Properties

Label 108.3.j.a.31.17
Level $108$
Weight $3$
Character 108.31
Analytic conductor $2.943$
Analytic rank $0$
Dimension $204$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [108,3,Mod(7,108)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(108, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([9, 16]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("108.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 108.j (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.94278685509\)
Analytic rank: \(0\)
Dimension: \(204\)
Relative dimension: \(34\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 31.17
Character \(\chi\) \(=\) 108.31
Dual form 108.3.j.a.7.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.103865 - 1.99730i) q^{2} +(0.204519 - 2.99302i) q^{3} +(-3.97842 - 0.414901i) q^{4} +(1.50670 - 8.54492i) q^{5} +(-5.95672 - 0.719357i) q^{6} +(7.53806 + 8.98351i) q^{7} +(-1.24190 + 7.90302i) q^{8} +(-8.91634 - 1.22426i) q^{9} +O(q^{10})\) \(q+(0.103865 - 1.99730i) q^{2} +(0.204519 - 2.99302i) q^{3} +(-3.97842 - 0.414901i) q^{4} +(1.50670 - 8.54492i) q^{5} +(-5.95672 - 0.719357i) q^{6} +(7.53806 + 8.98351i) q^{7} +(-1.24190 + 7.90302i) q^{8} +(-8.91634 - 1.22426i) q^{9} +(-16.9103 - 3.89685i) q^{10} +(-2.27133 + 0.400497i) q^{11} +(-2.05547 + 11.8226i) q^{12} +(-4.42594 + 1.61091i) q^{13} +(18.7257 - 14.1227i) q^{14} +(-25.2670 - 6.25718i) q^{15} +(15.6557 + 3.30130i) q^{16} +(6.77412 - 11.7331i) q^{17} +(-3.37131 + 17.6815i) q^{18} +(13.9009 - 8.02568i) q^{19} +(-9.53958 + 33.3702i) q^{20} +(28.4295 - 20.7243i) q^{21} +(0.564001 + 4.57813i) q^{22} +(-3.20904 + 3.82439i) q^{23} +(23.3999 + 5.33336i) q^{24} +(-47.2531 - 17.1987i) q^{25} +(2.75777 + 9.00726i) q^{26} +(-5.48779 + 26.4364i) q^{27} +(-26.2623 - 38.8678i) q^{28} +(34.0967 + 12.4102i) q^{29} +(-15.1218 + 49.8158i) q^{30} +(-0.283047 + 0.337322i) q^{31} +(8.21978 - 30.9263i) q^{32} +(0.734166 + 6.88006i) q^{33} +(-22.7310 - 14.7486i) q^{34} +(88.1209 - 50.8766i) q^{35} +(34.9651 + 8.57002i) q^{36} +(18.9267 - 32.7821i) q^{37} +(-14.5859 - 28.5979i) q^{38} +(3.91630 + 13.5764i) q^{39} +(65.6594 + 22.5194i) q^{40} +(2.35960 - 0.858824i) q^{41} +(-38.4398 - 58.9348i) q^{42} +(-17.5866 + 3.10099i) q^{43} +(9.20249 - 0.650970i) q^{44} +(-23.8954 + 74.3448i) q^{45} +(7.30515 + 6.80665i) q^{46} +(5.64102 + 6.72271i) q^{47} +(13.0828 - 46.1827i) q^{48} +(-15.3723 + 87.1809i) q^{49} +(-39.2590 + 92.5924i) q^{50} +(-33.7320 - 22.6747i) q^{51} +(18.2767 - 4.57256i) q^{52} -41.4639 q^{53} +(52.2315 + 13.7066i) q^{54} +20.0118i q^{55} +(-80.3584 + 48.4168i) q^{56} +(-21.1780 - 43.2471i) q^{57} +(28.3283 - 66.8123i) q^{58} +(25.5867 + 4.51163i) q^{59} +(97.9266 + 35.3770i) q^{60} +(51.1770 - 42.9426i) q^{61} +(0.644335 + 0.600365i) q^{62} +(-56.2138 - 89.3286i) q^{63} +(-60.9154 - 19.6296i) q^{64} +(7.09654 + 40.2465i) q^{65} +(13.8178 - 0.751752i) q^{66} +(32.3784 + 88.9589i) q^{67} +(-31.8184 + 43.8687i) q^{68} +(10.7902 + 10.3869i) q^{69} +(-92.4633 - 181.288i) q^{70} +(-100.208 - 57.8552i) q^{71} +(20.7486 - 68.9456i) q^{72} +(22.5335 + 39.0292i) q^{73} +(-63.5098 - 41.2073i) q^{74} +(-61.1403 + 137.912i) q^{75} +(-58.6335 + 26.1621i) q^{76} +(-20.7193 - 17.3856i) q^{77} +(27.5229 - 6.41192i) q^{78} +(-19.8334 + 54.4917i) q^{79} +(51.7978 - 128.803i) q^{80} +(78.0024 + 21.8318i) q^{81} +(-1.47025 - 4.80203i) q^{82} +(-22.8909 + 62.8923i) q^{83} +(-121.703 + 70.6545i) q^{84} +(-90.0519 - 75.5626i) q^{85} +(4.36697 + 35.4478i) q^{86} +(44.1173 - 99.5139i) q^{87} +(-0.344363 - 18.4478i) q^{88} +(54.3190 + 94.0833i) q^{89} +(146.007 + 55.4482i) q^{90} +(-47.8347 - 27.6174i) q^{91} +(14.3537 - 13.8836i) q^{92} +(0.951723 + 0.916153i) q^{93} +(14.0132 - 10.5686i) q^{94} +(-47.6343 - 130.874i) q^{95} +(-90.8819 - 30.9270i) q^{96} +(30.2853 + 171.757i) q^{97} +(172.530 + 39.7583i) q^{98} +(20.7423 - 0.790274i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 204 q - 6 q^{2} - 6 q^{4} - 12 q^{5} - 6 q^{6} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 39 q^{12} - 12 q^{13} + 39 q^{14} - 6 q^{16} - 6 q^{17} - 27 q^{18} - 69 q^{20} - 12 q^{21} - 6 q^{22} - 138 q^{24} - 12 q^{25} - 174 q^{26} - 12 q^{28} + 60 q^{29} - 153 q^{30} - 96 q^{32} + 48 q^{33} + 6 q^{34} + 24 q^{36} - 6 q^{37} + 72 q^{38} + 69 q^{40} - 192 q^{41} - 126 q^{42} - 219 q^{44} - 132 q^{45} - 3 q^{46} - 219 q^{48} - 12 q^{49} - 165 q^{50} + 21 q^{52} - 24 q^{53} + 78 q^{54} + 99 q^{56} - 150 q^{57} - 141 q^{58} + 210 q^{60} - 12 q^{61} + 294 q^{62} - 3 q^{64} - 156 q^{65} + 393 q^{66} + 375 q^{68} - 60 q^{69} - 165 q^{70} + 228 q^{72} - 6 q^{73} + 447 q^{74} - 54 q^{76} + 132 q^{77} + 750 q^{78} + 798 q^{80} + 228 q^{81} - 12 q^{82} + 762 q^{84} + 138 q^{85} + 606 q^{86} - 198 q^{88} - 114 q^{89} + 894 q^{90} + 723 q^{92} - 1020 q^{93} - 357 q^{94} + 474 q^{96} + 168 q^{97} + 510 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(e\left(\frac{1}{9}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.103865 1.99730i 0.0519327 0.998651i
\(3\) 0.204519 2.99302i 0.0681730 0.997674i
\(4\) −3.97842 0.414901i −0.994606 0.103725i
\(5\) 1.50670 8.54492i 0.301340 1.70898i −0.338912 0.940818i \(-0.610059\pi\)
0.640252 0.768165i \(-0.278830\pi\)
\(6\) −5.95672 0.719357i −0.992787 0.119893i
\(7\) 7.53806 + 8.98351i 1.07687 + 1.28336i 0.956849 + 0.290587i \(0.0938505\pi\)
0.120017 + 0.992772i \(0.461705\pi\)
\(8\) −1.24190 + 7.90302i −0.155238 + 0.987877i
\(9\) −8.91634 1.22426i −0.990705 0.136029i
\(10\) −16.9103 3.89685i −1.69103 0.389685i
\(11\) −2.27133 + 0.400497i −0.206485 + 0.0364089i −0.275934 0.961177i \(-0.588987\pi\)
0.0694489 + 0.997586i \(0.477876\pi\)
\(12\) −2.05547 + 11.8226i −0.171289 + 0.985221i
\(13\) −4.42594 + 1.61091i −0.340457 + 0.123916i −0.506590 0.862187i \(-0.669094\pi\)
0.166133 + 0.986103i \(0.446872\pi\)
\(14\) 18.7257 14.1227i 1.33755 1.00876i
\(15\) −25.2670 6.25718i −1.68446 0.417145i
\(16\) 15.6557 + 3.30130i 0.978482 + 0.206331i
\(17\) 6.77412 11.7331i 0.398478 0.690183i −0.595061 0.803681i \(-0.702872\pi\)
0.993538 + 0.113497i \(0.0362053\pi\)
\(18\) −3.37131 + 17.6815i −0.187295 + 0.982304i
\(19\) 13.9009 8.02568i 0.731626 0.422404i −0.0873908 0.996174i \(-0.527853\pi\)
0.819017 + 0.573770i \(0.194520\pi\)
\(20\) −9.53958 + 33.3702i −0.476979 + 1.66851i
\(21\) 28.4295 20.7243i 1.35379 0.986870i
\(22\) 0.564001 + 4.57813i 0.0256364 + 0.208097i
\(23\) −3.20904 + 3.82439i −0.139524 + 0.166278i −0.831281 0.555852i \(-0.812392\pi\)
0.691758 + 0.722130i \(0.256837\pi\)
\(24\) 23.3999 + 5.33336i 0.974996 + 0.222223i
\(25\) −47.2531 17.1987i −1.89013 0.687949i
\(26\) 2.75777 + 9.00726i 0.106068 + 0.346433i
\(27\) −5.48779 + 26.4364i −0.203252 + 0.979127i
\(28\) −26.2623 38.8678i −0.937940 1.38813i
\(29\) 34.0967 + 12.4102i 1.17575 + 0.427937i 0.854698 0.519126i \(-0.173742\pi\)
0.321049 + 0.947063i \(0.395965\pi\)
\(30\) −15.1218 + 49.8158i −0.504061 + 1.66053i
\(31\) −0.283047 + 0.337322i −0.00913054 + 0.0108813i −0.770590 0.637331i \(-0.780039\pi\)
0.761460 + 0.648212i \(0.224483\pi\)
\(32\) 8.21978 30.9263i 0.256868 0.966446i
\(33\) 0.734166 + 6.88006i 0.0222475 + 0.208487i
\(34\) −22.7310 14.7486i −0.668558 0.433783i
\(35\) 88.1209 50.8766i 2.51774 1.45362i
\(36\) 34.9651 + 8.57002i 0.971251 + 0.238056i
\(37\) 18.9267 32.7821i 0.511533 0.886002i −0.488377 0.872633i \(-0.662411\pi\)
0.999911 0.0133691i \(-0.00425565\pi\)
\(38\) −14.5859 28.5979i −0.383839 0.752575i
\(39\) 3.91630 + 13.5764i 0.100418 + 0.348113i
\(40\) 65.6594 + 22.5194i 1.64149 + 0.562986i
\(41\) 2.35960 0.858824i 0.0575512 0.0209469i −0.313084 0.949725i \(-0.601362\pi\)
0.370635 + 0.928778i \(0.379140\pi\)
\(42\) −38.4398 58.9348i −0.915233 1.40321i
\(43\) −17.5866 + 3.10099i −0.408990 + 0.0721160i −0.374358 0.927284i \(-0.622137\pi\)
−0.0346317 + 0.999400i \(0.511026\pi\)
\(44\) 9.20249 0.650970i 0.209148 0.0147948i
\(45\) −23.8954 + 74.3448i −0.531010 + 1.65211i
\(46\) 7.30515 + 6.80665i 0.158808 + 0.147971i
\(47\) 5.64102 + 6.72271i 0.120022 + 0.143036i 0.822710 0.568462i \(-0.192461\pi\)
−0.702688 + 0.711498i \(0.748017\pi\)
\(48\) 13.0828 46.1827i 0.272557 0.962140i
\(49\) −15.3723 + 87.1809i −0.313721 + 1.77920i
\(50\) −39.2590 + 92.5924i −0.785180 + 1.85185i
\(51\) −33.7320 22.6747i −0.661412 0.444602i
\(52\) 18.2767 4.57256i 0.351474 0.0879339i
\(53\) −41.4639 −0.782338 −0.391169 0.920319i \(-0.627929\pi\)
−0.391169 + 0.920319i \(0.627929\pi\)
\(54\) 52.2315 + 13.7066i 0.967250 + 0.253826i
\(55\) 20.0118i 0.363851i
\(56\) −80.3584 + 48.4168i −1.43497 + 0.864585i
\(57\) −21.1780 43.2471i −0.371545 0.758720i
\(58\) 28.3283 66.8123i 0.488419 1.15194i
\(59\) 25.5867 + 4.51163i 0.433674 + 0.0764684i 0.386224 0.922405i \(-0.373779\pi\)
0.0474502 + 0.998874i \(0.484890\pi\)
\(60\) 97.9266 + 35.3770i 1.63211 + 0.589617i
\(61\) 51.1770 42.9426i 0.838967 0.703977i −0.118364 0.992970i \(-0.537765\pi\)
0.957331 + 0.288993i \(0.0933206\pi\)
\(62\) 0.644335 + 0.600365i 0.0103925 + 0.00968331i
\(63\) −56.2138 89.3286i −0.892282 1.41791i
\(64\) −60.9154 19.6296i −0.951802 0.306712i
\(65\) 7.09654 + 40.2465i 0.109178 + 0.619177i
\(66\) 13.8178 0.751752i 0.209361 0.0113902i
\(67\) 32.3784 + 88.9589i 0.483260 + 1.32775i 0.906683 + 0.421813i \(0.138606\pi\)
−0.423423 + 0.905932i \(0.639172\pi\)
\(68\) −31.8184 + 43.8687i −0.467918 + 0.645128i
\(69\) 10.7902 + 10.3869i 0.156379 + 0.150535i
\(70\) −92.4633 181.288i −1.32090 2.58983i
\(71\) −100.208 57.8552i −1.41138 0.814862i −0.415863 0.909427i \(-0.636521\pi\)
−0.995519 + 0.0945652i \(0.969854\pi\)
\(72\) 20.7486 68.9456i 0.288174 0.957578i
\(73\) 22.5335 + 39.0292i 0.308678 + 0.534646i 0.978073 0.208260i \(-0.0667801\pi\)
−0.669395 + 0.742906i \(0.733447\pi\)
\(74\) −63.5098 41.2073i −0.858241 0.556855i
\(75\) −61.1403 + 137.912i −0.815204 + 1.83883i
\(76\) −58.6335 + 26.1621i −0.771494 + 0.344238i
\(77\) −20.7193 17.3856i −0.269082 0.225787i
\(78\) 27.5229 6.41192i 0.352858 0.0822041i
\(79\) −19.8334 + 54.4917i −0.251055 + 0.689769i 0.748587 + 0.663036i \(0.230733\pi\)
−0.999643 + 0.0267327i \(0.991490\pi\)
\(80\) 51.7978 128.803i 0.647473 1.61003i
\(81\) 78.0024 + 21.8318i 0.962992 + 0.269529i
\(82\) −1.47025 4.80203i −0.0179299 0.0585614i
\(83\) −22.8909 + 62.8923i −0.275794 + 0.757738i 0.722033 + 0.691858i \(0.243208\pi\)
−0.997828 + 0.0658799i \(0.979015\pi\)
\(84\) −121.703 + 70.6545i −1.44885 + 0.841125i
\(85\) −90.0519 75.5626i −1.05943 0.888971i
\(86\) 4.36697 + 35.4478i 0.0507787 + 0.412183i
\(87\) 44.1173 99.5139i 0.507095 1.14384i
\(88\) −0.344363 18.4478i −0.00391322 0.209634i
\(89\) 54.3190 + 94.0833i 0.610326 + 1.05712i 0.991185 + 0.132482i \(0.0422948\pi\)
−0.380860 + 0.924633i \(0.624372\pi\)
\(90\) 146.007 + 55.4482i 1.62230 + 0.616091i
\(91\) −47.8347 27.6174i −0.525656 0.303487i
\(92\) 14.3537 13.8836i 0.156018 0.150909i
\(93\) 0.951723 + 0.916153i 0.0102336 + 0.00985111i
\(94\) 14.0132 10.5686i 0.149076 0.112432i
\(95\) −47.6343 130.874i −0.501414 1.37762i
\(96\) −90.8819 30.9270i −0.946687 0.322156i
\(97\) 30.2853 + 171.757i 0.312220 + 1.77069i 0.587403 + 0.809295i \(0.300150\pi\)
−0.275183 + 0.961392i \(0.588738\pi\)
\(98\) 172.530 + 39.7583i 1.76051 + 0.405697i
\(99\) 20.7423 0.790274i 0.209518 0.00798256i
\(100\) 180.857 + 88.0292i 1.80857 + 0.880292i
\(101\) −57.1968 + 47.9938i −0.566305 + 0.475186i −0.880417 0.474200i \(-0.842738\pi\)
0.314112 + 0.949386i \(0.398293\pi\)
\(102\) −48.7918 + 65.0179i −0.478351 + 0.637430i
\(103\) 137.158 + 24.1847i 1.33163 + 0.234803i 0.793764 0.608226i \(-0.208119\pi\)
0.537868 + 0.843029i \(0.319230\pi\)
\(104\) −7.23447 36.9789i −0.0695622 0.355566i
\(105\) −134.252 274.153i −1.27859 2.61098i
\(106\) −4.30667 + 82.8160i −0.0406289 + 0.781283i
\(107\) 28.1004i 0.262621i 0.991341 + 0.131310i \(0.0419185\pi\)
−0.991341 + 0.131310i \(0.958082\pi\)
\(108\) 32.8013 102.898i 0.303715 0.952763i
\(109\) 12.7869 0.117311 0.0586555 0.998278i \(-0.481319\pi\)
0.0586555 + 0.998278i \(0.481319\pi\)
\(110\) 39.9696 + 2.07853i 0.363360 + 0.0188957i
\(111\) −94.2465 63.3526i −0.849068 0.570745i
\(112\) 88.3564 + 165.529i 0.788897 + 1.47793i
\(113\) 36.5416 207.238i 0.323377 1.83396i −0.197465 0.980310i \(-0.563271\pi\)
0.520842 0.853653i \(-0.325618\pi\)
\(114\) −88.5771 + 37.8071i −0.776992 + 0.331641i
\(115\) 27.8440 + 33.1832i 0.242122 + 0.288550i
\(116\) −130.502 63.5196i −1.12502 0.547583i
\(117\) 41.4354 8.94495i 0.354149 0.0764525i
\(118\) 11.6687 50.6358i 0.0988870 0.429117i
\(119\) 156.468 27.5896i 1.31486 0.231845i
\(120\) 80.8297 191.914i 0.673581 1.59929i
\(121\) −108.704 + 39.5651i −0.898382 + 0.326984i
\(122\) −80.4538 106.676i −0.659457 0.874394i
\(123\) −2.08790 7.23798i −0.0169748 0.0588453i
\(124\) 1.26603 1.22457i 0.0102100 0.00987559i
\(125\) −109.699 + 190.004i −0.877590 + 1.52003i
\(126\) −184.255 + 102.998i −1.46234 + 0.817442i
\(127\) 96.5648 55.7517i 0.760353 0.438990i −0.0690695 0.997612i \(-0.522003\pi\)
0.829422 + 0.558622i \(0.188670\pi\)
\(128\) −45.5331 + 119.627i −0.355728 + 0.934590i
\(129\) 5.68453 + 53.2712i 0.0440661 + 0.412955i
\(130\) 81.1214 9.99371i 0.624011 0.0768747i
\(131\) −10.1474 + 12.0932i −0.0774612 + 0.0923146i −0.803383 0.595462i \(-0.796969\pi\)
0.725922 + 0.687777i \(0.241413\pi\)
\(132\) −0.0662835 27.6764i −0.000502147 0.209670i
\(133\) 176.885 + 64.3807i 1.32996 + 0.484066i
\(134\) 181.041 55.4297i 1.35105 0.413654i
\(135\) 217.629 + 86.7244i 1.61206 + 0.642403i
\(136\) 84.3142 + 68.1074i 0.619958 + 0.500789i
\(137\) 99.8901 + 36.3570i 0.729125 + 0.265380i 0.679794 0.733403i \(-0.262069\pi\)
0.0493306 + 0.998783i \(0.484291\pi\)
\(138\) 21.8665 20.4724i 0.158453 0.148351i
\(139\) −36.3183 + 43.2824i −0.261283 + 0.311385i −0.880697 0.473679i \(-0.842926\pi\)
0.619415 + 0.785064i \(0.287370\pi\)
\(140\) −371.691 + 165.847i −2.65494 + 1.18462i
\(141\) 21.2749 15.5088i 0.150886 0.109991i
\(142\) −125.962 + 194.137i −0.887059 + 1.36716i
\(143\) 9.40763 5.43150i 0.0657876 0.0379825i
\(144\) −135.550 48.6022i −0.941320 0.337515i
\(145\) 157.417 272.655i 1.08564 1.88038i
\(146\) 80.2935 40.9524i 0.549955 0.280496i
\(147\) 257.790 + 63.8399i 1.75368 + 0.434285i
\(148\) −88.8999 + 122.568i −0.600675 + 0.828164i
\(149\) 110.073 40.0635i 0.738748 0.268882i 0.0548851 0.998493i \(-0.482521\pi\)
0.683863 + 0.729610i \(0.260299\pi\)
\(150\) 269.102 + 136.440i 1.79401 + 0.909599i
\(151\) −244.777 + 43.1607i −1.62104 + 0.285832i −0.909152 0.416464i \(-0.863269\pi\)
−0.711884 + 0.702297i \(0.752158\pi\)
\(152\) 46.1636 + 119.826i 0.303708 + 0.788330i
\(153\) −74.7647 + 96.3232i −0.488658 + 0.629564i
\(154\) −36.8762 + 39.5770i −0.239456 + 0.256993i
\(155\) 2.45592 + 2.92685i 0.0158446 + 0.0188829i
\(156\) −9.94785 55.6376i −0.0637683 0.356651i
\(157\) 32.2061 182.650i 0.205134 1.16337i −0.692094 0.721807i \(-0.743312\pi\)
0.897228 0.441567i \(-0.145577\pi\)
\(158\) 106.776 + 45.2730i 0.675800 + 0.286538i
\(159\) −8.48016 + 124.102i −0.0533343 + 0.780518i
\(160\) −251.878 116.834i −1.57424 0.730212i
\(161\) −58.5464 −0.363642
\(162\) 51.7065 153.527i 0.319176 0.947696i
\(163\) 3.07052i 0.0188375i −0.999956 0.00941877i \(-0.997002\pi\)
0.999956 0.00941877i \(-0.00299813\pi\)
\(164\) −9.74381 + 2.43777i −0.0594135 + 0.0148644i
\(165\) 59.8957 + 4.09279i 0.363004 + 0.0248048i
\(166\) 123.237 + 52.2524i 0.742393 + 0.314773i
\(167\) −90.6052 15.9761i −0.542546 0.0956655i −0.104343 0.994541i \(-0.533274\pi\)
−0.438203 + 0.898876i \(0.644385\pi\)
\(168\) 128.478 + 250.416i 0.764748 + 1.49057i
\(169\) −112.468 + 94.3715i −0.665489 + 0.558411i
\(170\) −160.274 + 172.013i −0.942791 + 1.01184i
\(171\) −133.771 + 54.5415i −0.782285 + 0.318956i
\(172\) 71.2534 5.04036i 0.414264 0.0293044i
\(173\) −49.4146 280.244i −0.285633 1.61991i −0.703014 0.711176i \(-0.748163\pi\)
0.417381 0.908732i \(-0.362948\pi\)
\(174\) −194.177 98.4516i −1.11596 0.565814i
\(175\) −201.692 554.144i −1.15253 3.16654i
\(176\) −36.8815 1.22829i −0.209554 0.00697891i
\(177\) 18.7364 75.6590i 0.105855 0.427452i
\(178\) 193.554 98.7194i 1.08738 0.554603i
\(179\) −37.3404 21.5585i −0.208606 0.120438i 0.392058 0.919941i \(-0.371763\pi\)
−0.600663 + 0.799502i \(0.705097\pi\)
\(180\) 125.912 285.861i 0.699511 1.58812i
\(181\) −52.2292 90.4636i −0.288559 0.499799i 0.684907 0.728630i \(-0.259843\pi\)
−0.973466 + 0.228832i \(0.926509\pi\)
\(182\) −60.1286 + 92.6718i −0.330377 + 0.509186i
\(183\) −118.061 161.956i −0.645144 0.885007i
\(184\) −26.2389 30.1107i −0.142603 0.163645i
\(185\) −251.603 211.120i −1.36002 1.14119i
\(186\) 1.92868 1.80572i 0.0103693 0.00970817i
\(187\) −10.6872 + 29.3628i −0.0571508 + 0.157021i
\(188\) −19.6531 29.0863i −0.104538 0.154714i
\(189\) −278.859 + 149.980i −1.47544 + 0.793543i
\(190\) −266.343 + 81.5468i −1.40180 + 0.429194i
\(191\) −86.7947 + 238.466i −0.454422 + 1.24852i 0.475160 + 0.879900i \(0.342390\pi\)
−0.929582 + 0.368616i \(0.879832\pi\)
\(192\) −71.2100 + 178.306i −0.370885 + 0.928679i
\(193\) −0.204011 0.171186i −0.00105705 0.000886973i 0.642259 0.766488i \(-0.277997\pi\)
−0.643316 + 0.765601i \(0.722442\pi\)
\(194\) 346.195 42.6493i 1.78451 0.219842i
\(195\) 121.910 13.0089i 0.625179 0.0667124i
\(196\) 97.3291 340.465i 0.496577 1.73706i
\(197\) 25.6282 + 44.3894i 0.130093 + 0.225327i 0.923712 0.383087i \(-0.125139\pi\)
−0.793620 + 0.608414i \(0.791806\pi\)
\(198\) 0.575993 41.5107i 0.00290905 0.209650i
\(199\) 86.0717 + 49.6935i 0.432521 + 0.249716i 0.700420 0.713731i \(-0.252996\pi\)
−0.267899 + 0.963447i \(0.586329\pi\)
\(200\) 194.606 352.083i 0.973028 1.76042i
\(201\) 272.878 78.7154i 1.35760 0.391619i
\(202\) 89.9173 + 119.224i 0.445135 + 0.590218i
\(203\) 145.536 + 399.856i 0.716925 + 1.96974i
\(204\) 124.793 + 104.205i 0.611728 + 0.510809i
\(205\) −3.78337 21.4566i −0.0184555 0.104666i
\(206\) 62.5501 271.434i 0.303641 1.31764i
\(207\) 33.2950 30.1709i 0.160845 0.145753i
\(208\) −74.6094 + 10.6086i −0.358699 + 0.0510029i
\(209\) −28.3593 + 23.7963i −0.135690 + 0.113858i
\(210\) −561.510 + 239.668i −2.67386 + 1.14127i
\(211\) 100.532 + 17.7265i 0.476456 + 0.0840120i 0.406719 0.913553i \(-0.366673\pi\)
0.0697369 + 0.997565i \(0.477784\pi\)
\(212\) 164.961 + 17.2034i 0.778119 + 0.0811482i
\(213\) −193.656 + 288.093i −0.909184 + 1.35255i
\(214\) 56.1250 + 2.91866i 0.262267 + 0.0136386i
\(215\) 154.948i 0.720688i
\(216\) −202.112 76.2016i −0.935704 0.352785i
\(217\) −5.16396 −0.0237970
\(218\) 1.32811 25.5393i 0.00609227 0.117153i
\(219\) 121.424 59.4610i 0.554446 0.271512i
\(220\) 8.30291 79.6154i 0.0377405 0.361888i
\(221\) −11.0809 + 62.8426i −0.0501396 + 0.284356i
\(222\) −136.323 + 181.659i −0.614069 + 0.818282i
\(223\) −211.508 252.065i −0.948464 1.13034i −0.991349 0.131256i \(-0.958099\pi\)
0.0428842 0.999080i \(-0.486345\pi\)
\(224\) 339.788 159.282i 1.51691 0.711079i
\(225\) 400.269 + 211.200i 1.77898 + 0.938666i
\(226\) −410.121 94.5095i −1.81469 0.418183i
\(227\) −339.879 + 59.9299i −1.49727 + 0.264008i −0.861454 0.507836i \(-0.830446\pi\)
−0.635812 + 0.771844i \(0.719335\pi\)
\(228\) 66.3120 + 180.842i 0.290842 + 0.793166i
\(229\) −273.587 + 99.5776i −1.19470 + 0.434837i −0.861373 0.507973i \(-0.830395\pi\)
−0.333331 + 0.942810i \(0.608173\pi\)
\(230\) 69.1689 52.1663i 0.300734 0.226810i
\(231\) −56.2729 + 58.4577i −0.243605 + 0.253064i
\(232\) −140.422 + 254.054i −0.605269 + 1.09506i
\(233\) 49.5426 85.8104i 0.212629 0.368285i −0.739907 0.672709i \(-0.765131\pi\)
0.952537 + 0.304424i \(0.0984640\pi\)
\(234\) −13.5620 83.6881i −0.0579575 0.357641i
\(235\) 65.9443 38.0730i 0.280614 0.162013i
\(236\) −99.9231 28.5652i −0.423403 0.121039i
\(237\) 159.039 + 70.5063i 0.671049 + 0.297495i
\(238\) −38.8531 315.380i −0.163248 1.32513i
\(239\) 74.1713 88.3940i 0.310340 0.369849i −0.588219 0.808702i \(-0.700171\pi\)
0.898559 + 0.438853i \(0.144615\pi\)
\(240\) −374.915 181.374i −1.56215 0.755727i
\(241\) 109.908 + 40.0034i 0.456051 + 0.165989i 0.559823 0.828612i \(-0.310869\pi\)
−0.103772 + 0.994601i \(0.533091\pi\)
\(242\) 67.7328 + 221.225i 0.279888 + 0.914151i
\(243\) 81.2960 228.998i 0.334552 0.942377i
\(244\) −221.421 + 149.610i −0.907462 + 0.613158i
\(245\) 721.792 + 262.711i 2.94609 + 1.07229i
\(246\) −14.6733 + 3.41838i −0.0596475 + 0.0138959i
\(247\) −48.5959 + 57.9143i −0.196745 + 0.234471i
\(248\) −2.31434 2.65584i −0.00933203 0.0107090i
\(249\) 183.556 + 81.3756i 0.737173 + 0.326810i
\(250\) 368.101 + 238.836i 1.47240 + 0.955345i
\(251\) −127.608 + 73.6744i −0.508397 + 0.293523i −0.732175 0.681117i \(-0.761495\pi\)
0.223777 + 0.974640i \(0.428161\pi\)
\(252\) 186.580 + 378.710i 0.740396 + 1.50282i
\(253\) 5.75715 9.97168i 0.0227555 0.0394138i
\(254\) −101.323 198.660i −0.398910 0.782125i
\(255\) −244.578 + 254.073i −0.959128 + 0.996366i
\(256\) 234.203 + 103.369i 0.914855 + 0.403783i
\(257\) −294.633 + 107.238i −1.14643 + 0.417267i −0.844232 0.535978i \(-0.819943\pi\)
−0.302199 + 0.953245i \(0.597721\pi\)
\(258\) 106.989 5.82069i 0.414686 0.0225608i
\(259\) 437.169 77.0847i 1.68791 0.297624i
\(260\) −11.5347 163.062i −0.0443644 0.627161i
\(261\) −288.824 152.396i −1.10661 0.583894i
\(262\) 23.0998 + 21.5235i 0.0881673 + 0.0821508i
\(263\) −131.924 157.221i −0.501613 0.597799i 0.454518 0.890737i \(-0.349811\pi\)
−0.956131 + 0.292938i \(0.905367\pi\)
\(264\) −55.2850 2.74223i −0.209413 0.0103872i
\(265\) −62.4737 + 354.306i −0.235750 + 1.33700i
\(266\) 146.960 346.605i 0.552481 1.30303i
\(267\) 292.702 143.336i 1.09626 0.536839i
\(268\) −91.9059 367.350i −0.342932 1.37071i
\(269\) −270.423 −1.00529 −0.502645 0.864493i \(-0.667640\pi\)
−0.502645 + 0.864493i \(0.667640\pi\)
\(270\) 195.819 425.662i 0.725255 1.57653i
\(271\) 232.697i 0.858661i 0.903148 + 0.429330i \(0.141250\pi\)
−0.903148 + 0.429330i \(0.858750\pi\)
\(272\) 144.788 161.327i 0.532310 0.593114i
\(273\) −92.4424 + 137.522i −0.338617 + 0.503743i
\(274\) 82.9911 195.734i 0.302887 0.714359i
\(275\) 114.216 + 20.1393i 0.415330 + 0.0732338i
\(276\) −38.6183 45.8003i −0.139921 0.165943i
\(277\) −57.6704 + 48.3912i −0.208196 + 0.174698i −0.740923 0.671590i \(-0.765612\pi\)
0.532727 + 0.846287i \(0.321167\pi\)
\(278\) 82.6759 + 77.0341i 0.297395 + 0.277101i
\(279\) 2.93671 2.66116i 0.0105258 0.00953819i
\(280\) 292.641 + 759.605i 1.04515 + 2.71287i
\(281\) 24.3783 + 138.256i 0.0867556 + 0.492015i 0.996964 + 0.0778647i \(0.0248102\pi\)
−0.910208 + 0.414151i \(0.864079\pi\)
\(282\) −28.7660 44.1032i −0.102007 0.156394i
\(283\) −48.0225 131.941i −0.169691 0.466221i 0.825474 0.564440i \(-0.190908\pi\)
−0.995165 + 0.0982185i \(0.968686\pi\)
\(284\) 374.666 + 271.749i 1.31925 + 0.956862i
\(285\) −401.451 + 115.804i −1.40860 + 0.406331i
\(286\) −9.87121 19.3540i −0.0345147 0.0676714i
\(287\) 25.5021 + 14.7236i 0.0888573 + 0.0513018i
\(288\) −111.152 + 265.686i −0.385945 + 0.922522i
\(289\) 52.7226 + 91.3183i 0.182431 + 0.315980i
\(290\) −528.223 342.729i −1.82146 1.18182i
\(291\) 520.265 55.5171i 1.78785 0.190780i
\(292\) −73.4546 164.624i −0.251557 0.563780i
\(293\) 255.034 + 213.999i 0.870422 + 0.730371i 0.964187 0.265223i \(-0.0854457\pi\)
−0.0937648 + 0.995594i \(0.529890\pi\)
\(294\) 154.283 508.254i 0.524772 1.72876i
\(295\) 77.1031 211.839i 0.261366 0.718098i
\(296\) 235.572 + 190.290i 0.795851 + 0.642873i
\(297\) 1.87689 62.2438i 0.00631949 0.209575i
\(298\) −68.5860 224.011i −0.230154 0.751715i
\(299\) 8.04230 22.0960i 0.0268973 0.0738997i
\(300\) 300.462 523.306i 1.00154 1.74435i
\(301\) −160.426 134.614i −0.532978 0.447221i
\(302\) 60.7811 + 493.375i 0.201262 + 1.63369i
\(303\) 131.949 + 181.007i 0.435474 + 0.597382i
\(304\) 244.124 79.7568i 0.803038 0.262358i
\(305\) −289.832 502.005i −0.950270 1.64592i
\(306\) 184.621 + 159.332i 0.603337 + 0.520694i
\(307\) −176.337 101.808i −0.574387 0.331622i 0.184513 0.982830i \(-0.440929\pi\)
−0.758900 + 0.651208i \(0.774263\pi\)
\(308\) 75.2169 + 77.7636i 0.244211 + 0.252479i
\(309\) 100.437 405.571i 0.325038 1.31253i
\(310\) 6.10089 4.60121i 0.0196803 0.0148426i
\(311\) −63.2509 173.780i −0.203379 0.558779i 0.795508 0.605943i \(-0.207204\pi\)
−0.998887 + 0.0471636i \(0.984982\pi\)
\(312\) −112.158 + 14.0900i −0.359481 + 0.0451604i
\(313\) −19.2606 109.232i −0.0615355 0.348985i −0.999994 0.00359201i \(-0.998857\pi\)
0.938458 0.345393i \(-0.112254\pi\)
\(314\) −361.462 83.2963i −1.15115 0.265275i
\(315\) −848.003 + 345.751i −2.69207 + 1.09762i
\(316\) 101.514 208.562i 0.321248 0.660008i
\(317\) 104.031 87.2920i 0.328172 0.275369i −0.463783 0.885949i \(-0.653508\pi\)
0.791955 + 0.610580i \(0.209064\pi\)
\(318\) 246.989 + 29.8274i 0.776695 + 0.0937968i
\(319\) −82.4151 14.5320i −0.258355 0.0455549i
\(320\) −259.514 + 490.941i −0.810981 + 1.53419i
\(321\) 84.1052 + 5.74707i 0.262010 + 0.0179036i
\(322\) −6.08094 + 116.935i −0.0188849 + 0.363152i
\(323\) 217.468i 0.673275i
\(324\) −301.269 119.219i −0.929841 0.367961i
\(325\) 236.845 0.728755
\(326\) −6.13275 0.318920i −0.0188121 0.000978284i
\(327\) 2.61516 38.2714i 0.00799743 0.117038i
\(328\) 3.85691 + 19.7145i 0.0117589 + 0.0601053i
\(329\) −17.8712 + 101.352i −0.0543196 + 0.308062i
\(330\) 14.3956 119.205i 0.0436231 0.361226i
\(331\) 114.419 + 136.359i 0.345677 + 0.411962i 0.910670 0.413133i \(-0.135566\pi\)
−0.564993 + 0.825095i \(0.691121\pi\)
\(332\) 117.164 240.715i 0.352903 0.725044i
\(333\) −208.891 + 269.125i −0.627300 + 0.808183i
\(334\) −41.3199 + 179.307i −0.123712 + 0.536846i
\(335\) 808.931 142.636i 2.41472 0.425780i
\(336\) 513.501 230.599i 1.52828 0.686306i
\(337\) 547.261 199.187i 1.62392 0.591059i 0.639797 0.768544i \(-0.279019\pi\)
0.984123 + 0.177486i \(0.0567963\pi\)
\(338\) 176.807 + 234.434i 0.523097 + 0.693590i
\(339\) −612.794 151.754i −1.80765 0.447652i
\(340\) 326.914 + 337.983i 0.961511 + 0.994066i
\(341\) 0.507797 0.879530i 0.00148914 0.00257927i
\(342\) 95.0416 + 272.845i 0.277899 + 0.797793i
\(343\) −401.424 + 231.762i −1.17033 + 0.675692i
\(344\) −2.66635 142.838i −0.00775101 0.415227i
\(345\) 105.013 76.5512i 0.304385 0.221887i
\(346\) −564.864 + 69.5881i −1.63255 + 0.201122i
\(347\) 174.936 208.480i 0.504138 0.600808i −0.452616 0.891705i \(-0.649509\pi\)
0.956754 + 0.290897i \(0.0939538\pi\)
\(348\) −216.806 + 377.604i −0.623005 + 1.08507i
\(349\) 239.597 + 87.2061i 0.686524 + 0.249874i 0.661646 0.749816i \(-0.269858\pi\)
0.0248779 + 0.999690i \(0.492080\pi\)
\(350\) −1127.74 + 345.283i −3.22212 + 0.986523i
\(351\) −18.2981 125.846i −0.0521313 0.358537i
\(352\) −6.28397 + 73.5359i −0.0178522 + 0.208909i
\(353\) −216.192 78.6876i −0.612443 0.222911i 0.0171289 0.999853i \(-0.494547\pi\)
−0.629572 + 0.776942i \(0.716770\pi\)
\(354\) −149.168 45.2806i −0.421378 0.127911i
\(355\) −645.351 + 769.100i −1.81789 + 2.16648i
\(356\) −177.069 396.840i −0.497384 1.11472i
\(357\) −50.5755 473.955i −0.141668 1.32761i
\(358\) −46.9372 + 72.3408i −0.131109 + 0.202069i
\(359\) −513.681 + 296.574i −1.43087 + 0.826112i −0.997187 0.0749550i \(-0.976119\pi\)
−0.433680 + 0.901067i \(0.642785\pi\)
\(360\) −557.873 281.175i −1.54965 0.781042i
\(361\) −51.6768 + 89.5068i −0.143149 + 0.247941i
\(362\) −186.108 + 94.9214i −0.514110 + 0.262214i
\(363\) 96.1871 + 333.446i 0.264978 + 0.918584i
\(364\) 178.848 + 129.720i 0.491341 + 0.356374i
\(365\) 367.452 133.742i 1.00672 0.366415i
\(366\) −335.738 + 218.982i −0.917317 + 0.598313i
\(367\) 328.288 57.8861i 0.894519 0.157728i 0.292553 0.956249i \(-0.405495\pi\)
0.601966 + 0.798522i \(0.294384\pi\)
\(368\) −62.8654 + 49.2795i −0.170830 + 0.133912i
\(369\) −22.0904 + 4.76881i −0.0598657 + 0.0129236i
\(370\) −447.803 + 480.599i −1.21028 + 1.29892i
\(371\) −312.558 372.492i −0.842473 1.00402i
\(372\) −3.40624 4.03972i −0.00915657 0.0108595i
\(373\) 10.8367 61.4578i 0.0290527 0.164766i −0.966829 0.255423i \(-0.917785\pi\)
0.995882 + 0.0906564i \(0.0288965\pi\)
\(374\) 57.5364 + 24.3953i 0.153841 + 0.0652282i
\(375\) 546.250 + 367.190i 1.45667 + 0.979174i
\(376\) −60.1353 + 36.2322i −0.159934 + 0.0963621i
\(377\) −170.902 −0.453320
\(378\) 270.591 + 572.543i 0.715849 + 1.51466i
\(379\) 341.891i 0.902088i −0.892502 0.451044i \(-0.851052\pi\)
0.892502 0.451044i \(-0.148948\pi\)
\(380\) 135.210 + 540.437i 0.355815 + 1.42220i
\(381\) −147.117 300.423i −0.386133 0.788511i
\(382\) 467.274 + 198.124i 1.22323 + 0.518648i
\(383\) 173.175 + 30.5355i 0.452155 + 0.0797272i 0.395088 0.918643i \(-0.370714\pi\)
0.0570670 + 0.998370i \(0.481825\pi\)
\(384\) 348.735 + 160.748i 0.908164 + 0.418614i
\(385\) −179.776 + 150.850i −0.466951 + 0.391818i
\(386\) −0.363099 + 0.389692i −0.000940672 + 0.00100956i
\(387\) 160.604 6.11896i 0.414998 0.0158113i
\(388\) −49.2259 695.886i −0.126871 1.79352i
\(389\) 18.0397 + 102.308i 0.0463746 + 0.263003i 0.999176 0.0405915i \(-0.0129242\pi\)
−0.952801 + 0.303595i \(0.901813\pi\)
\(390\) −13.3205 244.842i −0.0341552 0.627800i
\(391\) 23.1336 + 63.5590i 0.0591651 + 0.162555i
\(392\) −669.901 229.758i −1.70893 0.586117i
\(393\) 34.1199 + 32.8447i 0.0868191 + 0.0835743i
\(394\) 91.3209 46.5768i 0.231779 0.118215i
\(395\) 435.744 + 251.577i 1.10315 + 0.636904i
\(396\) −82.8496 5.46196i −0.209216 0.0137928i
\(397\) −309.052 535.294i −0.778469 1.34835i −0.932824 0.360333i \(-0.882663\pi\)
0.154354 0.988016i \(-0.450670\pi\)
\(398\) 108.193 166.750i 0.271841 0.418969i
\(399\) 228.869 516.252i 0.573607 1.29386i
\(400\) −683.003 425.255i −1.70751 1.06314i
\(401\) −157.870 132.468i −0.393690 0.330345i 0.424359 0.905494i \(-0.360500\pi\)
−0.818048 + 0.575149i \(0.804944\pi\)
\(402\) −128.876 553.195i −0.320587 1.37611i
\(403\) 0.709353 1.94893i 0.00176018 0.00483606i
\(404\) 247.466 167.209i 0.612539 0.413883i
\(405\) 304.077 633.630i 0.750808 1.56452i
\(406\) 813.749 249.148i 2.00431 0.613664i
\(407\) −29.8598 + 82.0391i −0.0733656 + 0.201570i
\(408\) 221.091 238.425i 0.541889 0.584375i
\(409\) −197.638 165.838i −0.483222 0.405472i 0.368368 0.929680i \(-0.379917\pi\)
−0.851590 + 0.524208i \(0.824361\pi\)
\(410\) −43.2482 + 5.32794i −0.105483 + 0.0129950i
\(411\) 129.247 291.538i 0.314469 0.709337i
\(412\) −535.639 153.124i −1.30009 0.371660i
\(413\) 152.344 + 263.868i 0.368872 + 0.638905i
\(414\) −56.8021 69.6338i −0.137203 0.168198i
\(415\) 502.919 + 290.361i 1.21185 + 0.699664i
\(416\) 13.4392 + 150.119i 0.0323058 + 0.360864i
\(417\) 122.117 + 117.553i 0.292848 + 0.281903i
\(418\) 44.5828 + 59.1137i 0.106657 + 0.141420i
\(419\) −41.7733 114.771i −0.0996975 0.273917i 0.879810 0.475326i \(-0.157670\pi\)
−0.979507 + 0.201410i \(0.935448\pi\)
\(420\) 420.367 + 1146.40i 1.00087 + 2.72952i
\(421\) −19.2591 109.224i −0.0457461 0.259439i 0.953354 0.301855i \(-0.0976058\pi\)
−0.999100 + 0.0424156i \(0.986495\pi\)
\(422\) 45.8470 198.952i 0.108642 0.471450i
\(423\) −42.0670 66.8481i −0.0994491 0.158033i
\(424\) 51.4942 327.690i 0.121449 0.772854i
\(425\) −521.893 + 437.920i −1.22798 + 1.03040i
\(426\) 555.293 + 416.713i 1.30351 + 0.978199i
\(427\) 771.550 + 136.045i 1.80691 + 0.318607i
\(428\) 11.6589 111.795i 0.0272404 0.261204i
\(429\) −14.3325 29.2681i −0.0334092 0.0682239i
\(430\) 309.478 + 16.0937i 0.719716 + 0.0374273i
\(431\) 697.944i 1.61936i −0.586872 0.809679i \(-0.699641\pi\)
0.586872 0.809679i \(-0.300359\pi\)
\(432\) −173.190 + 395.764i −0.400903 + 0.916121i
\(433\) −599.940 −1.38554 −0.692772 0.721157i \(-0.743611\pi\)
−0.692772 + 0.721157i \(0.743611\pi\)
\(434\) −0.536356 + 10.3140i −0.00123584 + 0.0237649i
\(435\) −783.866 526.916i −1.80199 1.21130i
\(436\) −50.8717 5.30529i −0.116678 0.0121681i
\(437\) −13.9152 + 78.9172i −0.0318426 + 0.180589i
\(438\) −106.150 248.695i −0.242351 0.567798i
\(439\) 501.455 + 597.611i 1.14227 + 1.36130i 0.922615 + 0.385722i \(0.126048\pi\)
0.219652 + 0.975578i \(0.429508\pi\)
\(440\) −158.153 24.8527i −0.359440 0.0564834i
\(441\) 243.797 758.515i 0.552828 1.71999i
\(442\) 124.365 + 28.6590i 0.281368 + 0.0648393i
\(443\) −682.883 + 120.411i −1.54150 + 0.271807i −0.878840 0.477117i \(-0.841682\pi\)
−0.662656 + 0.748924i \(0.730571\pi\)
\(444\) 348.668 + 291.147i 0.785287 + 0.655736i
\(445\) 885.776 322.396i 1.99051 0.724485i
\(446\) −525.418 + 396.263i −1.17807 + 0.888483i
\(447\) −97.3987 337.646i −0.217894 0.755360i
\(448\) −282.841 695.202i −0.631342 1.55179i
\(449\) −263.993 + 457.250i −0.587959 + 1.01837i 0.406541 + 0.913633i \(0.366735\pi\)
−0.994499 + 0.104742i \(0.966598\pi\)
\(450\) 463.404 777.522i 1.02979 1.72783i
\(451\) −5.01548 + 2.89569i −0.0111208 + 0.00642060i
\(452\) −231.361 + 809.319i −0.511861 + 1.79053i
\(453\) 79.1195 + 741.448i 0.174657 + 1.63675i
\(454\) 84.3964 + 685.066i 0.185895 + 1.50896i
\(455\) −308.060 + 367.132i −0.677056 + 0.806884i
\(456\) 368.083 113.662i 0.807200 0.249258i
\(457\) 125.330 + 45.6162i 0.274244 + 0.0998167i 0.475481 0.879726i \(-0.342274\pi\)
−0.201237 + 0.979543i \(0.564496\pi\)
\(458\) 170.470 + 556.779i 0.372206 + 1.21567i
\(459\) 273.007 + 243.472i 0.594786 + 0.530441i
\(460\) −97.0076 143.569i −0.210886 0.312107i
\(461\) −497.956 181.241i −1.08017 0.393148i −0.260196 0.965556i \(-0.583787\pi\)
−0.819969 + 0.572408i \(0.806009\pi\)
\(462\) 110.913 + 118.466i 0.240071 + 0.256419i
\(463\) 314.968 375.364i 0.680277 0.810722i −0.309867 0.950780i \(-0.600284\pi\)
0.990143 + 0.140058i \(0.0447289\pi\)
\(464\) 492.838 + 306.853i 1.06215 + 0.661322i
\(465\) 9.26241 6.75202i 0.0199192 0.0145205i
\(466\) −166.243 107.864i −0.356745 0.231468i
\(467\) 168.249 97.1384i 0.360276 0.208005i −0.308926 0.951086i \(-0.599970\pi\)
0.669202 + 0.743081i \(0.266636\pi\)
\(468\) −168.559 + 18.3952i −0.360169 + 0.0393060i
\(469\) −555.093 + 961.449i −1.18357 + 2.05000i
\(470\) −69.1939 135.665i −0.147221 0.288649i
\(471\) −540.088 133.749i −1.14668 0.283968i
\(472\) −67.4318 + 196.610i −0.142864 + 0.416546i
\(473\) 38.7030 14.0867i 0.0818246 0.0297817i
\(474\) 157.341 310.325i 0.331943 0.654694i
\(475\) −794.892 + 140.161i −1.67346 + 0.295076i
\(476\) −633.944 + 44.8442i −1.33182 + 0.0942106i
\(477\) 369.707 + 50.7626i 0.775067 + 0.106420i
\(478\) −168.846 157.324i −0.353233 0.329129i
\(479\) −13.8081 16.4559i −0.0288270 0.0343547i 0.751438 0.659803i \(-0.229360\pi\)
−0.780265 + 0.625449i \(0.784916\pi\)
\(480\) −401.200 + 729.981i −0.835834 + 1.52079i
\(481\) −30.9596 + 175.581i −0.0643652 + 0.365033i
\(482\) 91.3144 215.365i 0.189449 0.446815i
\(483\) −11.9738 + 175.231i −0.0247906 + 0.362796i
\(484\) 448.887 112.305i 0.927453 0.232036i
\(485\) 1513.28 3.12016
\(486\) −448.934 186.158i −0.923732 0.383040i
\(487\) 669.554i 1.37485i 0.726254 + 0.687427i \(0.241260\pi\)
−0.726254 + 0.687427i \(0.758740\pi\)
\(488\) 275.819 + 457.783i 0.565203 + 0.938080i
\(489\) −9.19012 0.627979i −0.0187937 0.00128421i
\(490\) 599.682 1414.35i 1.22384 2.88643i
\(491\) 571.962 + 100.852i 1.16489 + 0.205402i 0.722468 0.691404i \(-0.243007\pi\)
0.442424 + 0.896806i \(0.354119\pi\)
\(492\) 5.30349 + 29.6620i 0.0107795 + 0.0602886i
\(493\) 376.585 315.992i 0.763864 0.640958i
\(494\) 110.625 + 103.076i 0.223937 + 0.208656i
\(495\) 24.4996 178.432i 0.0494941 0.360469i
\(496\) −5.54490 + 4.34659i −0.0111792 + 0.00876329i
\(497\) −235.632 1336.34i −0.474109 2.68881i
\(498\) 181.597 358.165i 0.364652 0.719207i
\(499\) −164.520 452.016i −0.329700 0.905844i −0.988187 0.153252i \(-0.951025\pi\)
0.658487 0.752592i \(-0.271197\pi\)
\(500\) 515.261 710.402i 1.03052 1.42080i
\(501\) −66.3474 + 267.916i −0.132430 + 0.534762i
\(502\) 133.896 + 262.523i 0.266725 + 0.522955i
\(503\) 373.012 + 215.359i 0.741575 + 0.428148i 0.822642 0.568560i \(-0.192499\pi\)
−0.0810668 + 0.996709i \(0.525833\pi\)
\(504\) 775.777 333.321i 1.53924 0.661352i
\(505\) 323.925 + 561.054i 0.641435 + 1.11100i
\(506\) −19.3185 12.5345i −0.0381788 0.0247717i
\(507\) 259.454 + 355.918i 0.511744 + 0.702009i
\(508\) −407.307 + 181.739i −0.801786 + 0.357754i
\(509\) 444.761 + 373.199i 0.873793 + 0.733200i 0.964893 0.262642i \(-0.0845939\pi\)
−0.0911001 + 0.995842i \(0.529038\pi\)
\(510\) 482.058 + 514.885i 0.945212 + 1.00958i
\(511\) −180.760 + 496.634i −0.353738 + 0.971887i
\(512\) 230.784 457.037i 0.450749 0.892651i
\(513\) 135.885 + 411.533i 0.264883 + 0.802209i
\(514\) 183.584 + 599.609i 0.357167 + 1.16655i
\(515\) 413.312 1135.57i 0.802548 2.20498i
\(516\) −0.513222 214.294i −0.000994616 0.415298i
\(517\) −15.5051 13.0103i −0.0299905 0.0251650i
\(518\) −108.555 881.164i −0.209565 1.70109i
\(519\) −848.882 + 90.5836i −1.63561 + 0.174535i
\(520\) −326.882 + 6.10188i −0.628619 + 0.0117344i
\(521\) 193.570 + 335.273i 0.371535 + 0.643517i 0.989802 0.142451i \(-0.0454983\pi\)
−0.618267 + 0.785968i \(0.712165\pi\)
\(522\) −334.380 + 561.040i −0.640576 + 1.07479i
\(523\) 142.838 + 82.4674i 0.273112 + 0.157681i 0.630301 0.776351i \(-0.282931\pi\)
−0.357189 + 0.934032i \(0.616265\pi\)
\(524\) 45.3882 43.9018i 0.0866187 0.0837820i
\(525\) −1699.81 + 490.335i −3.23774 + 0.933972i
\(526\) −327.720 + 247.163i −0.623043 + 0.469891i
\(527\) 2.04045 + 5.60608i 0.00387181 + 0.0106377i
\(528\) −11.2193 + 110.136i −0.0212486 + 0.208591i
\(529\) 87.5319 + 496.418i 0.165467 + 0.938408i
\(530\) 701.167 + 161.579i 1.32296 + 0.304866i
\(531\) −222.617 71.5521i −0.419241 0.134750i
\(532\) −677.010 329.523i −1.27258 0.619405i
\(533\) −9.05997 + 7.60221i −0.0169981 + 0.0142631i
\(534\) −255.884 599.502i −0.479183 1.12266i
\(535\) 240.116 + 42.3389i 0.448815 + 0.0791382i
\(536\) −743.255 + 145.409i −1.38667 + 0.271285i
\(537\) −72.1618 + 107.351i −0.134380 + 0.199910i
\(538\) −28.0876 + 540.116i −0.0522074 + 1.00393i
\(539\) 204.173i 0.378800i
\(540\) −829.836 435.321i −1.53673 0.806150i
\(541\) 543.641 1.00488 0.502441 0.864612i \(-0.332436\pi\)
0.502441 + 0.864612i \(0.332436\pi\)
\(542\) 464.766 + 24.1692i 0.857502 + 0.0445926i
\(543\) −281.441 + 137.821i −0.518308 + 0.253815i
\(544\) −307.180 305.942i −0.564669 0.562393i
\(545\) 19.2660 109.263i 0.0353504 0.200482i
\(546\) 265.071 + 198.919i 0.485478 + 0.364321i
\(547\) −557.244 664.097i −1.01873 1.21407i −0.976623 0.214958i \(-0.931038\pi\)
−0.0421038 0.999113i \(-0.513406\pi\)
\(548\) −382.321 186.088i −0.697666 0.339577i
\(549\) −508.884 + 320.237i −0.926930 + 0.583310i
\(550\) 52.0873 226.031i 0.0947042 0.410966i
\(551\) 573.574 101.137i 1.04097 0.183551i
\(552\) −95.4882 + 72.3754i −0.172986 + 0.131115i
\(553\) −639.032 + 232.589i −1.15557 + 0.420594i
\(554\) 90.6619 + 120.211i 0.163650 + 0.216988i
\(555\) −683.344 + 709.875i −1.23125 + 1.27905i
\(556\) 162.447 157.127i 0.292172 0.282603i
\(557\) 251.191 435.076i 0.450972 0.781106i −0.547475 0.836822i \(-0.684411\pi\)
0.998447 + 0.0557163i \(0.0177442\pi\)
\(558\) −5.01011 6.14190i −0.00897868 0.0110070i
\(559\) 72.8417 42.0552i 0.130307 0.0752329i
\(560\) 1547.56 505.596i 2.76349 0.902850i
\(561\) 85.6979 + 37.9923i 0.152759 + 0.0677224i
\(562\) 278.672 34.3308i 0.495857 0.0610868i
\(563\) −34.7389 + 41.4002i −0.0617032 + 0.0735351i −0.796013 0.605279i \(-0.793061\pi\)
0.734310 + 0.678814i \(0.237506\pi\)
\(564\) −91.0752 + 52.8735i −0.161481 + 0.0937474i
\(565\) −1715.77 624.490i −3.03677 1.10529i
\(566\) −268.513 + 82.2113i −0.474405 + 0.145250i
\(567\) 391.860 + 865.305i 0.691112 + 1.52611i
\(568\) 581.679 720.096i 1.02408 1.26777i
\(569\) 216.377 + 78.7548i 0.380276 + 0.138409i 0.525083 0.851051i \(-0.324034\pi\)
−0.144808 + 0.989460i \(0.546256\pi\)
\(570\) 189.599 + 813.848i 0.332630 + 1.42780i
\(571\) −305.971 + 364.642i −0.535850 + 0.638602i −0.964252 0.264987i \(-0.914632\pi\)
0.428402 + 0.903588i \(0.359077\pi\)
\(572\) −39.6811 + 17.7056i −0.0693725 + 0.0309538i
\(573\) 695.984 + 308.549i 1.21463 + 0.538480i
\(574\) 32.0563 49.4060i 0.0558472 0.0860732i
\(575\) 217.412 125.523i 0.378108 0.218301i
\(576\) 519.111 + 249.600i 0.901234 + 0.433333i
\(577\) −146.058 + 252.980i −0.253133 + 0.438440i −0.964387 0.264496i \(-0.914795\pi\)
0.711253 + 0.702936i \(0.248128\pi\)
\(578\) 187.866 95.8182i 0.325028 0.165775i
\(579\) −0.554087 + 0.575600i −0.000956972 + 0.000994127i
\(580\) −739.397 + 1019.42i −1.27482 + 1.75763i
\(581\) −737.546 + 268.445i −1.26944 + 0.462039i
\(582\) −56.8469 1044.89i −0.0976751 1.79535i
\(583\) 94.1784 16.6062i 0.161541 0.0284840i
\(584\) −336.433 + 129.612i −0.576083 + 0.221939i
\(585\) −14.0031 367.539i −0.0239369 0.628273i
\(586\) 453.909 487.152i 0.774589 0.831318i
\(587\) 536.993 + 639.963i 0.914809 + 1.09023i 0.995620 + 0.0934972i \(0.0298046\pi\)
−0.0808107 + 0.996729i \(0.525751\pi\)
\(588\) −999.112 360.939i −1.69917 0.613843i
\(589\) −1.22736 + 6.96072i −0.00208381 + 0.0118179i
\(590\) −415.098 176.001i −0.703556 0.298306i
\(591\) 138.100 67.6274i 0.233672 0.114429i
\(592\) 404.535 450.744i 0.683336 0.761391i
\(593\) −253.977 −0.428292 −0.214146 0.976802i \(-0.568697\pi\)
−0.214146 + 0.976802i \(0.568697\pi\)
\(594\) −124.125 10.2137i −0.208964 0.0171947i
\(595\) 1378.58i 2.31694i
\(596\) −454.541 + 113.720i −0.762653 + 0.190805i
\(597\) 166.337 247.451i 0.278621 0.414491i
\(598\) −43.2971 18.3579i −0.0724032 0.0306988i
\(599\) −1092.94 192.715i −1.82460 0.321727i −0.846907 0.531742i \(-0.821538\pi\)
−0.977698 + 0.210015i \(0.932649\pi\)
\(600\) −1013.99 654.466i −1.68999 1.09078i
\(601\) 303.355 254.545i 0.504750 0.423536i −0.354527 0.935046i \(-0.615358\pi\)
0.859277 + 0.511510i \(0.170914\pi\)
\(602\) −285.527 + 306.438i −0.474297 + 0.509033i
\(603\) −179.788 832.828i −0.298156 1.38114i
\(604\) 991.732 70.1536i 1.64194 0.116148i
\(605\) 174.296 + 988.481i 0.288092 + 1.63385i
\(606\) 375.230 244.741i 0.619192 0.403863i
\(607\) −185.277 509.044i −0.305234 0.838622i −0.993569 0.113230i \(-0.963880\pi\)
0.688335 0.725393i \(-0.258342\pi\)
\(608\) −133.942 495.872i −0.220300 0.815580i
\(609\) 1226.54 353.813i 2.01403 0.580974i
\(610\) −1032.76 + 526.742i −1.69305 + 0.863511i
\(611\) −35.7965 20.6671i −0.0585868 0.0338251i
\(612\) 337.410 352.195i 0.551324 0.575482i
\(613\) −343.368 594.730i −0.560143 0.970196i −0.997483 0.0709000i \(-0.977413\pi\)
0.437341 0.899296i \(-0.355920\pi\)
\(614\) −221.657 + 341.623i −0.361004 + 0.556390i
\(615\) −64.9937 + 6.93544i −0.105681 + 0.0112771i
\(616\) 163.130 142.154i 0.264821 0.230769i
\(617\) 657.785 + 551.947i 1.06610 + 0.894566i 0.994694 0.102881i \(-0.0328062\pi\)
0.0714083 + 0.997447i \(0.477251\pi\)
\(618\) −799.615 242.727i −1.29388 0.392762i
\(619\) 80.2415 220.462i 0.129631 0.356158i −0.857849 0.513901i \(-0.828200\pi\)
0.987480 + 0.157743i \(0.0504219\pi\)
\(620\) −8.55634 12.6632i −0.0138005 0.0204246i
\(621\) −83.4926 105.823i −0.134449 0.170408i
\(622\) −353.661 + 108.281i −0.568587 + 0.174086i
\(623\) −435.738 + 1197.18i −0.699419 + 1.92164i
\(624\) 16.4927 + 225.477i 0.0264306 + 0.361342i
\(625\) 495.256 + 415.569i 0.792410 + 0.664911i
\(626\) −220.171 + 27.1238i −0.351710 + 0.0433287i
\(627\) 65.4227 + 89.7468i 0.104342 + 0.143137i
\(628\) −203.911 + 713.296i −0.324699 + 1.13582i
\(629\) −256.424 444.139i −0.407669 0.706104i
\(630\) 602.490 + 1729.63i 0.956334 + 2.74544i
\(631\) −124.225 71.7213i −0.196870 0.113663i 0.398325 0.917244i \(-0.369592\pi\)
−0.595195 + 0.803582i \(0.702925\pi\)
\(632\) −406.018 224.417i −0.642434 0.355090i
\(633\) 73.6166 297.269i 0.116298 0.469620i
\(634\) −163.543 216.847i −0.257955 0.342030i
\(635\) −330.900 909.139i −0.521102 1.43172i
\(636\) 85.2279 490.214i 0.134006 0.770776i
\(637\) −72.4036 410.621i −0.113663 0.644617i
\(638\) −37.5849 + 163.098i −0.0589105 + 0.255640i
\(639\) 822.660 + 638.537i 1.28742 + 0.999276i
\(640\) 953.602 + 569.319i 1.49000 + 0.889561i
\(641\) 334.138 280.375i 0.521276 0.437403i −0.343800 0.939043i \(-0.611714\pi\)
0.865076 + 0.501640i \(0.167270\pi\)
\(642\) 20.2142 167.386i 0.0314864 0.260727i
\(643\) 1138.09 + 200.676i 1.76997 + 0.312094i 0.961164 0.275978i \(-0.0890017\pi\)
0.808809 + 0.588072i \(0.200113\pi\)
\(644\) 232.922 + 24.2910i 0.361681 + 0.0377189i
\(645\) 463.762 + 31.6898i 0.719012 + 0.0491314i
\(646\) −434.349 22.5874i −0.672366 0.0349650i
\(647\) 935.380i 1.44572i 0.690995 + 0.722859i \(0.257173\pi\)
−0.690995 + 0.722859i \(0.742827\pi\)
\(648\) −269.409 + 589.341i −0.415754 + 0.909477i
\(649\) −59.9229 −0.0923312
\(650\) 24.6000 473.052i 0.0378462 0.727772i
\(651\) −1.05613 + 15.4558i −0.00162231 + 0.0237417i
\(652\) −1.27396 + 12.2158i −0.00195393 + 0.0187359i
\(653\) −140.779 + 798.399i −0.215588 + 1.22266i 0.664294 + 0.747471i \(0.268732\pi\)
−0.879882 + 0.475191i \(0.842379\pi\)
\(654\) −76.1679 9.19834i −0.116465 0.0140647i
\(655\) 88.0464 + 104.930i 0.134422 + 0.160198i
\(656\) 39.7765 5.65575i 0.0606348 0.00862157i
\(657\) −153.135 375.584i −0.233082 0.571666i
\(658\) 200.575 + 46.2211i 0.304825 + 0.0702448i
\(659\) 209.650 36.9669i 0.318133 0.0560954i −0.0123016 0.999924i \(-0.503916\pi\)
0.330435 + 0.943829i \(0.392805\pi\)
\(660\) −236.592 41.1336i −0.358473 0.0623237i
\(661\) −88.9075 + 32.3597i −0.134505 + 0.0489556i −0.408395 0.912805i \(-0.633912\pi\)
0.273891 + 0.961761i \(0.411689\pi\)
\(662\) 284.235 214.366i 0.429358 0.323816i
\(663\) 185.823 + 46.0177i 0.280276 + 0.0694083i
\(664\) −468.610 259.013i −0.705738 0.390080i
\(665\) 816.640 1414.46i 1.22803 2.12701i
\(666\) 515.827 + 445.171i 0.774515 + 0.668425i
\(667\) −156.879 + 90.5741i −0.235201 + 0.135793i
\(668\) 353.837 + 101.152i 0.529697 + 0.151425i
\(669\) −797.693 + 581.494i −1.19237 + 0.869199i
\(670\) −200.868 1630.49i −0.299803 2.43357i
\(671\) −99.0416 + 118.033i −0.147603 + 0.175906i
\(672\) −407.240 1049.57i −0.606012 1.56186i
\(673\) −635.081 231.150i −0.943656 0.343463i −0.176048 0.984382i \(-0.556331\pi\)
−0.767609 + 0.640919i \(0.778553\pi\)
\(674\) −340.994 1113.73i −0.505926 1.65242i
\(675\) 713.988 1154.82i 1.05776 1.71085i
\(676\) 486.598 328.787i 0.719820 0.486371i
\(677\) −916.610 333.619i −1.35393 0.492790i −0.439757 0.898117i \(-0.644935\pi\)
−0.914172 + 0.405327i \(0.867158\pi\)
\(678\) −366.746 + 1208.17i −0.540924 + 1.78196i
\(679\) −1314.68 + 1566.78i −1.93621 + 2.30748i
\(680\) 709.008 617.841i 1.04266 0.908589i
\(681\) 109.860 + 1029.52i 0.161321 + 1.51178i
\(682\) −1.70394 1.10558i −0.00249845 0.00162108i
\(683\) −193.748 + 111.861i −0.283672 + 0.163778i −0.635085 0.772442i \(-0.719035\pi\)
0.351412 + 0.936221i \(0.385701\pi\)
\(684\) 554.826 161.488i 0.811149 0.236093i
\(685\) 461.172 798.774i 0.673244 1.16609i
\(686\) 421.205 + 825.837i 0.614001 + 1.20384i
\(687\) 242.084 + 839.218i 0.352379 + 1.22157i
\(688\) −285.568 9.51043i −0.415069 0.0138233i
\(689\) 183.517 66.7948i 0.266353 0.0969445i
\(690\) −141.989 217.693i −0.205780 0.315497i
\(691\) 204.026 35.9752i 0.295262 0.0520626i −0.0240551 0.999711i \(-0.507658\pi\)
0.319317 + 0.947648i \(0.396547\pi\)
\(692\) 80.3186 + 1135.43i 0.116067 + 1.64080i
\(693\) 163.456 + 180.382i 0.235867 + 0.260291i
\(694\) −398.228 371.053i −0.573816 0.534659i
\(695\) 315.124 + 375.550i 0.453416 + 0.540360i
\(696\) 731.671 + 472.246i 1.05125 + 0.678515i
\(697\) 5.90752 33.5032i 0.00847565 0.0480678i
\(698\) 199.063 469.489i 0.285190 0.672621i
\(699\) −246.700 165.832i −0.352932 0.237242i
\(700\) 572.501 + 2288.30i 0.817859 + 3.26900i
\(701\) −318.924 −0.454955 −0.227478 0.973783i \(-0.573048\pi\)
−0.227478 + 0.973783i \(0.573048\pi\)
\(702\) −253.254 + 23.4757i −0.360760 + 0.0334412i
\(703\) 607.600i 0.864296i
\(704\) 146.221 + 20.1888i 0.207700 + 0.0286773i
\(705\) −100.466 205.159i −0.142505 0.291006i
\(706\) −179.618 + 423.628i −0.254416 + 0.600040i
\(707\) −862.306 152.048i −1.21967 0.215060i
\(708\) −105.932 + 293.230i −0.149622 + 0.414166i
\(709\) 469.253 393.750i 0.661852 0.555360i −0.248789 0.968558i \(-0.580033\pi\)
0.910641 + 0.413198i \(0.135588\pi\)
\(710\) 1469.09 + 1368.84i 2.06915 + 1.92795i
\(711\) 243.553 461.586i 0.342550 0.649207i
\(712\) −811.000 + 312.442i −1.13905 + 0.438823i
\(713\) −0.381741 2.16496i −0.000535401 0.00303641i
\(714\) −951.885 + 51.7869i −1.33317 + 0.0725307i
\(715\) −32.2372 88.5710i −0.0450870 0.123876i
\(716\) 139.611 + 101.261i 0.194988 + 0.141426i
\(717\) −249.396 240.075i −0.347832 0.334832i
\(718\) 538.994 + 1056.78i 0.750688 + 1.47184i
\(719\) −983.957 568.088i −1.36851 0.790108i −0.377770 0.925900i \(-0.623309\pi\)
−0.990737 + 0.135792i \(0.956642\pi\)
\(720\) −619.535 + 1085.04i −0.860465 + 1.50699i
\(721\) 816.643 + 1414.47i 1.13265 + 1.96181i
\(722\) 173.405 + 112.511i 0.240173 + 0.155832i
\(723\) 142.209 320.776i 0.196693 0.443674i
\(724\) 170.256 + 381.572i 0.235161 + 0.527034i
\(725\) −1397.73 1172.84i −1.92791 1.61771i
\(726\) 675.982 157.481i 0.931105 0.216916i
\(727\) 393.913 1082.27i 0.541834 1.48868i −0.302653 0.953101i \(-0.597872\pi\)
0.844487 0.535576i \(-0.179905\pi\)
\(728\) 277.666 343.740i 0.381410 0.472171i
\(729\) −668.768 290.155i −0.917378 0.398018i
\(730\) −228.957 747.804i −0.313639 1.02439i
\(731\) −82.7492 + 227.352i −0.113200 + 0.311015i
\(732\) 402.502 + 693.315i 0.549867 + 0.947151i
\(733\) 405.935 + 340.620i 0.553800 + 0.464693i 0.876225 0.481902i \(-0.160054\pi\)
−0.322426 + 0.946595i \(0.604498\pi\)
\(734\) −81.5182 661.703i −0.111060 0.901503i
\(735\) 933.919 2106.61i 1.27064 2.86613i
\(736\) 91.8965 + 130.679i 0.124859 + 0.177554i
\(737\) −109.170 189.088i −0.148127 0.256564i
\(738\) 7.23032 + 44.6165i 0.00979718 + 0.0604560i
\(739\) −1010.52 583.424i −1.36742 0.789478i −0.376819 0.926287i \(-0.622982\pi\)
−0.990597 + 0.136809i \(0.956315\pi\)
\(740\) 913.390 + 944.315i 1.23431 + 1.27610i
\(741\) 163.400 + 157.293i 0.220513 + 0.212271i
\(742\) −776.442 + 585.583i −1.04642 + 0.789195i
\(743\) 297.963 + 818.648i 0.401028 + 1.10181i 0.961778 + 0.273829i \(0.0882904\pi\)
−0.560751 + 0.827985i \(0.689487\pi\)
\(744\) −8.42232 + 6.38371i −0.0113203 + 0.00858025i
\(745\) −176.491 1000.93i −0.236901 1.34353i
\(746\) −121.624 28.0274i −0.163035 0.0375703i
\(747\) 281.100 532.745i 0.376305 0.713179i
\(748\) 54.7009 112.384i 0.0731295 0.150246i
\(749\) −252.441 + 211.823i −0.337037 + 0.282807i
\(750\) 790.126 1052.89i 1.05350 1.40385i
\(751\) 925.603 + 163.209i 1.23249 + 0.217322i 0.751696 0.659510i \(-0.229236\pi\)
0.480798 + 0.876832i \(0.340347\pi\)
\(752\) 66.1205 + 123.872i 0.0879263 + 0.164723i
\(753\) 194.411 + 397.000i 0.258182 + 0.527225i
\(754\) −17.7508 + 341.342i −0.0235421 + 0.452708i
\(755\) 2156.62i 2.85646i
\(756\) 1171.65 480.984i 1.54980 0.636222i
\(757\) 1407.53 1.85935 0.929677 0.368376i \(-0.120086\pi\)
0.929677 + 0.368376i \(0.120086\pi\)
\(758\) −682.860 35.5107i −0.900871 0.0468478i
\(759\) −28.6680 19.2707i −0.0377707 0.0253896i
\(760\) 1093.46 213.922i 1.43876 0.281476i
\(761\) −40.6037 + 230.275i −0.0533558 + 0.302596i −0.999794 0.0202889i \(-0.993541\pi\)
0.946438 + 0.322884i \(0.104653\pi\)
\(762\) −615.315 + 262.633i −0.807500 + 0.344663i
\(763\) 96.3883 + 114.871i 0.126328 + 0.150552i
\(764\) 444.246 912.709i 0.581474 1.19465i
\(765\) 710.426 + 783.989i 0.928662 + 1.02482i
\(766\) 78.9755 342.712i 0.103101 0.447405i
\(767\) −120.513 + 21.2498i −0.157123 + 0.0277050i
\(768\) 357.283 679.833i 0.465212 0.885199i
\(769\) 352.803 128.410i 0.458781 0.166983i −0.102282 0.994755i \(-0.532615\pi\)
0.561064 + 0.827773i \(0.310392\pi\)
\(770\) 282.620 + 374.735i 0.367039 + 0.486669i
\(771\) 260.706 + 903.774i 0.338141 + 1.17221i
\(772\) 0.740619 + 0.765694i 0.000959351 + 0.000991832i
\(773\) 82.5621 143.002i 0.106807 0.184996i −0.807668 0.589638i \(-0.799271\pi\)
0.914475 + 0.404642i \(0.132604\pi\)
\(774\) 4.45982 321.411i 0.00576204 0.415259i
\(775\) 19.1763 11.0715i 0.0247437 0.0142858i
\(776\) −1395.01 + 26.0405i −1.79769 + 0.0335573i
\(777\) −141.307 1324.22i −0.181862 1.70427i
\(778\) 206.214 25.4044i 0.265057 0.0326535i
\(779\) 25.9079 30.8758i 0.0332579 0.0396352i
\(780\) −490.407 + 1.17450i −0.628727 + 0.00150577i
\(781\) 250.777 + 91.2753i 0.321097 + 0.116870i
\(782\) 129.349 39.6031i 0.165408 0.0506434i
\(783\) −515.196 + 833.289i −0.657977 + 1.06423i
\(784\) −528.476 + 1314.13i −0.674076 + 1.67619i
\(785\) −1512.20 550.397i −1.92637 0.701142i
\(786\) 69.1446 64.7363i 0.0879703 0.0823617i
\(787\) 681.597 812.295i 0.866070 1.03214i −0.133088 0.991104i \(-0.542489\pi\)
0.999158 0.0410374i \(-0.0130663\pi\)
\(788\) −83.5428 187.233i −0.106019 0.237605i
\(789\) −497.547 + 362.697i −0.630605 + 0.459692i
\(790\) 547.734 844.183i 0.693334 1.06859i
\(791\) 2137.18 1233.90i 2.70187 1.55992i
\(792\) −19.5144 + 164.908i −0.0246394 + 0.208217i
\(793\) −157.330 + 272.503i −0.198398 + 0.343636i
\(794\) −1101.24 + 561.672i −1.38696 + 0.707396i
\(795\) 1047.67 + 259.447i 1.31782 + 0.326349i
\(796\) −321.812 233.413i −0.404286 0.293233i
\(797\) 649.352 236.345i 0.814745 0.296543i 0.0991628 0.995071i \(-0.468384\pi\)
0.715583 + 0.698528i \(0.246161\pi\)
\(798\) −1007.34 510.741i −1.26233 0.640026i
\(799\) 117.091 20.6464i 0.146547 0.0258402i
\(800\) −920.303 + 1319.99i −1.15038 + 1.64999i
\(801\) −369.145 905.379i −0.460855 1.13031i
\(802\) −280.976 + 301.554i −0.350344 + 0.376003i
\(803\) −66.8122 79.6236i −0.0832032 0.0991577i
\(804\) −1118.28 + 199.946i −1.39090 + 0.248689i
\(805\) −88.2118 + 500.274i −0.109580 + 0.621459i
\(806\) −3.81892 1.61922i −0.00473812 0.00200895i
\(807\) −55.3066 + 809.381i −0.0685336 + 1.00295i
\(808\) −308.263 511.631i −0.381514 0.633207i
\(809\) 10.7246 0.0132566 0.00662832 0.999978i \(-0.497890\pi\)
0.00662832 + 0.999978i \(0.497890\pi\)
\(810\) −1233.97 673.146i −1.52342 0.831044i
\(811\) 1400.90i 1.72738i 0.504026 + 0.863688i \(0.331852\pi\)
−0.504026 + 0.863688i \(0.668148\pi\)
\(812\) −413.102 1651.18i −0.508747 2.03347i
\(813\) 696.467 + 47.5909i 0.856663 + 0.0585374i
\(814\) 160.755 + 68.1600i 0.197488 + 0.0837347i
\(815\) −26.2373 4.62635i −0.0321930 0.00567650i
\(816\) −453.243 466.349i −0.555445 0.571506i
\(817\) −219.581 + 184.251i −0.268766 + 0.225521i
\(818\) −351.756 + 377.518i −0.430020 + 0.461513i
\(819\) 392.700 + 304.808i 0.479487 + 0.372171i
\(820\) 6.14951 + 86.9331i 0.00749940 + 0.106016i
\(821\) 142.689 + 809.228i 0.173799 + 0.985661i 0.939521 + 0.342490i \(0.111270\pi\)
−0.765723 + 0.643171i \(0.777619\pi\)
\(822\) −568.864 288.425i −0.692049 0.350882i
\(823\) −321.791 884.112i −0.390997 1.07426i −0.966547 0.256489i \(-0.917434\pi\)
0.575550 0.817767i \(-0.304788\pi\)
\(824\) −361.469 + 1053.93i −0.438676 + 1.27904i
\(825\) 83.6366 337.731i 0.101378 0.409371i
\(826\) 542.847 276.870i 0.657199 0.335194i
\(827\) −876.335 505.952i −1.05965 0.611792i −0.134318 0.990938i \(-0.542884\pi\)
−0.925337 + 0.379146i \(0.876218\pi\)
\(828\) −144.979 + 106.218i −0.175096 + 0.128283i
\(829\) −460.400 797.436i −0.555368 0.961925i −0.997875 0.0651600i \(-0.979244\pi\)
0.442507 0.896765i \(-0.354089\pi\)
\(830\) 632.173 974.323i 0.761655 1.17388i
\(831\) 133.041 + 182.506i 0.160098 + 0.219622i
\(832\) 301.229 11.2500i 0.362055 0.0135216i
\(833\) 918.770 + 770.939i 1.10296 + 0.925497i
\(834\) 247.473 231.696i 0.296731 0.277813i
\(835\) −273.030 + 750.143i −0.326982 + 0.898375i
\(836\) 122.698 82.9054i 0.146768 0.0991691i
\(837\) −7.36428 9.33389i −0.00879842 0.0111516i
\(838\) −233.571 + 71.5130i −0.278725 + 0.0853377i
\(839\) 139.473 383.198i 0.166237 0.456732i −0.828403 0.560133i \(-0.810750\pi\)
0.994640 + 0.103401i \(0.0329723\pi\)
\(840\) 2333.36 720.528i 2.77781 0.857771i
\(841\) 364.326 + 305.706i 0.433206 + 0.363503i
\(842\) −220.153 + 27.1217i −0.261465 + 0.0322110i
\(843\) 418.790 44.6888i 0.496785 0.0530116i
\(844\) −392.605 112.235i −0.465171 0.132979i
\(845\) 636.942 + 1103.22i 0.753777 + 1.30558i
\(846\) −137.885 + 77.0772i −0.162985 + 0.0911078i
\(847\) −1174.85 678.302i −1.38708 0.800828i
\(848\) −649.148 136.885i −0.765504 0.161421i
\(849\) −404.723 + 116.748i −0.476705 + 0.137512i
\(850\) 820.452 + 1087.86i 0.965238 + 1.27984i
\(851\) 64.6347 + 177.582i 0.0759514 + 0.208675i
\(852\) 889.976 1065.81i 1.04457 1.25095i
\(853\) −199.253 1130.02i −0.233591 1.32476i −0.845561 0.533879i \(-0.820734\pi\)
0.611970 0.790881i \(-0.290377\pi\)
\(854\) 351.860 1526.89i 0.412015 1.78792i
\(855\) 264.500 + 1225.24i 0.309357 + 1.43303i
\(856\) −222.078 34.8980i −0.259437 0.0407687i
\(857\) 248.410 208.441i 0.289861 0.243222i −0.486249 0.873821i \(-0.661635\pi\)
0.776109 + 0.630599i \(0.217191\pi\)
\(858\) −59.9458 + 25.5865i −0.0698669 + 0.0298211i
\(859\) −978.617 172.557i −1.13925 0.200881i −0.427974 0.903791i \(-0.640772\pi\)
−0.711278 + 0.702910i \(0.751883\pi\)
\(860\) 64.2880 616.449i 0.0747535 0.716801i
\(861\) 49.2837 73.3169i 0.0572401 0.0851532i
\(862\) −1394.00 72.4922i −1.61717 0.0840976i
\(863\) 1635.75i 1.89543i −0.319121 0.947714i \(-0.603387\pi\)
0.319121 0.947714i \(-0.396613\pi\)
\(864\) 772.472 + 387.019i 0.894065 + 0.447938i
\(865\) −2469.11 −2.85447
\(866\) −62.3130 + 1198.26i −0.0719550 + 1.38367i
\(867\) 284.100 139.124i 0.327682 0.160466i
\(868\) 20.5444 + 2.14253i 0.0236687 + 0.00246835i
\(869\) 23.2244 131.712i 0.0267254 0.151567i
\(870\) −1133.83 + 1510.89i −1.30325 + 1.73665i
\(871\) −286.610 341.568i −0.329059 0.392157i
\(872\) −15.8801 + 101.055i −0.0182111 + 0.115889i
\(873\) −59.7599 1568.52i −0.0684535 1.79670i
\(874\) 156.176 + 35.9897i 0.178691 + 0.0411781i
\(875\) −2533.82 + 446.780i −2.89579 + 0.510606i
\(876\) −507.745 + 186.182i −0.579618 + 0.212537i
\(877\) 1496.49 544.677i 1.70637 0.621068i 0.709845 0.704358i \(-0.248765\pi\)
0.996525 + 0.0832905i \(0.0265429\pi\)
\(878\) 1245.69 939.486i 1.41878 1.07003i
\(879\) 692.662 719.554i 0.788011 0.818606i
\(880\) −66.0650 + 313.299i −0.0750738 + 0.356021i
\(881\) −418.502 + 724.867i −0.475031 + 0.822777i −0.999591 0.0285961i \(-0.990896\pi\)
0.524560 + 0.851373i \(0.324230\pi\)
\(882\) −1489.66 565.719i −1.68896 0.641405i
\(883\) 951.790 549.516i 1.07791 0.622329i 0.147575 0.989051i \(-0.452853\pi\)
0.930331 + 0.366722i \(0.119520\pi\)
\(884\) 70.1578 245.417i 0.0793640 0.277621i
\(885\) −618.269 274.096i −0.698609 0.309713i
\(886\) 169.568 + 1376.43i 0.191387 + 1.55353i
\(887\) −607.213 + 723.649i −0.684570 + 0.815838i −0.990688 0.136155i \(-0.956525\pi\)
0.306118 + 0.951994i \(0.400970\pi\)
\(888\) 617.722 666.154i 0.695633 0.750173i
\(889\) 1228.76 + 447.231i 1.38218 + 0.503072i
\(890\) −551.921 1802.65i −0.620135 2.02545i
\(891\) −185.913 18.3476i −0.208657 0.0205921i
\(892\) 736.885 + 1090.58i 0.826104 + 1.22262i
\(893\) 132.370 + 48.1786i 0.148230 + 0.0539514i
\(894\) −684.497 + 159.465i −0.765657 + 0.178372i
\(895\) −240.476 + 286.588i −0.268688 + 0.320210i
\(896\) −1417.91 + 492.712i −1.58248 + 0.549902i
\(897\) −64.4891 28.5898i −0.0718942 0.0318727i
\(898\) 885.846 + 574.767i 0.986466 + 0.640052i
\(899\) −13.8372 + 7.98889i −0.0153917 + 0.00888642i
\(900\) −1504.81 1006.31i −1.67202 1.11813i
\(901\) −280.882 + 486.501i −0.311744 + 0.539957i
\(902\) 5.26263 + 10.3182i 0.00583440 + 0.0114392i
\(903\) −435.712 + 452.628i −0.482516 + 0.501249i
\(904\) 1592.42 + 546.158i 1.76153 + 0.604157i
\(905\) −851.697 + 309.992i −0.941102 + 0.342533i
\(906\) 1489.11 81.0146i 1.64361 0.0894201i
\(907\) −1707.97 + 301.161i −1.88310 + 0.332041i −0.992449 0.122655i \(-0.960859\pi\)
−0.890647 + 0.454696i \(0.849748\pi\)
\(908\) 1377.05 97.4103i 1.51657 0.107280i
\(909\) 568.743 357.906i 0.625680 0.393736i
\(910\) 701.277 + 653.422i 0.770634 + 0.718046i
\(911\) −242.902 289.479i −0.266632 0.317760i 0.616071 0.787691i \(-0.288723\pi\)
−0.882703 + 0.469931i \(0.844279\pi\)
\(912\) −188.786 746.979i −0.207002 0.819056i
\(913\) 26.8047 152.017i 0.0293589 0.166503i
\(914\) 104.127 245.583i 0.113924 0.268690i
\(915\) −1561.79 + 764.805i −1.70687 + 0.835853i
\(916\) 1129.76 282.650i 1.23336 0.308570i
\(917\) −185.131 −0.201888
\(918\) 514.644 519.988i 0.560614 0.566436i
\(919\) 577.379i 0.628268i −0.949379 0.314134i \(-0.898286\pi\)
0.949379 0.314134i \(-0.101714\pi\)
\(920\) −296.827 + 178.842i −0.322638 + 0.194393i
\(921\) −340.778 + 506.958i −0.370009 + 0.550443i
\(922\) −413.714 + 975.744i −0.448713 + 1.05829i
\(923\) 536.715 + 94.6374i 0.581490 + 0.102532i
\(924\) 248.131 209.222i 0.268541 0.226430i
\(925\) −1458.16 + 1223.54i −1.57639 + 1.32275i
\(926\) −717.001 668.074i −0.774300 0.721462i
\(927\) −1193.34 383.556i −1.28731 0.413760i
\(928\) 664.068 952.474i 0.715590 1.02637i
\(929\) 58.9907 + 334.553i 0.0634991 + 0.360121i 0.999956 + 0.00933976i \(0.00297298\pi\)
−0.936457 + 0.350782i \(0.885916\pi\)
\(930\) −12.5238 19.2011i −0.0134664 0.0206464i
\(931\) 485.997 + 1335.27i 0.522016 + 1.43423i
\(932\) −232.704 + 320.835i −0.249683 + 0.344243i
\(933\) −533.064 + 153.770i −0.571344 + 0.164812i
\(934\) −176.539 346.133i −0.189014 0.370592i
\(935\) 234.801 + 135.562i 0.251124 + 0.144986i
\(936\) 19.2333 + 338.574i 0.0205484 + 0.361724i
\(937\) 583.029 + 1009.84i 0.622230 + 1.07773i 0.989070 + 0.147449i \(0.0471063\pi\)
−0.366840 + 0.930284i \(0.619560\pi\)
\(938\) 1862.65 + 1208.55i 1.98577 + 1.28843i
\(939\) −330.874 + 35.3073i −0.352368 + 0.0376010i
\(940\) −278.151 + 124.110i −0.295905 + 0.132032i
\(941\) 398.127 + 334.068i 0.423089 + 0.355014i 0.829337 0.558749i \(-0.188718\pi\)
−0.406248 + 0.913763i \(0.633163\pi\)
\(942\) −323.233 + 1064.83i −0.343135 + 1.13039i
\(943\) −4.28758 + 11.7800i −0.00454675 + 0.0124921i
\(944\) 385.685 + 155.102i 0.408564 + 0.164303i
\(945\) 861.407 + 2608.80i 0.911542 + 2.76064i
\(946\) −24.1156 78.7647i −0.0254921 0.0832608i
\(947\) 456.322 1253.73i 0.481861 1.32390i −0.426036 0.904706i \(-0.640090\pi\)
0.907896 0.419195i \(-0.137688\pi\)
\(948\) −603.470 346.489i −0.636572 0.365495i
\(949\) −162.605 136.441i −0.171343 0.143774i
\(950\) 197.382 + 1602.20i 0.207770 + 1.68652i
\(951\) −239.990 329.218i −0.252356 0.346181i
\(952\) 23.7226 + 1270.84i 0.0249187 + 1.33491i
\(953\) 8.15378 + 14.1228i 0.00855591 + 0.0148193i 0.870272 0.492572i \(-0.163943\pi\)
−0.861716 + 0.507391i \(0.830610\pi\)
\(954\) 139.788 733.143i 0.146528 0.768494i
\(955\) 1906.90 + 1100.95i 1.99676 + 1.15283i
\(956\) −331.760 + 320.895i −0.347029 + 0.335664i
\(957\) −60.3500 + 243.698i −0.0630617 + 0.254648i
\(958\) −34.3016 + 25.8698i −0.0358054 + 0.0270040i
\(959\) 426.364 + 1171.43i 0.444592 + 1.22151i
\(960\) 1416.32 + 877.137i 1.47533 + 0.913685i
\(961\) 166.842 + 946.209i 0.173613 + 0.984609i
\(962\) 347.472 + 80.0725i 0.361198 + 0.0832355i
\(963\) 34.4022 250.553i 0.0357240 0.260180i
\(964\) −420.664 204.751i −0.436374 0.212398i
\(965\) −1.77015 + 1.48533i −0.00183436 + 0.00153921i
\(966\) 348.745 + 42.1158i 0.361019 + 0.0435981i
\(967\) −817.785 144.198i −0.845693 0.149118i −0.266020 0.963968i \(-0.585709\pi\)
−0.579673 + 0.814849i \(0.696820\pi\)
\(968\) −177.684 908.228i −0.183558 0.938252i
\(969\) −650.885 44.4763i −0.671708 0.0458991i
\(970\) 157.177 3022.47i 0.162038 3.11595i
\(971\) 308.493i 0.317706i 0.987302 + 0.158853i \(0.0507796\pi\)
−0.987302 + 0.158853i \(0.949220\pi\)
\(972\) −418.441 + 877.320i −0.430495 + 0.902593i
\(973\) −662.598 −0.680984
\(974\) 1337.30 + 69.5434i 1.37300 + 0.0713998i
\(975\) 48.4393 708.883i 0.0496814 0.727059i
\(976\) 942.979 503.346i 0.966167 0.515723i
\(977\) 98.4489 558.332i 0.100767 0.571476i −0.892060 0.451916i \(-0.850741\pi\)
0.992827 0.119560i \(-0.0381482\pi\)
\(978\) −2.20880 + 18.2902i −0.00225848 + 0.0187017i
\(979\) −161.057 191.940i −0.164511 0.196057i
\(980\) −2762.59 1344.65i −2.81897 1.37209i
\(981\) −114.012 15.6545i −0.116220 0.0159576i
\(982\) 260.840 1131.91i 0.265621 1.15265i
\(983\) 36.2725 6.39583i 0.0368998 0.00650644i −0.155168 0.987888i \(-0.549592\pi\)
0.192068 + 0.981382i \(0.438481\pi\)
\(984\) 59.7948 7.51181i 0.0607671 0.00763396i
\(985\) 417.918 152.110i 0.424282 0.154426i
\(986\) −592.017 784.974i −0.600423 0.796120i
\(987\) 299.695 + 74.2172i 0.303642 + 0.0751947i
\(988\) 217.364 210.245i 0.220004 0.212799i
\(989\) 44.5767 77.2091i 0.0450725 0.0780678i
\(990\) −353.838 67.4660i −0.357412 0.0681474i
\(991\) −988.565 + 570.748i −0.997543 + 0.575932i −0.907520 0.420008i \(-0.862027\pi\)
−0.0900228 + 0.995940i \(0.528694\pi\)
\(992\) 8.10553 + 11.5263i 0.00817090 + 0.0116192i
\(993\) 431.527 314.571i 0.434569 0.316788i
\(994\) −2693.54 + 331.829i −2.70980 + 0.333832i
\(995\) 554.311 660.602i 0.557097 0.663922i
\(996\) −696.502 399.904i −0.699299 0.401510i
\(997\) 1263.46 + 459.861i 1.26726 + 0.461245i 0.886199 0.463306i \(-0.153337\pi\)
0.381060 + 0.924550i \(0.375559\pi\)
\(998\) −919.900 + 281.648i −0.921744 + 0.282212i
\(999\) 762.774 + 680.256i 0.763538 + 0.680937i
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 108.3.j.a.31.17 yes 204
3.2 odd 2 324.3.j.a.307.18 204
4.3 odd 2 inner 108.3.j.a.31.10 yes 204
12.11 even 2 324.3.j.a.307.25 204
27.7 even 9 inner 108.3.j.a.7.10 204
27.20 odd 18 324.3.j.a.19.25 204
108.7 odd 18 inner 108.3.j.a.7.17 yes 204
108.47 even 18 324.3.j.a.19.18 204
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
108.3.j.a.7.10 204 27.7 even 9 inner
108.3.j.a.7.17 yes 204 108.7 odd 18 inner
108.3.j.a.31.10 yes 204 4.3 odd 2 inner
108.3.j.a.31.17 yes 204 1.1 even 1 trivial
324.3.j.a.19.18 204 108.47 even 18
324.3.j.a.19.25 204 27.20 odd 18
324.3.j.a.307.18 204 3.2 odd 2
324.3.j.a.307.25 204 12.11 even 2