233 + 1.16716i 0.940578 + 0.339578i \(0.110284\pi\)
−0.561344 + 0.827582i \(0.689716\pi\)
\(734\) −7.20300 + 22.1686i −0.265868 + 0.818256i
\(735\) 1.23820 + 0.899605i 0.0456717 + 0.0331824i
\(736\) 29.6132 1.09156
\(737\) −16.0398 6.92315i −0.590835 0.255018i
\(738\) −7.71958 −0.284162
\(739\) 16.5629 + 12.0336i 0.609276 + 0.442665i 0.849159 0.528137i \(-0.177109\pi\)
−0.239883 + 0.970802i \(0.577109\pi\)
\(740\) −0.0917661 + 0.282427i −0.00337339 + 0.0103822i
\(741\) −9.83935 30.2824i −0.361457 1.11245i
\(742\) 1.02480 0.744560i 0.0376216 0.0273337i
\(743\) −27.6761 + 20.1079i −1.01534 + 0.737687i −0.965322 0.261061i \(-0.915928\pi\)
−0.0500170 + 0.998748i \(0.515928\pi\)
\(744\) −0.844101 2.59788i −0.0309462 0.0952427i
\(745\) −0.204261 + 0.628650i −0.00748354 + 0.0230320i
\(746\) −22.1335 16.0809i −0.810366 0.588765i
\(747\) 6.64449 0.243109
\(748\) −0.973149 1.64198i −0.0355819 0.0600367i
\(749\) −3.87216 −0.141486
\(750\) −2.11695 1.53806i −0.0773002 0.0561619i
\(751\) −12.2108 + 37.5810i −0.445579 + 1.37135i 0.436269 + 0.899816i \(0.356300\pi\)
−0.881848 + 0.471535i \(0.843700\pi\)
\(752\) −9.72363 29.9263i −0.354584 1.09130i
\(753\) −3.57549 + 2.59775i −0.130298 + 0.0946672i
\(754\) 30.8835 22.4381i 1.12471 0.817149i
\(755\) −0.265850 0.818202i −0.00967527 0.0297774i
\(756\) 0.194195 0.597669i 0.00706279 0.0217370i
\(757\) −5.12215 3.72146i −0.186168 0.135259i 0.490798 0.871274i \(-0.336705\pi\)
−0.676966 + 0.736015i \(0.736705\pi\)
\(758\) −5.75738 −0.209118
\(759\) −27.9879 + 31.8062i −1.01589 + 1.15449i
\(760\) −2.90885 −0.105515
\(761\) −17.9903 13.0707i −0.652148 0.473813i 0.211855 0.977301i \(-0.432050\pi\)
−0.864002 + 0.503488i \(0.832050\pi\)
\(762\) 8.43001 25.9449i 0.305387 0.939884i
\(763\) −0.176744 0.543963i −0.00639857 0.0196928i
\(764\) −6.48083 + 4.70860i −0.234468 + 0.170351i
\(765\) −0.152450 + 0.110762i −0.00551185 + 0.00400459i
\(766\) −3.94878 12.1531i −0.142675 0.439110i
\(767\) −16.5023 + 50.7887i −0.595862 + 1.83387i
\(768\) 13.7738 + 10.0072i 0.497018 + 0.361105i
\(769\) −13.6823 −0.493398 −0.246699 0.969092i \(-0.579346\pi\)
−0.246699 + 0.969092i \(0.579346\pi\)
\(770\) 0.0115735 0.123676i 0.000417081 0.00445699i
\(771\) 1.64334 0.0591835
\(772\) 5.42897 + 3.94438i 0.195393 + 0.141961i
\(773\) −13.4191 + 41.2998i −0.482652 + 1.48545i 0.352700 + 0.935737i \(0.385264\pi\)
−0.835352 + 0.549715i \(0.814736\pi\)
\(774\) 1.69491 + 5.21640i 0.0609223 + 0.187500i
\(775\) −2.63756 + 1.91630i −0.0947438 + 0.0688354i
\(776\) 25.1509 18.2732i 0.902864 0.655969i
\(777\) 0.258006 + 0.794060i 0.00925591 + 0.0284868i
\(778\) −10.4225 + 32.0772i −0.373666 + 1.15002i
\(779\) −26.2770 19.0914i −0.941473 0.684020i
\(780\) −0.509114 −0.0182292
\(781\) 26.2395 5.89113i 0.938922 0.210801i
\(782\) −11.2462 −0.402165
\(783\) 36.2791 + 26.3583i 1.29651 + 0.941969i
\(784\) 5.41721 16.6724i 0.193472 0.595445i
\(785\) −0.962372 2.96188i −0.0343485 0.105714i
\(786\) −13.0061 + 9.44946i −0.463911 + 0.337051i
\(787\) 18.9055 13.7357i 0.673909 0.489624i −0.197422 0.980319i \(-0.563257\pi\)
0.871332 + 0.490695i \(0.163257\pi\)
\(788\) −0.270631 0.832917i −0.00964083 0.0296714i
\(789\) 7.08383 21.8018i 0.252191 0.776164i
\(790\) −0.594604 0.432005i −0.0211550 0.0153700i
\(791\) 1.92967 0.0686113
\(792\) 11.5604 2.59546i 0.410780 0.0922258i
\(793\) 8.09388 0.287422
\(794\) −23.5554 17.1140i −0.835949 0.607352i
\(795\) 0.372524 1.14651i 0.0132121 0.0406626i
\(796\) −1.81889 5.59796i −0.0644688 0.198415i
\(797\) −22.3779 + 16.2585i −0.792664 + 0.575904i −0.908753 0.417335i \(-0.862964\pi\)
0.116089 + 0.993239i \(0.462964\pi\)
\(798\) −1.47845 + 1.07415i −0.0523364 + 0.0380246i
\(799\) −3.86192 11.8858i −0.136625 0.420488i
\(800\) 4.83029 14.8661i 0.170776 0.525596i
\(801\) −7.16553 5.20607i −0.253182 0.183947i
\(802\) 10.5909 0.373977
\(803\) −1.56482 + 16.7219i −0.0552215 + 0.590104i
\(804\) 4.10956 0.144933
\(805\) 0.239213 + 0.173798i 0.00843114 + 0.00612558i
\(806\) 0.972946 2.99442i 0.0342705 0.105474i
\(807\) −9.91265 30.5080i −0.348942 1.07393i
\(808\) −26.6376 + 19.3533i −0.937106 + 0.680847i
\(809\) 43.4998 31.6045i 1.52937 1.11115i 0.572787 0.819704i \(-0.305862\pi\)
0.956586 0.291450i \(-0.0941377\pi\)
\(810\) 0.248959 + 0.766217i 0.00874752 + 0.0269221i
\(811\) −6.47042 + 19.9139i −0.227207 + 0.699272i 0.770853 + 0.637013i \(0.219830\pi\)
−0.998060 + 0.0622588i \(0.980170\pi\)
\(812\) 0.716087 + 0.520267i 0.0251297 + 0.0182578i
\(813\) 15.8743 0.556737
\(814\) −8.32188 + 9.45723i −0.291682 + 0.331476i
\(815\) −0.0635631 −0.00222652
\(816\) −2.76145 2.00631i −0.0966703 0.0702351i
\(817\) −7.13135 + 21.9481i −0.249495 + 0.767865i
\(818\) 5.19353 + 15.9840i 0.181587 + 0.558869i
\(819\) 0.732269 0.532024i 0.0255875 0.0185904i
\(820\) −0.420153 + 0.305259i −0.0146724 + 0.0106601i
\(821\) −2.95993 9.10971i −0.103302 0.317931i 0.886026 0.463635i \(-0.153455\pi\)
−0.989328 + 0.145704i \(0.953455\pi\)
\(822\) −4.94843 + 15.2297i −0.172596 + 0.531197i
\(823\) 27.9795 + 20.3283i 0.975305 + 0.708601i 0.956654 0.291225i \(-0.0940630\pi\)
0.0186507 + 0.999826i \(0.494063\pi\)
\(824\) −13.2582 −0.461872
\(825\) 11.4018 + 19.2381i 0.396961 + 0.669786i
\(826\) 3.06496 0.106644
\(827\) 7.57543 + 5.50387i 0.263424 + 0.191388i 0.711655 0.702529i \(-0.247946\pi\)
−0.448231 + 0.893918i \(0.647946\pi\)
\(828\) −1.94742 + 5.99353i −0.0676774 + 0.208290i
\(829\) −11.4060 35.1042i −0.396148 1.21922i −0.928064 0.372422i \(-0.878528\pi\)
0.531915 0.846798i \(-0.321472\pi\)
\(830\) −0.895158 + 0.650370i −0.0310714 + 0.0225747i
\(831\) −13.5032 + 9.81063i −0.468420 + 0.340327i
\(832\) 10.9273 + 33.6308i 0.378836 + 1.16594i
\(833\) 2.15155 6.62178i 0.0745466 0.229431i
\(834\) −15.2320 11.0667i −0.527442 0.383209i
\(835\) 3.02690 0.104750
\(836\) 10.2272 + 4.41430i 0.353716 + 0.152672i
\(837\) 3.69859 0.127842
\(838\) 14.7426 + 10.7111i 0.509275 + 0.370010i
\(839\) −9.22019 + 28.3768i −0.318316 + 0.979677i 0.656052 + 0.754716i \(0.272225\pi\)
−0.974368 + 0.224961i \(0.927775\pi\)
\(840\) 0.0404093 + 0.124367i 0.00139425 + 0.00429107i
\(841\) −27.6372 + 20.0796i −0.953006 + 0.692399i
\(842\) −29.1940 + 21.2107i −1.00609 + 0.730968i
\(843\) −10.2275 31.4769i −0.352253 1.08412i
\(844\) 3.59709 11.0707i 0.123817 0.381070i
\(845\) −0.419311 0.304647i −0.0144247 0.0104802i
\(846\) 17.3346 0.595977
\(847\) −1.02205 + 1.86741i −0.0351179 + 0.0641648i
\(848\) −13.8080 −0.474170
\(849\) −34.3052 24.9242i −1.17735 0.855396i
\(850\) −1.83440 + 5.64571i −0.0629195 + 0.193646i
\(851\) −9.26633 28.5188i −0.317646 0.977613i
\(852\) −5.11789 + 3.71836i −0.175336 + 0.127389i
\(853\) −20.3224 + 14.7651i −0.695826 + 0.505548i −0.878570 0.477613i \(-0.841502\pi\)
0.182744 + 0.983161i \(0.441502\pi\)
\(854\) −0.143550 0.441802i −0.00491218 0.0151181i
\(855\) 0.339838 1.04591i 0.0116222 0.0357695i
\(856\) 49.7579 + 36.1512i 1.70069 + 1.23562i
\(857\) 41.2563 1.40929 0.704644 0.709561i \(-0.251107\pi\)
0.704644 + 0.709561i \(0.251107\pi\)
\(858\) −19.8288 8.55857i −0.676945 0.292185i
\(859\) 43.7534 1.49285 0.746423 0.665472i \(-0.231770\pi\)
0.746423 + 0.665472i \(0.231770\pi\)
\(860\) 0.298523 + 0.216890i 0.0101796 + 0.00739589i
\(861\) −0.451211 + 1.38869i −0.0153772 + 0.0473263i
\(862\) 0.899483 + 2.76832i 0.0306365 + 0.0942895i
\(863\) 4.06545 2.95372i 0.138390 0.100546i −0.516437 0.856325i \(-0.672742\pi\)
0.654826 + 0.755780i \(0.272742\pi\)
\(864\) −14.3463 + 10.4232i −0.488072 + 0.354605i
\(865\) 0.344537 + 1.06038i 0.0117146 + 0.0360539i
\(866\) −0.968728 + 2.98144i −0.0329187 + 0.101313i
\(867\) −1.09676 0.796845i −0.0372480 0.0270623i
\(868\) 0.0730039 0.00247791
\(869\) 6.42196 + 10.8357i 0.217850 + 0.367575i
\(870\) −2.08508 −0.0706909
\(871\) 17.1501 + 12.4603i 0.581111 + 0.422202i
\(872\) −2.80735 + 8.64013i −0.0950688 + 0.292592i
\(873\) 3.63200 + 11.1782i 0.122925 + 0.378323i
\(874\) 53.0987 38.5784i 1.79609 1.30494i
\(875\) 0.253201 0.183961i 0.00855976 0.00621903i
\(876\) −1.22085 3.75738i −0.0412486 0.126950i
\(877\) 0.387309 1.19201i 0.0130785 0.0402515i −0.944304 0.329074i \(-0.893264\pi\)
0.957383 + 0.288822i \(0.0932636\pi\)
\(878\) −12.1505 8.82783i −0.410058 0.297925i
\(879\) 23.1418 0.780552
\(880\) −0.894486 + 1.01652i −0.0301531 + 0.0342669i
\(881\) 15.7916 0.532032 0.266016 0.963969i \(-0.414293\pi\)
0.266016 + 0.963969i \(0.414293\pi\)
\(882\) 7.81303 + 5.67650i 0.263078 + 0.191138i
\(883\) 1.47395 4.53635i 0.0496023 0.152660i −0.923187 0.384350i \(-0.874426\pi\)
0.972790 + 0.231690i \(0.0744255\pi\)
\(884\) 0.715702 + 2.20271i 0.0240717 + 0.0740850i
\(885\) 2.35979 1.71449i 0.0793235 0.0576319i
\(886\) 14.9674 10.8745i 0.502840 0.365334i
\(887\) 4.15504 + 12.7879i 0.139513 + 0.429376i 0.996265 0.0863528i \(-0.0275212\pi\)
−0.856752 + 0.515729i \(0.827521\pi\)
\(888\) 4.09808 12.6126i 0.137523 0.423251i
\(889\) 2.63972 + 1.91787i 0.0885333 + 0.0643232i
\(890\) 1.47493 0.0494398
\(891\) 1.28643 13.7470i 0.0430970 0.460540i
\(892\) −9.13697 −0.305929
\(893\) 59.0062 + 42.8705i 1.97457 + 1.43461i
\(894\) 2.03828 6.27317i 0.0681702 0.209806i
\(895\) −0.135188 0.416066i −0.00451884 0.0139076i
\(896\) 0.657822 0.477936i 0.0219763 0.0159667i
\(897\) 41.5909 30.2176i 1.38868 1.00893i
\(898\) −3.22085 9.91276i −0.107481 0.330793i
\(899\) −1.60980 + 4.95446i −0.0536899 + 0.165240i
\(900\) 2.69116 + 1.95524i 0.0897053 + 0.0651747i
\(901\) −5.48412 −0.182703
\(902\) −21.4956 + 4.82607i −0.715726 + 0.160691i
\(903\) 1.03745 0.0345243
\(904\) −24.7966 18.0158i −0.824723 0.599196i
\(905\) 0.344980 1.06174i 0.0114675 0.0352934i
\(906\) 2.65286 + 8.16467i 0.0881355 + 0.271253i
\(907\) 34.3492 24.9561i 1.14055 0.828655i 0.153351 0.988172i \(-0.450994\pi\)
0.987195 + 0.159517i \(0.0509936\pi\)
\(908\) −3.39699 + 2.46806i −0.112733 + 0.0819053i
\(909\) −3.84669 11.8389i −0.127587 0.392672i
\(910\) −0.0465775 + 0.143351i −0.00154403 + 0.00475203i
\(911\) −5.18588 3.76776i −0.171816 0.124832i 0.498554 0.866859i \(-0.333865\pi\)
−0.670370 + 0.742027i \(0.733865\pi\)
\(912\) 19.9204 0.659631
\(913\) 18.5020 4.15395i 0.612326 0.137476i
\(914\) 17.1175 0.566198
\(915\) −0.357659 0.259855i −0.0118238 0.00859053i
\(916\) 1.67292 5.14873i 0.0552750 0.170119i
\(917\) −0.594189 1.82873i −0.0196218 0.0603898i
\(918\) 5.44832 3.95844i 0.179821 0.130648i
\(919\) 23.9576 17.4062i 0.790289 0.574179i −0.117760 0.993042i \(-0.537571\pi\)
0.908049 + 0.418863i \(0.137571\pi\)
\(920\) −1.45131 4.46667i −0.0478482 0.147262i
\(921\) −4.79566 + 14.7595i −0.158022 + 0.486343i
\(922\) 4.74506 + 3.44749i 0.156270 + 0.113537i
\(923\) −32.6323 −1.07410
\(924\) 0.0466573 0.498586i 0.00153491 0.0164023i
\(925\) −15.8282 −0.520427
\(926\) 20.5478 + 14.9289i 0.675243 + 0.490593i
\(927\) 1.54895 4.76717i 0.0508741 0.156574i
\(928\) −7.71825 23.7543i −0.253364 0.779774i
\(929\) −49.1161 + 35.6849i −1.61145 + 1.17078i −0.752741 + 0.658317i \(0.771269\pi\)
−0.858706 + 0.512468i \(0.828731\pi\)
\(930\) −0.139129 + 0.101083i −0.00456223 + 0.00331465i
\(931\) 12.5565 + 38.6450i 0.411523 + 1.26654i
\(932\) 2.10109 6.46650i 0.0688236 0.211817i
\(933\) −5.14941 3.74127i −0.168584 0.122484i
\(934\) −14.4130 −0.471607
\(935\) −0.355262 + 0.403730i −0.0116183 + 0.0132034i
\(936\) −14.3769 −0.469922
\(937\) −3.68585 2.67793i −0.120412 0.0874841i 0.525950 0.850516i \(-0.323710\pi\)
−0.646361 + 0.763032i \(0.723710\pi\)
\(938\) 0.375973 1.15713i 0.0122760 0.0377815i
\(939\) −11.8403 36.4405i −0.386392 1.18919i
\(940\) 0.943471 0.685472i 0.0307726 0.0223576i
\(941\) 25.1899 18.3015i 0.821167 0.596613i −0.0958795 0.995393i \(-0.530566\pi\)
0.917047 + 0.398780i \(0.130566\pi\)
\(942\) 9.60332 + 29.5560i 0.312893 + 0.962985i
\(943\) 16.2053 49.8749i 0.527718 1.62415i
\(944\) −27.0292 19.6379i −0.879726 0.639159i
\(945\) −0.177061 −0.00575981
\(946\) 7.98073 + 13.4658i 0.259476 + 0.437810i
\(947\) −15.7144 −0.510651 −0.255325 0.966855i \(-0.582183\pi\)
−0.255325 + 0.966855i \(0.582183\pi\)
\(948\) −2.39707 1.74158i −0.0778533 0.0565637i
\(949\) 6.29761 19.3820i 0.204429 0.629168i
\(950\) −10.7057 32.9486i −0.347337 1.06899i
\(951\) −5.44128 + 3.95332i −0.176445 + 0.128195i
\(952\) 0.481274 0.349666i 0.0155982 0.0113327i
\(953\) −8.52938 26.2507i −0.276294 0.850345i −0.988874 0.148754i \(-0.952474\pi\)
0.712580 0.701590i \(-0.247526\pi\)
\(954\) 2.35062 7.23447i 0.0761042 0.234225i
\(955\) 1.82600 + 1.32666i 0.0590878 + 0.0429298i
\(956\) −7.90354 −0.255619
\(957\) 32.8081 + 14.1607i 1.06053 + 0.457751i
\(958\) −19.7488 −0.638054
\(959\) −1.54952 1.12579i −0.0500366 0.0363537i
\(960\) 0.596854 1.83693i 0.0192634 0.0592866i
\(961\) −9.44675 29.0741i −0.304734 0.937875i
\(962\) 12.3666 8.98486i 0.398715 0.289683i
\(963\) −18.8118 + 13.6676i −0.606202 + 0.440431i
\(964\) 2.28561 + 7.03440i 0.0736147 + 0.226563i
\(965\) 0.584268 1.79819i 0.0188082 0.0578858i
\(966\) −2.38705 1.73430i −0.0768022 0.0558001i
\(967\) 41.8082 1.34446 0.672230 0.740343i \(-0.265337\pi\)
0.672230 + 0.740343i \(0.265337\pi\)
\(968\) 30.5679 14.4544i 0.982490 0.464583i
\(969\) 7.91177 0.254163
\(970\) −1.58344 1.15044i −0.0508413 0.0369383i
\(971\) 10.1330 31.1863i 0.325184 1.00081i −0.646173 0.763191i \(-0.723631\pi\)
0.971357 0.237624i \(-0.0763685\pi\)
\(972\) −2.00670 6.17598i −0.0643649 0.198095i
\(973\) 1.82185 1.32365i 0.0584057 0.0424342i
\(974\) −14.8464 + 10.7865i −0.475708 + 0.345622i
\(975\) −8.38548 25.8079i −0.268550 0.826513i
\(976\) −1.56478 + 4.81591i −0.0500875 + 0.154153i
\(977\) 46.1922 + 33.5606i 1.47782 + 1.07370i 0.978251 + 0.207423i \(0.0665076\pi\)
0.499567 + 0.866275i \(0.333492\pi\)
\(978\) 0.634283 0.0202821
\(979\) −23.2075 10.0169i −0.741716 0.320142i
\(980\) 0.649707 0.0207541
\(981\) −2.77869 2.01884i −0.0887167 0.0644565i
\(982\) −1.25068 + 3.84919i −0.0399107 + 0.122833i
\(983\) 5.61747 + 17.2888i 0.179169 + 0.551427i 0.999799 0.0200334i \(-0.00637724\pi\)
−0.820630 + 0.571460i \(0.806377\pi\)
\(984\) 18.7632 13.6322i 0.598148 0.434580i
\(985\) −0.199628 + 0.145038i −0.00636069 + 0.00462131i
\(986\) 2.93117 + 9.02121i 0.0933474 + 0.287294i
\(987\) 1.01321 3.11835i 0.0322509 0.0992581i
\(988\) −10.9352 7.94488i −0.347895 0.252760i
\(989\) −37.2603 −1.18481
\(990\) −0.380314 0.641698i −0.0120872 0.0203945i
\(991\) 35.5365 1.12885 0.564427 0.825483i \(-0.309097\pi\)
0.564427 + 0.825483i \(0.309097\pi\)
\(992\) −1.66660 1.21086i −0.0529147 0.0384448i
\(993\) −12.7405 + 39.2114i −0.404309 + 1.24433i
\(994\) 0.578754 + 1.78122i 0.0183570 + 0.0564969i
\(995\) −1.34169 + 0.974792i −0.0425343 + 0.0309030i
\(996\) −3.60872 + 2.62189i −0.114347 + 0.0830777i
\(997\) 3.09280 + 9.51865i 0.0979499 + 0.301459i 0.988011 0.154382i \(-0.0493387\pi\)
−0.890061 + 0.455841i \(0.849339\pi\)
\(998\) 2.49557 7.68056i 0.0789958 0.243124i
\(999\) 14.5272 + 10.5546i 0.459619 + 0.333933i
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 187.2.g.e.103.2 yes 8
11.3 even 5 inner 187.2.g.e.69.2 8
11.5 even 5 2057.2.a.u.1.1 4
11.6 odd 10 2057.2.a.r.1.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
187.2.g.e.69.2 8 11.3 even 5 inner
187.2.g.e.103.2 yes 8 1.1 even 1 trivial
2057.2.a.r.1.4 4 11.6 odd 10
2057.2.a.u.1.1 4 11.5 even 5