Properties

Label 230.3.i.a.109.21
Level $230$
Weight $3$
Character 230.109
Analytic conductor $6.267$
Analytic rank $0$
Dimension $240$
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] = [230,3,Mod(19,230)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(230, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([11, 15]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("230.19");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 230 = 2 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 230.i (of order \(22\), degree \(10\), 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: \(6.26704608029\)
Analytic rank: \(0\)
Dimension: \(240\)
Relative dimension: \(24\) over \(\Q(\zeta_{22})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label 109.21
Character \(\chi\) \(=\) 230.109
Dual form 230.3.i.a.19.21

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.28641 + 0.587486i) q^{2} +(0.810314 - 2.75968i) q^{3} +(1.30972 + 1.51150i) q^{4} +(-1.47339 + 4.77798i) q^{5} +(2.66367 - 3.07404i) q^{6} +(0.976678 - 6.79294i) q^{7} +(0.796860 + 2.71386i) q^{8} +(0.612076 + 0.393358i) q^{9} +O(q^{10})\) \(q+(1.28641 + 0.587486i) q^{2} +(0.810314 - 2.75968i) q^{3} +(1.30972 + 1.51150i) q^{4} +(-1.47339 + 4.77798i) q^{5} +(2.66367 - 3.07404i) q^{6} +(0.976678 - 6.79294i) q^{7} +(0.796860 + 2.71386i) q^{8} +(0.612076 + 0.393358i) q^{9} +(-4.70239 + 5.28087i) q^{10} +(15.1121 - 6.90144i) q^{11} +(5.23253 - 2.38962i) q^{12} +(16.4246 - 2.36151i) q^{13} +(5.24717 - 8.16475i) q^{14} +(11.9918 + 7.93775i) q^{15} +(-0.569259 + 3.95929i) q^{16} +(-5.15630 + 5.95069i) q^{17} +(0.556292 + 0.865607i) q^{18} +(-8.26853 + 7.16472i) q^{19} +(-9.15165 + 4.03080i) q^{20} +(-17.9549 - 8.19973i) q^{21} +23.4949 q^{22} +(-9.37166 - 21.0041i) q^{23} +8.13507 q^{24} +(-20.6582 - 14.0797i) q^{25} +(22.5162 + 6.61136i) q^{26} +(21.1446 - 18.3219i) q^{27} +(11.5467 - 7.42062i) q^{28} +(-29.7713 + 34.3579i) q^{29} +(10.7631 + 17.2562i) q^{30} +(23.0191 - 6.75902i) q^{31} +(-3.05833 + 4.75885i) q^{32} +(-6.80024 - 47.2967i) q^{33} +(-10.1291 + 4.62580i) q^{34} +(31.0175 + 14.6752i) q^{35} +(0.207090 + 1.44034i) q^{36} +(22.6337 + 14.5458i) q^{37} +(-14.8459 + 4.35915i) q^{38} +(6.79212 - 47.2402i) q^{39} +(-14.1408 - 0.191190i) q^{40} +(-58.9339 + 37.8745i) q^{41} +(-18.2802 - 21.0965i) q^{42} +(-73.8331 - 21.6794i) q^{43} +(30.2241 + 13.8029i) q^{44} +(-2.78128 + 2.34492i) q^{45} +(0.283775 - 32.5257i) q^{46} +13.1589i q^{47} +(10.4651 + 4.77924i) q^{48} +(1.82497 + 0.535860i) q^{49} +(-18.3034 - 30.2487i) q^{50} +(12.2438 + 19.0517i) q^{51} +(25.0811 + 21.7329i) q^{52} +(-10.5429 + 73.3276i) q^{53} +(37.9645 - 11.1474i) q^{54} +(10.7090 + 82.3737i) q^{55} +(19.2133 - 2.76246i) q^{56} +(13.0722 + 28.6241i) q^{57} +(-58.4830 + 26.7083i) q^{58} +(7.25963 + 50.4918i) q^{59} +(3.70798 + 28.5218i) q^{60} +(-32.2208 - 109.734i) q^{61} +(33.5829 + 4.82850i) q^{62} +(3.26986 - 3.77362i) q^{63} +(-6.73003 + 4.32513i) q^{64} +(-12.9167 + 81.9560i) q^{65} +(19.0382 - 64.8382i) q^{66} +(-12.4827 + 27.3333i) q^{67} -15.7478 q^{68} +(-65.5585 + 8.84282i) q^{69} +(31.2799 + 37.1008i) q^{70} +(25.3017 - 55.4031i) q^{71} +(-0.579777 + 1.97454i) q^{72} +(42.4065 - 36.7454i) q^{73} +(20.5708 + 32.0088i) q^{74} +(-55.5950 + 45.6011i) q^{75} +(-21.6589 - 3.11408i) q^{76} +(-32.1215 - 109.396i) q^{77} +(36.4904 - 56.7802i) q^{78} +(-85.9651 + 12.3599i) q^{79} +(-18.0787 - 8.55349i) q^{80} +(-30.7085 - 67.2422i) q^{81} +(-98.0641 + 14.0995i) q^{82} +(-6.98972 - 4.49202i) q^{83} +(-11.1220 - 37.8782i) q^{84} +(-20.8350 - 33.4044i) q^{85} +(-82.2436 - 71.2645i) q^{86} +(70.6926 + 110.000i) q^{87} +(30.7717 + 35.5125i) q^{88} +(25.6344 - 87.3029i) q^{89} +(-4.95549 + 1.38257i) q^{90} -113.878i q^{91} +(19.4734 - 41.6748i) q^{92} -69.0023i q^{93} +(-7.73065 + 16.9278i) q^{94} +(-22.0501 - 50.0633i) q^{95} +(10.6547 + 12.2962i) q^{96} +(-115.919 + 74.4964i) q^{97} +(2.03286 + 1.76148i) q^{98} +(11.9645 + 1.72023i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 240 q + 48 q^{4} - 8 q^{6} + 96 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 240 q + 48 q^{4} - 8 q^{6} + 96 q^{9} + 154 q^{15} - 96 q^{16} + 44 q^{20} + 16 q^{24} - 84 q^{25} + 32 q^{26} - 100 q^{29} - 352 q^{30} + 124 q^{31} + 28 q^{35} - 192 q^{36} + 72 q^{39} + 116 q^{41} - 148 q^{46} - 188 q^{49} + 144 q^{50} + 324 q^{54} + 796 q^{55} - 264 q^{56} + 400 q^{59} + 176 q^{60} - 616 q^{61} + 192 q^{64} + 462 q^{65} - 176 q^{66} + 120 q^{69} - 504 q^{70} + 464 q^{71} - 528 q^{74} - 934 q^{75} - 968 q^{79} - 264 q^{80} + 664 q^{81} - 352 q^{84} - 1196 q^{85} + 396 q^{86} + 376 q^{94} + 126 q^{95} - 32 q^{96} - 3300 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(51\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{22}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.28641 + 0.587486i 0.643207 + 0.293743i
\(3\) 0.810314 2.75968i 0.270105 0.919892i −0.707014 0.707199i \(-0.749958\pi\)
0.977119 0.212693i \(-0.0682234\pi\)
\(4\) 1.30972 + 1.51150i 0.327430 + 0.377875i
\(5\) −1.47339 + 4.77798i −0.294678 + 0.955597i
\(6\) 2.66367 3.07404i 0.443945 0.512340i
\(7\) 0.976678 6.79294i 0.139525 0.970421i −0.792976 0.609253i \(-0.791469\pi\)
0.932501 0.361167i \(-0.117622\pi\)
\(8\) 0.796860 + 2.71386i 0.0996075 + 0.339232i
\(9\) 0.612076 + 0.393358i 0.0680085 + 0.0437064i
\(10\) −4.70239 + 5.28087i −0.470239 + 0.528087i
\(11\) 15.1121 6.90144i 1.37382 0.627404i 0.414587 0.910010i \(-0.363926\pi\)
0.959236 + 0.282606i \(0.0911987\pi\)
\(12\) 5.23253 2.38962i 0.436045 0.199135i
\(13\) 16.4246 2.36151i 1.26343 0.181654i 0.522154 0.852851i \(-0.325129\pi\)
0.741279 + 0.671197i \(0.234220\pi\)
\(14\) 5.24717 8.16475i 0.374798 0.583197i
\(15\) 11.9918 + 7.93775i 0.799452 + 0.529183i
\(16\) −0.569259 + 3.95929i −0.0355787 + 0.247455i
\(17\) −5.15630 + 5.95069i −0.303312 + 0.350041i −0.886860 0.462038i \(-0.847118\pi\)
0.583548 + 0.812078i \(0.301664\pi\)
\(18\) 0.556292 + 0.865607i 0.0309051 + 0.0480893i
\(19\) −8.26853 + 7.16472i −0.435186 + 0.377091i −0.844724 0.535202i \(-0.820235\pi\)
0.409538 + 0.912293i \(0.365690\pi\)
\(20\) −9.15165 + 4.03080i −0.457582 + 0.201540i
\(21\) −17.9549 8.19973i −0.854996 0.390463i
\(22\) 23.4949 1.06795
\(23\) −9.37166 21.0041i −0.407463 0.913222i
\(24\) 8.13507 0.338961
\(25\) −20.6582 14.0797i −0.826329 0.563187i
\(26\) 22.5162 + 6.61136i 0.866008 + 0.254283i
\(27\) 21.1446 18.3219i 0.783132 0.678588i
\(28\) 11.5467 7.42062i 0.412382 0.265022i
\(29\) −29.7713 + 34.3579i −1.02660 + 1.18476i −0.0439942 + 0.999032i \(0.514008\pi\)
−0.982602 + 0.185723i \(0.940537\pi\)
\(30\) 10.7631 + 17.2562i 0.358769 + 0.575208i
\(31\) 23.0191 6.75902i 0.742552 0.218033i 0.111490 0.993766i \(-0.464438\pi\)
0.631062 + 0.775733i \(0.282619\pi\)
\(32\) −3.05833 + 4.75885i −0.0955727 + 0.148714i
\(33\) −6.80024 47.2967i −0.206068 1.43323i
\(34\) −10.1291 + 4.62580i −0.297914 + 0.136053i
\(35\) 31.0175 + 14.6752i 0.886215 + 0.419292i
\(36\) 0.207090 + 1.44034i 0.00575250 + 0.0400095i
\(37\) 22.6337 + 14.5458i 0.611721 + 0.393129i 0.809502 0.587117i \(-0.199737\pi\)
−0.197781 + 0.980246i \(0.563374\pi\)
\(38\) −14.8459 + 4.35915i −0.390682 + 0.114715i
\(39\) 6.79212 47.2402i 0.174157 1.21129i
\(40\) −14.1408 0.191190i −0.353521 0.00477974i
\(41\) −58.9339 + 37.8745i −1.43741 + 0.923769i −0.437716 + 0.899113i \(0.644212\pi\)
−0.999696 + 0.0246551i \(0.992151\pi\)
\(42\) −18.2802 21.0965i −0.435243 0.502298i
\(43\) −73.8331 21.6794i −1.71705 0.504171i −0.732723 0.680527i \(-0.761751\pi\)
−0.984326 + 0.176356i \(0.943569\pi\)
\(44\) 30.2241 + 13.8029i 0.686912 + 0.313702i
\(45\) −2.78128 + 2.34492i −0.0618063 + 0.0521093i
\(46\) 0.283775 32.5257i 0.00616902 0.707080i
\(47\) 13.1589i 0.279976i 0.990153 + 0.139988i \(0.0447064\pi\)
−0.990153 + 0.139988i \(0.955294\pi\)
\(48\) 10.4651 + 4.77924i 0.218022 + 0.0995674i
\(49\) 1.82497 + 0.535860i 0.0372443 + 0.0109359i
\(50\) −18.3034 30.2487i −0.366069 0.604974i
\(51\) 12.2438 + 19.0517i 0.240074 + 0.373562i
\(52\) 25.0811 + 21.7329i 0.482329 + 0.417940i
\(53\) −10.5429 + 73.3276i −0.198923 + 1.38354i 0.608494 + 0.793558i \(0.291774\pi\)
−0.807417 + 0.589981i \(0.799135\pi\)
\(54\) 37.9645 11.1474i 0.703047 0.206433i
\(55\) 10.7090 + 82.3737i 0.194709 + 1.49770i
\(56\) 19.2133 2.76246i 0.343095 0.0493297i
\(57\) 13.0722 + 28.6241i 0.229337 + 0.502178i
\(58\) −58.4830 + 26.7083i −1.00833 + 0.460488i
\(59\) 7.25963 + 50.4918i 0.123044 + 0.855793i 0.954075 + 0.299567i \(0.0968422\pi\)
−0.831031 + 0.556226i \(0.812249\pi\)
\(60\) 3.70798 + 28.5218i 0.0617997 + 0.475363i
\(61\) −32.2208 109.734i −0.528211 1.79892i −0.598169 0.801370i \(-0.704105\pi\)
0.0699581 0.997550i \(-0.477713\pi\)
\(62\) 33.5829 + 4.82850i 0.541660 + 0.0778790i
\(63\) 3.26986 3.77362i 0.0519025 0.0598987i
\(64\) −6.73003 + 4.32513i −0.105157 + 0.0675801i
\(65\) −12.9167 + 81.9560i −0.198718 + 1.26086i
\(66\) 19.0382 64.8382i 0.288458 0.982397i
\(67\) −12.4827 + 27.3333i −0.186309 + 0.407960i −0.979621 0.200856i \(-0.935628\pi\)
0.793312 + 0.608816i \(0.208355\pi\)
\(68\) −15.7478 −0.231585
\(69\) −65.5585 + 8.84282i −0.950123 + 0.128157i
\(70\) 31.2799 + 37.1008i 0.446856 + 0.530011i
\(71\) 25.3017 55.4031i 0.356363 0.780325i −0.643526 0.765424i \(-0.722529\pi\)
0.999889 0.0149012i \(-0.00474338\pi\)
\(72\) −0.579777 + 1.97454i −0.00805245 + 0.0274241i
\(73\) 42.4065 36.7454i 0.580910 0.503362i −0.314110 0.949387i \(-0.601706\pi\)
0.895021 + 0.446025i \(0.147161\pi\)
\(74\) 20.5708 + 32.0088i 0.277984 + 0.432552i
\(75\) −55.5950 + 45.6011i −0.741267 + 0.608014i
\(76\) −21.6589 3.11408i −0.284986 0.0409748i
\(77\) −32.1215 109.396i −0.417163 1.42073i
\(78\) 36.4904 56.7802i 0.467826 0.727951i
\(79\) −85.9651 + 12.3599i −1.08817 + 0.156455i −0.662969 0.748647i \(-0.730704\pi\)
−0.425196 + 0.905101i \(0.639795\pi\)
\(80\) −18.0787 8.55349i −0.225983 0.106919i
\(81\) −30.7085 67.2422i −0.379117 0.830151i
\(82\) −98.0641 + 14.0995i −1.19590 + 0.171945i
\(83\) −6.98972 4.49202i −0.0842135 0.0541207i 0.497856 0.867259i \(-0.334121\pi\)
−0.582070 + 0.813139i \(0.697757\pi\)
\(84\) −11.1220 37.8782i −0.132405 0.450931i
\(85\) −20.8350 33.4044i −0.245118 0.392993i
\(86\) −82.2436 71.2645i −0.956321 0.828657i
\(87\) 70.6926 + 110.000i 0.812559 + 1.26437i
\(88\) 30.7717 + 35.5125i 0.349679 + 0.403551i
\(89\) 25.6344 87.3029i 0.288027 0.980931i −0.680650 0.732609i \(-0.738303\pi\)
0.968677 0.248323i \(-0.0798793\pi\)
\(90\) −4.95549 + 1.38257i −0.0550610 + 0.0153619i
\(91\) 113.878i 1.25141i
\(92\) 19.4734 41.6748i 0.211668 0.452987i
\(93\) 69.0023i 0.741960i
\(94\) −7.73065 + 16.9278i −0.0822410 + 0.180083i
\(95\) −22.0501 50.0633i −0.232107 0.526982i
\(96\) 10.6547 + 12.2962i 0.110986 + 0.128085i
\(97\) −115.919 + 74.4964i −1.19504 + 0.768004i −0.978091 0.208180i \(-0.933246\pi\)
−0.216947 + 0.976183i \(0.569610\pi\)
\(98\) 2.03286 + 1.76148i 0.0207435 + 0.0179743i
\(99\) 11.9645 + 1.72023i 0.120853 + 0.0173761i
\(100\) −5.77511 49.6654i −0.0577511 0.496654i
\(101\) 120.978 + 77.7481i 1.19781 + 0.769783i 0.978575 0.205889i \(-0.0660087\pi\)
0.219231 + 0.975673i \(0.429645\pi\)
\(102\) 4.55797 + 31.7014i 0.0446859 + 0.310798i
\(103\) −7.68593 16.8298i −0.0746207 0.163397i 0.868645 0.495434i \(-0.164991\pi\)
−0.943266 + 0.332038i \(0.892264\pi\)
\(104\) 19.4969 + 42.6923i 0.187470 + 0.410503i
\(105\) 65.6328 73.7068i 0.625074 0.701970i
\(106\) −56.6414 + 88.1358i −0.534353 + 0.831470i
\(107\) −137.191 + 40.2829i −1.28216 + 0.376476i −0.850697 0.525656i \(-0.823820\pi\)
−0.431461 + 0.902132i \(0.642002\pi\)
\(108\) 55.3870 + 7.96345i 0.512843 + 0.0737356i
\(109\) 34.8051 + 30.1588i 0.319312 + 0.276686i 0.799737 0.600350i \(-0.204972\pi\)
−0.480425 + 0.877036i \(0.659518\pi\)
\(110\) −34.6171 + 112.258i −0.314701 + 1.02053i
\(111\) 58.4820 50.6749i 0.526865 0.456531i
\(112\) 26.3392 + 7.73389i 0.235172 + 0.0690526i
\(113\) 16.9586 37.1342i 0.150076 0.328621i −0.819631 0.572892i \(-0.805821\pi\)
0.969707 + 0.244271i \(0.0785487\pi\)
\(114\) 44.5022i 0.390370i
\(115\) 114.165 13.8303i 0.992742 0.120264i
\(116\) −90.9240 −0.783828
\(117\) 10.9820 + 5.01533i 0.0938636 + 0.0428661i
\(118\) −20.3243 + 69.2183i −0.172240 + 0.586596i
\(119\) 35.3867 + 40.8384i 0.297367 + 0.343180i
\(120\) −11.9861 + 38.8692i −0.0998846 + 0.323910i
\(121\) 101.506 117.144i 0.838894 0.968135i
\(122\) 23.0179 160.093i 0.188671 1.31224i
\(123\) 56.7664 + 193.329i 0.461516 + 1.57178i
\(124\) 40.3649 + 25.9409i 0.325523 + 0.209201i
\(125\) 97.7101 77.9598i 0.781681 0.623678i
\(126\) 6.42334 2.93344i 0.0509789 0.0232813i
\(127\) −137.090 + 62.6069i −1.07945 + 0.492968i −0.874112 0.485724i \(-0.838556\pi\)
−0.205337 + 0.978691i \(0.565829\pi\)
\(128\) −11.1986 + 1.61011i −0.0874887 + 0.0125790i
\(129\) −119.656 + 186.188i −0.927566 + 1.44332i
\(130\) −64.7642 + 97.8410i −0.498186 + 0.752623i
\(131\) 4.58232 31.8707i 0.0349796 0.243288i −0.964829 0.262880i \(-0.915328\pi\)
0.999808 + 0.0195920i \(0.00623672\pi\)
\(132\) 62.5825 72.2241i 0.474110 0.547152i
\(133\) 40.5938 + 63.1653i 0.305217 + 0.474927i
\(134\) −32.1159 + 27.8286i −0.239671 + 0.207676i
\(135\) 56.3874 + 128.024i 0.417684 + 0.948324i
\(136\) −20.2582 9.25160i −0.148957 0.0680265i
\(137\) −118.780 −0.867010 −0.433505 0.901151i \(-0.642723\pi\)
−0.433505 + 0.901151i \(0.642723\pi\)
\(138\) −89.5304 27.1391i −0.648771 0.196660i
\(139\) 68.0035 0.489234 0.244617 0.969620i \(-0.421338\pi\)
0.244617 + 0.969620i \(0.421338\pi\)
\(140\) 18.4428 + 66.1034i 0.131734 + 0.472167i
\(141\) 36.3143 + 10.6628i 0.257548 + 0.0756229i
\(142\) 65.0970 56.4069i 0.458430 0.397232i
\(143\) 231.912 149.041i 1.62176 1.04224i
\(144\) −1.90585 + 2.19946i −0.0132350 + 0.0152740i
\(145\) −120.297 192.869i −0.829632 1.33013i
\(146\) 76.1396 22.3566i 0.521504 0.153128i
\(147\) 2.95760 4.60212i 0.0201197 0.0313069i
\(148\) 7.65787 + 53.2617i 0.0517424 + 0.359876i
\(149\) 37.5292 17.1390i 0.251874 0.115027i −0.285478 0.958385i \(-0.592152\pi\)
0.537351 + 0.843359i \(0.319425\pi\)
\(150\) −98.3082 + 26.0006i −0.655388 + 0.173337i
\(151\) 12.2211 + 84.9995i 0.0809343 + 0.562911i 0.989429 + 0.145015i \(0.0463231\pi\)
−0.908495 + 0.417895i \(0.862768\pi\)
\(152\) −26.0329 16.7303i −0.171269 0.110068i
\(153\) −5.49680 + 1.61401i −0.0359268 + 0.0105491i
\(154\) 22.9469 159.599i 0.149006 1.03636i
\(155\) −1.62169 + 119.944i −0.0104625 + 0.773830i
\(156\) 80.2993 51.6053i 0.514739 0.330803i
\(157\) 20.9203 + 24.1433i 0.133250 + 0.153779i 0.818453 0.574573i \(-0.194832\pi\)
−0.685203 + 0.728352i \(0.740286\pi\)
\(158\) −117.848 34.6033i −0.745873 0.219008i
\(159\) 193.817 + 88.5134i 1.21898 + 0.556688i
\(160\) −18.2316 21.6243i −0.113947 0.135152i
\(161\) −151.833 + 43.1469i −0.943060 + 0.267993i
\(162\) 104.542i 0.645322i
\(163\) 37.7878 + 17.2571i 0.231827 + 0.105872i 0.527942 0.849280i \(-0.322964\pi\)
−0.296115 + 0.955152i \(0.595691\pi\)
\(164\) −134.434 39.4735i −0.819721 0.240692i
\(165\) 236.002 + 37.1952i 1.43032 + 0.225425i
\(166\) −6.35267 9.88495i −0.0382691 0.0595479i
\(167\) 21.2300 + 18.3959i 0.127126 + 0.110155i 0.716103 0.697994i \(-0.245924\pi\)
−0.588978 + 0.808149i \(0.700469\pi\)
\(168\) 7.94534 55.2611i 0.0472937 0.328935i
\(169\) 102.037 29.9609i 0.603772 0.177283i
\(170\) −7.17787 55.2122i −0.0422228 0.324778i
\(171\) −7.87927 + 1.13287i −0.0460776 + 0.00662496i
\(172\) −63.9325 139.993i −0.371700 0.813911i
\(173\) 173.001 79.0069i 1.00001 0.456687i 0.152974 0.988230i \(-0.451115\pi\)
0.847031 + 0.531543i \(0.178388\pi\)
\(174\) 26.3166 + 183.036i 0.151245 + 1.05193i
\(175\) −115.819 + 126.579i −0.661822 + 0.723308i
\(176\) 18.7221 + 63.7617i 0.106376 + 0.362282i
\(177\) 145.224 + 20.8800i 0.820472 + 0.117966i
\(178\) 84.2657 97.2478i 0.473403 0.546336i
\(179\) −22.8023 + 14.6541i −0.127387 + 0.0818666i −0.602782 0.797906i \(-0.705941\pi\)
0.475396 + 0.879772i \(0.342305\pi\)
\(180\) −7.18705 1.13272i −0.0399281 0.00629287i
\(181\) 71.2894 242.789i 0.393864 1.34138i −0.489219 0.872161i \(-0.662718\pi\)
0.883083 0.469217i \(-0.155464\pi\)
\(182\) 66.9017 146.494i 0.367592 0.804913i
\(183\) −328.940 −1.79748
\(184\) 49.5342 42.1706i 0.269208 0.229188i
\(185\) −102.848 + 86.7116i −0.555933 + 0.468711i
\(186\) 40.5378 88.7655i 0.217945 0.477234i
\(187\) −36.8540 + 125.513i −0.197080 + 0.671193i
\(188\) −19.8896 + 17.2345i −0.105796 + 0.0916727i
\(189\) −103.808 161.528i −0.549249 0.854648i
\(190\) 1.04589 77.3563i 0.00550467 0.407138i
\(191\) 230.757 + 33.1778i 1.20815 + 0.173706i 0.716814 0.697264i \(-0.245600\pi\)
0.491336 + 0.870970i \(0.336509\pi\)
\(192\) 6.48251 + 22.0774i 0.0337631 + 0.114987i
\(193\) −91.4883 + 142.359i −0.474033 + 0.737609i −0.993119 0.117113i \(-0.962636\pi\)
0.519086 + 0.854722i \(0.326272\pi\)
\(194\) −192.885 + 27.7327i −0.994252 + 0.142952i
\(195\) 215.706 + 102.056i 1.10618 + 0.523364i
\(196\) 1.58025 + 3.46027i 0.00806251 + 0.0176544i
\(197\) 328.042 47.1654i 1.66519 0.239418i 0.755632 0.654997i \(-0.227330\pi\)
0.909557 + 0.415579i \(0.136421\pi\)
\(198\) 14.3806 + 9.24188i 0.0726295 + 0.0466762i
\(199\) −29.0191 98.8300i −0.145825 0.496633i 0.853892 0.520451i \(-0.174236\pi\)
−0.999716 + 0.0238177i \(0.992418\pi\)
\(200\) 21.7485 67.2830i 0.108743 0.336415i
\(201\) 65.3162 + 56.5968i 0.324956 + 0.281576i
\(202\) 109.952 + 171.089i 0.544319 + 0.846977i
\(203\) 204.314 + 235.791i 1.00647 + 1.16153i
\(204\) −12.7607 + 43.4588i −0.0625522 + 0.213033i
\(205\) −94.1310 337.389i −0.459176 1.64580i
\(206\) 26.1655i 0.127017i
\(207\) 2.52595 16.5425i 0.0122027 0.0799156i
\(208\) 66.3741i 0.319106i
\(209\) −75.5075 + 165.338i −0.361280 + 0.791093i
\(210\) 127.733 56.2592i 0.608251 0.267901i
\(211\) −120.851 139.470i −0.572755 0.660994i 0.393276 0.919420i \(-0.371342\pi\)
−0.966031 + 0.258426i \(0.916796\pi\)
\(212\) −124.643 + 80.1031i −0.587938 + 0.377845i
\(213\) −132.392 114.719i −0.621560 0.538585i
\(214\) −200.150 28.7772i −0.935280 0.134473i
\(215\) 212.369 320.831i 0.987761 1.49224i
\(216\) 66.5722 + 42.7834i 0.308205 + 0.198071i
\(217\) −23.4314 162.969i −0.107979 0.751009i
\(218\) 27.0559 + 59.2441i 0.124110 + 0.271762i
\(219\) −67.0429 146.803i −0.306132 0.670335i
\(220\) −110.482 + 124.073i −0.502191 + 0.563969i
\(221\) −70.6378 + 109.915i −0.319628 + 0.497351i
\(222\) 105.003 30.8316i 0.472986 0.138881i
\(223\) 151.496 + 21.7818i 0.679353 + 0.0976762i 0.473349 0.880875i \(-0.343045\pi\)
0.206004 + 0.978551i \(0.433954\pi\)
\(224\) 29.3396 + 25.4229i 0.130980 + 0.113495i
\(225\) −7.10607 16.7439i −0.0315825 0.0744174i
\(226\) 43.6316 37.8070i 0.193060 0.167288i
\(227\) −131.011 38.4684i −0.577142 0.169464i −0.0198823 0.999802i \(-0.506329\pi\)
−0.557260 + 0.830338i \(0.688147\pi\)
\(228\) −26.1444 + 57.2483i −0.114668 + 0.251089i
\(229\) 252.367i 1.10204i −0.834493 0.551019i \(-0.814239\pi\)
0.834493 0.551019i \(-0.185761\pi\)
\(230\) 154.989 + 49.2789i 0.673865 + 0.214256i
\(231\) −327.926 −1.41959
\(232\) −116.966 53.4166i −0.504164 0.230244i
\(233\) −16.1146 + 54.8814i −0.0691616 + 0.235543i −0.986819 0.161831i \(-0.948260\pi\)
0.917657 + 0.397374i \(0.130078\pi\)
\(234\) 11.1810 + 12.9036i 0.0477821 + 0.0551435i
\(235\) −62.8729 19.3882i −0.267544 0.0825029i
\(236\) −66.8102 + 77.1031i −0.283094 + 0.326708i
\(237\) −35.5494 + 247.251i −0.149997 + 1.04325i
\(238\) 21.5299 + 73.3242i 0.0904619 + 0.308085i
\(239\) 380.129 + 244.294i 1.59050 + 1.02215i 0.971586 + 0.236688i \(0.0760621\pi\)
0.618911 + 0.785461i \(0.287574\pi\)
\(240\) −38.2543 + 42.9602i −0.159393 + 0.179001i
\(241\) −119.045 + 54.3662i −0.493964 + 0.225586i −0.646791 0.762667i \(-0.723890\pi\)
0.152827 + 0.988253i \(0.451162\pi\)
\(242\) 199.400 91.0627i 0.823965 0.376292i
\(243\) 38.7912 5.57734i 0.159635 0.0229520i
\(244\) 123.663 192.423i 0.506814 0.788619i
\(245\) −5.24923 + 7.93015i −0.0214254 + 0.0323680i
\(246\) −40.5527 + 282.050i −0.164848 + 1.14655i
\(247\) −118.888 + 137.204i −0.481328 + 0.555482i
\(248\) 36.6860 + 57.0846i 0.147928 + 0.230180i
\(249\) −18.0604 + 15.6494i −0.0725317 + 0.0628491i
\(250\) 171.496 42.8853i 0.685984 0.171541i
\(251\) −215.634 98.4770i −0.859101 0.392338i −0.0633714 0.997990i \(-0.520185\pi\)
−0.795730 + 0.605652i \(0.792913\pi\)
\(252\) 9.98642 0.0396287
\(253\) −286.584 252.737i −1.13274 0.998961i
\(254\) −213.135 −0.839115
\(255\) −109.068 + 30.4299i −0.427719 + 0.119333i
\(256\) −15.3519 4.50772i −0.0599683 0.0176083i
\(257\) −45.8450 + 39.7249i −0.178385 + 0.154572i −0.739477 0.673182i \(-0.764927\pi\)
0.561092 + 0.827754i \(0.310382\pi\)
\(258\) −263.310 + 169.219i −1.02058 + 0.655888i
\(259\) 120.914 139.543i 0.466851 0.538775i
\(260\) −140.794 + 87.8160i −0.541514 + 0.337754i
\(261\) −31.7372 + 9.31890i −0.121599 + 0.0357046i
\(262\) 24.6184 38.3069i 0.0939632 0.146210i
\(263\) 54.5595 + 379.470i 0.207451 + 1.44285i 0.781436 + 0.623986i \(0.214488\pi\)
−0.573985 + 0.818866i \(0.694603\pi\)
\(264\) 122.938 56.1437i 0.465673 0.212666i
\(265\) −334.824 158.414i −1.26349 0.597789i
\(266\) 15.1118 + 105.105i 0.0568113 + 0.395131i
\(267\) −220.156 141.486i −0.824554 0.529908i
\(268\) −57.6632 + 16.9314i −0.215161 + 0.0631770i
\(269\) 23.5686 163.923i 0.0876157 0.609380i −0.897951 0.440095i \(-0.854945\pi\)
0.985567 0.169286i \(-0.0541461\pi\)
\(270\) −2.67458 + 197.818i −0.00990586 + 0.732660i
\(271\) −125.702 + 80.7841i −0.463847 + 0.298096i −0.751613 0.659605i \(-0.770724\pi\)
0.287766 + 0.957701i \(0.407087\pi\)
\(272\) −20.6252 23.8028i −0.0758280 0.0875102i
\(273\) −314.266 92.2770i −1.15116 0.338011i
\(274\) −152.801 69.7818i −0.557667 0.254678i
\(275\) −409.359 70.2013i −1.48858 0.255277i
\(276\) −99.2293 87.5100i −0.359526 0.317065i
\(277\) 190.670i 0.688339i 0.938908 + 0.344169i \(0.111839\pi\)
−0.938908 + 0.344169i \(0.888161\pi\)
\(278\) 87.4807 + 39.9511i 0.314679 + 0.143709i
\(279\) 16.7482 + 4.91771i 0.0600293 + 0.0176262i
\(280\) −15.1098 + 95.8712i −0.0539635 + 0.342397i
\(281\) 207.713 + 323.208i 0.739194 + 1.15021i 0.983570 + 0.180527i \(0.0577804\pi\)
−0.244376 + 0.969680i \(0.578583\pi\)
\(282\) 40.4509 + 35.0509i 0.143443 + 0.124294i
\(283\) −8.71697 + 60.6279i −0.0308020 + 0.214233i −0.999409 0.0343627i \(-0.989060\pi\)
0.968607 + 0.248595i \(0.0799690\pi\)
\(284\) 116.880 34.3190i 0.411549 0.120842i
\(285\) −156.026 + 20.2842i −0.547460 + 0.0711726i
\(286\) 385.894 55.4832i 1.34928 0.193997i
\(287\) 199.720 + 437.326i 0.695888 + 1.52378i
\(288\) −3.74386 + 1.70976i −0.0129995 + 0.00593668i
\(289\) 32.3057 + 224.691i 0.111785 + 0.777478i
\(290\) −41.4434 318.782i −0.142908 1.09925i
\(291\) 111.655 + 380.263i 0.383696 + 1.30675i
\(292\) 111.081 + 15.9711i 0.380415 + 0.0546955i
\(293\) −0.889714 + 1.02678i −0.00303657 + 0.00350438i −0.757266 0.653107i \(-0.773465\pi\)
0.754229 + 0.656611i \(0.228011\pi\)
\(294\) 6.50838 4.18268i 0.0221373 0.0142268i
\(295\) −251.945 39.7078i −0.854052 0.134603i
\(296\) −21.4393 + 73.0154i −0.0724300 + 0.246674i
\(297\) 193.091 422.809i 0.650137 1.42360i
\(298\) 58.3470 0.195795
\(299\) −203.527 322.853i −0.680693 1.07978i
\(300\) −141.740 24.3071i −0.472467 0.0810237i
\(301\) −219.378 + 480.370i −0.728830 + 1.59592i
\(302\) −34.2146 + 116.524i −0.113293 + 0.385842i
\(303\) 312.590 270.861i 1.03165 0.893931i
\(304\) −23.6602 36.8160i −0.0778297 0.121105i
\(305\) 571.782 + 7.73071i 1.87469 + 0.0253466i
\(306\) −8.01937 1.15301i −0.0262071 0.00376801i
\(307\) −8.37712 28.5299i −0.0272870 0.0929311i 0.944724 0.327868i \(-0.106330\pi\)
−0.972011 + 0.234936i \(0.924512\pi\)
\(308\) 123.281 191.830i 0.400265 0.622824i
\(309\) −52.6729 + 7.57323i −0.170463 + 0.0245088i
\(310\) −72.5513 + 153.344i −0.234036 + 0.494659i
\(311\) −211.026 462.082i −0.678539 1.48579i −0.864183 0.503177i \(-0.832164\pi\)
0.185644 0.982617i \(-0.440563\pi\)
\(312\) 133.616 19.2110i 0.428255 0.0615738i
\(313\) −88.6784 56.9902i −0.283318 0.182077i 0.391262 0.920279i \(-0.372039\pi\)
−0.674579 + 0.738202i \(0.735675\pi\)
\(314\) 12.7283 + 43.3487i 0.0405361 + 0.138053i
\(315\) 13.2125 + 21.1833i 0.0419444 + 0.0672487i
\(316\) −131.272 113.748i −0.415419 0.359962i
\(317\) −179.850 279.852i −0.567349 0.882812i 0.432474 0.901647i \(-0.357641\pi\)
−0.999823 + 0.0188343i \(0.994005\pi\)
\(318\) 197.329 + 227.730i 0.620531 + 0.716131i
\(319\) −212.786 + 724.683i −0.667042 + 2.27173i
\(320\) −10.7494 38.5286i −0.0335919 0.120402i
\(321\) 411.244i 1.28113i
\(322\) −220.668 33.6948i −0.685304 0.104642i
\(323\) 86.1469i 0.266709i
\(324\) 61.4170 134.484i 0.189559 0.415075i
\(325\) −372.553 182.469i −1.14632 0.561443i
\(326\) 38.4724 + 44.3996i 0.118014 + 0.136195i
\(327\) 111.431 71.6126i 0.340769 0.218999i
\(328\) −149.748 129.757i −0.456549 0.395602i
\(329\) 89.3876 + 12.8520i 0.271695 + 0.0390638i
\(330\) 281.745 + 186.496i 0.853773 + 0.565140i
\(331\) −348.145 223.739i −1.05180 0.675949i −0.103920 0.994586i \(-0.533139\pi\)
−0.947877 + 0.318637i \(0.896775\pi\)
\(332\) −2.36490 16.4482i −0.00712320 0.0495429i
\(333\) 8.13184 + 17.8062i 0.0244199 + 0.0534722i
\(334\) 16.5033 + 36.1371i 0.0494110 + 0.108195i
\(335\) −112.206 99.9149i −0.334944 0.298253i
\(336\) 42.6861 66.4208i 0.127042 0.197681i
\(337\) −204.127 + 59.9371i −0.605718 + 0.177855i −0.570189 0.821514i \(-0.693130\pi\)
−0.0355293 + 0.999369i \(0.511312\pi\)
\(338\) 148.864 + 21.4034i 0.440426 + 0.0633237i
\(339\) −88.7365 76.8906i −0.261760 0.226816i
\(340\) 23.2027 75.2427i 0.0682431 0.221302i
\(341\) 301.219 261.008i 0.883341 0.765419i
\(342\) −10.8015 3.17162i −0.0315835 0.00927374i
\(343\) 145.117 317.762i 0.423082 0.926420i
\(344\) 217.648i 0.632697i
\(345\) 54.3425 326.266i 0.157514 0.945699i
\(346\) 268.966 0.777359
\(347\) −56.6059 25.8510i −0.163129 0.0744987i 0.332177 0.943217i \(-0.392217\pi\)
−0.495306 + 0.868718i \(0.664944\pi\)
\(348\) −73.6770 + 250.921i −0.211716 + 0.721037i
\(349\) −165.652 191.173i −0.474648 0.547773i 0.467051 0.884231i \(-0.345317\pi\)
−0.941699 + 0.336458i \(0.890771\pi\)
\(350\) −223.354 + 94.7909i −0.638155 + 0.270831i
\(351\) 304.025 350.863i 0.866167 0.999610i
\(352\) −13.3747 + 93.0229i −0.0379962 + 0.264269i
\(353\) −45.6408 155.438i −0.129294 0.440335i 0.869244 0.494383i \(-0.164606\pi\)
−0.998538 + 0.0540479i \(0.982788\pi\)
\(354\) 174.551 + 112.177i 0.493082 + 0.316884i
\(355\) 227.436 + 202.522i 0.640664 + 0.570484i
\(356\) 165.532 75.5960i 0.464978 0.212348i
\(357\) 141.375 64.5638i 0.396009 0.180851i
\(358\) −37.9422 + 5.45527i −0.105984 + 0.0152382i
\(359\) −200.974 + 312.722i −0.559817 + 0.871092i −0.999636 0.0269943i \(-0.991406\pi\)
0.439818 + 0.898087i \(0.355043\pi\)
\(360\) −8.58007 5.67943i −0.0238335 0.0157762i
\(361\) −34.3403 + 238.842i −0.0951255 + 0.661613i
\(362\) 234.343 270.446i 0.647356 0.747089i
\(363\) −241.029 375.048i −0.663991 1.03319i
\(364\) 172.127 149.148i 0.472875 0.409749i
\(365\) 113.088 + 256.758i 0.309829 + 0.703446i
\(366\) −423.153 193.247i −1.15615 0.527998i
\(367\) −27.8878 −0.0759886 −0.0379943 0.999278i \(-0.512097\pi\)
−0.0379943 + 0.999278i \(0.512097\pi\)
\(368\) 88.4961 25.1483i 0.240479 0.0683377i
\(369\) −50.9703 −0.138131
\(370\) −183.247 + 51.1255i −0.495261 + 0.138177i
\(371\) 487.813 + 143.235i 1.31486 + 0.386078i
\(372\) 104.297 90.3737i 0.280368 0.242940i
\(373\) −136.837 + 87.9399i −0.366856 + 0.235764i −0.711061 0.703131i \(-0.751785\pi\)
0.344205 + 0.938895i \(0.388148\pi\)
\(374\) −121.147 + 139.811i −0.323921 + 0.373825i
\(375\) −135.968 332.820i −0.362581 0.887521i
\(376\) −35.7113 + 10.4858i −0.0949769 + 0.0278877i
\(377\) −407.846 + 634.621i −1.08182 + 1.68334i
\(378\) −38.6445 268.778i −0.102234 0.711053i
\(379\) 314.600 143.673i 0.830078 0.379084i 0.0453860 0.998970i \(-0.485548\pi\)
0.784692 + 0.619885i \(0.212821\pi\)
\(380\) 46.7911 98.8977i 0.123135 0.260257i
\(381\) 61.6889 + 429.055i 0.161913 + 1.12613i
\(382\) 277.357 + 178.247i 0.726066 + 0.466614i
\(383\) −9.17927 + 2.69528i −0.0239667 + 0.00703727i −0.293694 0.955900i \(-0.594885\pi\)
0.269727 + 0.962937i \(0.413066\pi\)
\(384\) −4.63097 + 32.2091i −0.0120598 + 0.0838778i
\(385\) 570.019 + 7.70688i 1.48057 + 0.0200179i
\(386\) −201.325 + 129.384i −0.521568 + 0.335192i
\(387\) −36.6638 42.3122i −0.0947384 0.109334i
\(388\) −264.422 77.6414i −0.681501 0.200107i
\(389\) −385.561 176.080i −0.991160 0.452647i −0.147231 0.989102i \(-0.547036\pi\)
−0.843929 + 0.536455i \(0.819763\pi\)
\(390\) 217.530 + 258.010i 0.557770 + 0.661564i
\(391\) 173.312 + 52.5357i 0.443253 + 0.134362i
\(392\) 5.37972i 0.0137238i
\(393\) −84.2398 38.4710i −0.214351 0.0978907i
\(394\) 449.707 + 132.046i 1.14139 + 0.335142i
\(395\) 67.6048 428.951i 0.171151 1.08595i
\(396\) 13.0700 + 20.3373i 0.0330050 + 0.0513568i
\(397\) 422.391 + 366.004i 1.06396 + 0.921923i 0.997120 0.0758407i \(-0.0241640\pi\)
0.0668363 + 0.997764i \(0.478709\pi\)
\(398\) 20.7306 144.185i 0.0520869 0.362273i
\(399\) 207.209 60.8422i 0.519322 0.152487i
\(400\) 67.5054 73.7769i 0.168763 0.184442i
\(401\) −76.6528 + 11.0210i −0.191154 + 0.0274838i −0.237227 0.971454i \(-0.576238\pi\)
0.0460728 + 0.998938i \(0.485329\pi\)
\(402\) 50.7739 + 111.179i 0.126303 + 0.276565i
\(403\) 362.119 165.374i 0.898558 0.410358i
\(404\) 40.9318 + 284.687i 0.101316 + 0.704671i
\(405\) 366.528 47.6505i 0.905007 0.117656i
\(406\) 124.309 + 423.357i 0.306179 + 1.04275i
\(407\) 442.428 + 63.6115i 1.08705 + 0.156294i
\(408\) −41.9469 + 48.4093i −0.102811 + 0.118650i
\(409\) 551.434 354.385i 1.34825 0.866467i 0.350703 0.936487i \(-0.385943\pi\)
0.997546 + 0.0700196i \(0.0223062\pi\)
\(410\) 77.1197 489.323i 0.188097 1.19347i
\(411\) −96.2494 + 327.795i −0.234184 + 0.797556i
\(412\) 15.3719 33.6597i 0.0373103 0.0816983i
\(413\) 350.078 0.847647
\(414\) 12.9679 19.7966i 0.0313235 0.0478178i
\(415\) 31.7614 26.7782i 0.0765335 0.0645259i
\(416\) −38.9938 + 85.3846i −0.0937352 + 0.205251i
\(417\) 55.1042 187.668i 0.132144 0.450043i
\(418\) −194.268 + 168.334i −0.464756 + 0.402713i
\(419\) 189.258 + 294.491i 0.451689 + 0.702842i 0.990181 0.139789i \(-0.0446423\pi\)
−0.538492 + 0.842630i \(0.681006\pi\)
\(420\) 197.369 + 2.66850i 0.469925 + 0.00635357i
\(421\) −469.308 67.4763i −1.11475 0.160276i −0.439766 0.898112i \(-0.644939\pi\)
−0.674980 + 0.737836i \(0.735848\pi\)
\(422\) −73.5282 250.414i −0.174238 0.593399i
\(423\) −5.17615 + 8.05424i −0.0122368 + 0.0190408i
\(424\) −207.402 + 29.8199i −0.489155 + 0.0703299i
\(425\) 190.304 50.3317i 0.447774 0.118427i
\(426\) −102.916 225.354i −0.241586 0.529000i
\(427\) −776.887 + 111.700i −1.81941 + 0.261591i
\(428\) −240.569 154.605i −0.562078 0.361226i
\(429\) −223.383 760.772i −0.520706 1.77336i
\(430\) 461.678 287.958i 1.07367 0.669670i
\(431\) 610.138 + 528.687i 1.41563 + 1.22665i 0.937323 + 0.348461i \(0.113296\pi\)
0.478310 + 0.878191i \(0.341250\pi\)
\(432\) 60.5048 + 94.1473i 0.140057 + 0.217934i
\(433\) 298.225 + 344.170i 0.688741 + 0.794850i 0.987185 0.159577i \(-0.0510132\pi\)
−0.298444 + 0.954427i \(0.596468\pi\)
\(434\) 65.5994 223.411i 0.151151 0.514772i
\(435\) −629.735 + 175.695i −1.44767 + 0.403897i
\(436\) 92.1074i 0.211255i
\(437\) 227.978 + 106.528i 0.521689 + 0.243770i
\(438\) 228.237i 0.521088i
\(439\) 161.042 352.633i 0.366838 0.803264i −0.632744 0.774361i \(-0.718071\pi\)
0.999582 0.0289027i \(-0.00920129\pi\)
\(440\) −215.017 + 94.7030i −0.488674 + 0.215234i
\(441\) 0.906237 + 1.04585i 0.00205496 + 0.00237155i
\(442\) −155.443 + 99.8969i −0.351680 + 0.226011i
\(443\) −108.622 94.1219i −0.245198 0.212465i 0.523588 0.851972i \(-0.324593\pi\)
−0.768785 + 0.639507i \(0.779139\pi\)
\(444\) 153.190 + 22.0254i 0.345023 + 0.0496068i
\(445\) 379.362 + 251.112i 0.852499 + 0.564297i
\(446\) 182.090 + 117.022i 0.408273 + 0.262381i
\(447\) −16.8877 117.456i −0.0377800 0.262766i
\(448\) 22.8073 + 49.9410i 0.0509091 + 0.111475i
\(449\) 169.665 + 371.514i 0.377873 + 0.827426i 0.999043 + 0.0437499i \(0.0139305\pi\)
−0.621170 + 0.783676i \(0.713342\pi\)
\(450\) 0.695463 25.7143i 0.00154547 0.0571429i
\(451\) −629.223 + 979.091i −1.39517 + 2.17093i
\(452\) 78.3393 23.0025i 0.173317 0.0508905i
\(453\) 244.474 + 35.1501i 0.539678 + 0.0775939i
\(454\) −145.935 126.454i −0.321443 0.278532i
\(455\) 544.107 + 167.787i 1.19584 + 0.368762i
\(456\) −67.2651 + 58.2855i −0.147511 + 0.127819i
\(457\) −330.188 96.9520i −0.722513 0.212149i −0.100255 0.994962i \(-0.531966\pi\)
−0.622257 + 0.782813i \(0.713784\pi\)
\(458\) 148.262 324.648i 0.323716 0.708838i
\(459\) 220.298i 0.479952i
\(460\) 170.429 + 154.447i 0.370499 + 0.335754i
\(461\) 307.244 0.666473 0.333237 0.942843i \(-0.391859\pi\)
0.333237 + 0.942843i \(0.391859\pi\)
\(462\) −421.848 192.652i −0.913091 0.416995i
\(463\) 254.619 867.153i 0.549933 1.87290i 0.0659504 0.997823i \(-0.478992\pi\)
0.483983 0.875077i \(-0.339190\pi\)
\(464\) −119.085 137.432i −0.256649 0.296189i
\(465\) 329.692 + 101.667i 0.709014 + 0.218639i
\(466\) −52.9722 + 61.1331i −0.113674 + 0.131187i
\(467\) 65.3197 454.309i 0.139871 0.972824i −0.792126 0.610358i \(-0.791026\pi\)
0.931997 0.362466i \(-0.118065\pi\)
\(468\) 6.80275 + 23.1680i 0.0145358 + 0.0495044i
\(469\) 173.482 + 111.490i 0.369898 + 0.237719i
\(470\) −69.4903 61.8782i −0.147852 0.131656i
\(471\) 83.5798 38.1696i 0.177452 0.0810396i
\(472\) −131.243 + 59.9365i −0.278056 + 0.126984i
\(473\) −1265.39 + 181.935i −2.67524 + 0.384642i
\(474\) −190.988 + 297.183i −0.402928 + 0.626968i
\(475\) 271.690 31.5922i 0.571979 0.0665100i
\(476\) −15.3805 + 106.974i −0.0323120 + 0.224735i
\(477\) −35.2970 + 40.7349i −0.0739980 + 0.0853982i
\(478\) 345.484 + 537.583i 0.722769 + 1.12465i
\(479\) −501.641 + 434.674i −1.04727 + 0.907462i −0.995831 0.0912148i \(-0.970925\pi\)
−0.0514352 + 0.998676i \(0.516380\pi\)
\(480\) −74.4493 + 32.7908i −0.155103 + 0.0683142i
\(481\) 406.099 + 185.459i 0.844281 + 0.385570i
\(482\) −185.081 −0.383985
\(483\) −3.96074 + 453.972i −0.00820030 + 0.939900i
\(484\) 310.008 0.640513
\(485\) −185.149 663.620i −0.381750 1.36829i
\(486\) 53.1782 + 15.6145i 0.109420 + 0.0321286i
\(487\) 289.510 250.861i 0.594475 0.515116i −0.304847 0.952401i \(-0.598605\pi\)
0.899323 + 0.437285i \(0.144060\pi\)
\(488\) 272.127 174.885i 0.557638 0.358372i
\(489\) 78.2440 90.2984i 0.160008 0.184659i
\(490\) −11.4115 + 7.11761i −0.0232888 + 0.0145257i
\(491\) −533.343 + 156.604i −1.08624 + 0.318948i −0.775371 0.631506i \(-0.782437\pi\)
−0.310866 + 0.950454i \(0.600619\pi\)
\(492\) −217.868 + 339.009i −0.442821 + 0.689043i
\(493\) −50.9435 354.320i −0.103334 0.718701i
\(494\) −233.545 + 106.656i −0.472762 + 0.215903i
\(495\) −25.8476 + 54.6314i −0.0522173 + 0.110367i
\(496\) 13.6571 + 94.9869i 0.0275344 + 0.191506i
\(497\) −351.638 225.984i −0.707522 0.454697i
\(498\) −32.4269 + 9.52141i −0.0651143 + 0.0191193i
\(499\) 122.764 853.840i 0.246019 1.71110i −0.374764 0.927120i \(-0.622276\pi\)
0.620783 0.783982i \(-0.286815\pi\)
\(500\) 245.809 + 45.5832i 0.491618 + 0.0911663i
\(501\) 67.9698 43.6815i 0.135668 0.0871887i
\(502\) −219.541 253.364i −0.437333 0.504710i
\(503\) 732.928 + 215.207i 1.45711 + 0.427847i 0.911887 0.410442i \(-0.134626\pi\)
0.545226 + 0.838289i \(0.316444\pi\)
\(504\) 12.8467 + 5.86688i 0.0254894 + 0.0116406i
\(505\) −549.728 + 463.479i −1.08857 + 0.917781i
\(506\) −220.186 493.488i −0.435150 0.975273i
\(507\) 305.868i 0.603290i
\(508\) −274.180 125.214i −0.539724 0.246484i
\(509\) 47.9295 + 14.0734i 0.0941640 + 0.0276490i 0.328475 0.944513i \(-0.393465\pi\)
−0.234311 + 0.972162i \(0.575283\pi\)
\(510\) −158.184 24.9306i −0.310165 0.0488836i
\(511\) −208.192 323.953i −0.407421 0.633959i
\(512\) −17.1007 14.8178i −0.0333997 0.0289410i
\(513\) −43.5634 + 302.990i −0.0849189 + 0.590624i
\(514\) −82.3135 + 24.1694i −0.160143 + 0.0470222i
\(515\) 91.7371 11.9263i 0.178130 0.0231579i
\(516\) −438.140 + 62.9950i −0.849108 + 0.122083i
\(517\) 90.8153 + 198.858i 0.175658 + 0.384638i
\(518\) 237.525 108.474i 0.458543 0.209410i
\(519\) −77.8483 541.447i −0.149997 1.04325i
\(520\) −232.710 + 30.2535i −0.447518 + 0.0581797i
\(521\) 25.9215 + 88.2805i 0.0497533 + 0.169444i 0.980622 0.195910i \(-0.0627660\pi\)
−0.930869 + 0.365354i \(0.880948\pi\)
\(522\) −46.3020 6.65722i −0.0887011 0.0127533i
\(523\) 432.240 498.832i 0.826463 0.953789i −0.173053 0.984913i \(-0.555363\pi\)
0.999516 + 0.0311236i \(0.00990855\pi\)
\(524\) 54.1742 34.8156i 0.103386 0.0664420i
\(525\) 255.467 + 422.191i 0.486604 + 0.804174i
\(526\) −152.747 + 520.208i −0.290393 + 0.988989i
\(527\) −78.4727 + 171.831i −0.148905 + 0.326056i
\(528\) 191.132 0.361993
\(529\) −353.344 + 393.686i −0.667947 + 0.744209i
\(530\) −337.656 400.490i −0.637087 0.755642i
\(531\) −15.4179 + 33.7605i −0.0290356 + 0.0635790i
\(532\) −42.3076 + 144.086i −0.0795256 + 0.270839i
\(533\) −878.526 + 761.247i −1.64827 + 1.42823i
\(534\) −200.091 311.347i −0.374702 0.583047i
\(535\) 9.66503 714.848i 0.0180655 1.33616i
\(536\) −84.1257 12.0954i −0.156951 0.0225661i
\(537\) 21.9637 + 74.8013i 0.0409007 + 0.139295i
\(538\) 126.622 197.027i 0.235356 0.366221i
\(539\) 31.2773 4.49699i 0.0580284 0.00834322i
\(540\) −119.656 + 252.905i −0.221585 + 0.468342i
\(541\) −356.865 781.426i −0.659640 1.44441i −0.882857 0.469642i \(-0.844383\pi\)
0.223217 0.974769i \(-0.428344\pi\)
\(542\) −209.165 + 30.0734i −0.385913 + 0.0554859i
\(543\) −612.253 393.471i −1.12754 0.724625i
\(544\) −12.5488 42.7372i −0.0230676 0.0785611i
\(545\) −195.379 + 121.862i −0.358494 + 0.223601i
\(546\) −350.065 303.333i −0.641145 0.555556i
\(547\) −101.141 157.378i −0.184900 0.287711i 0.736412 0.676533i \(-0.236518\pi\)
−0.921313 + 0.388822i \(0.872882\pi\)
\(548\) −155.569 179.536i −0.283885 0.327621i
\(549\) 23.4431 79.8400i 0.0427015 0.145428i
\(550\) −485.362 330.800i −0.882477 0.601455i
\(551\) 497.392i 0.902708i
\(552\) −76.2391 170.870i −0.138114 0.309547i
\(553\) 596.028i 1.07781i
\(554\) −112.016 + 245.280i −0.202195 + 0.442744i
\(555\) 155.957 + 354.090i 0.281004 + 0.638000i
\(556\) 89.0657 + 102.787i 0.160190 + 0.184869i
\(557\) 318.074 204.414i 0.571049 0.366991i −0.223025 0.974813i \(-0.571593\pi\)
0.794073 + 0.607822i \(0.207957\pi\)
\(558\) 18.6560 + 16.1655i 0.0334337 + 0.0289705i
\(559\) −1263.88 181.718i −2.26096 0.325077i
\(560\) −75.7604 + 114.453i −0.135286 + 0.204381i
\(561\) 316.512 + 203.410i 0.564193 + 0.362585i
\(562\) 77.3252 + 537.808i 0.137589 + 0.956954i
\(563\) 166.121 + 363.754i 0.295063 + 0.646099i 0.997867 0.0652855i \(-0.0207958\pi\)
−0.702803 + 0.711384i \(0.748069\pi\)
\(564\) 31.4447 + 68.8543i 0.0557530 + 0.122082i
\(565\) 152.440 + 135.741i 0.269805 + 0.240250i
\(566\) −46.8316 + 72.8715i −0.0827414 + 0.128748i
\(567\) −486.765 + 142.927i −0.858492 + 0.252076i
\(568\) 170.518 + 24.5168i 0.300208 + 0.0431633i
\(569\) −271.448 235.211i −0.477061 0.413376i 0.382857 0.923808i \(-0.374940\pi\)
−0.859918 + 0.510432i \(0.829486\pi\)
\(570\) −212.631 65.5692i −0.373036 0.115034i
\(571\) 536.451 464.837i 0.939493 0.814075i −0.0432474 0.999064i \(-0.513770\pi\)
0.982741 + 0.184989i \(0.0592249\pi\)
\(572\) 529.015 + 155.333i 0.924852 + 0.271561i
\(573\) 278.545 609.929i 0.486117 1.06445i
\(574\) 679.915i 1.18452i
\(575\) −102.129 + 565.857i −0.177616 + 0.984100i
\(576\) −5.82061 −0.0101052
\(577\) 578.655 + 264.263i 1.00287 + 0.457994i 0.848032 0.529946i \(-0.177788\pi\)
0.154836 + 0.987940i \(0.450515\pi\)
\(578\) −90.4443 + 308.025i −0.156478 + 0.532915i
\(579\) 318.729 + 367.833i 0.550482 + 0.635291i
\(580\) 133.967 434.433i 0.230977 0.749023i
\(581\) −37.3407 + 43.0935i −0.0642698 + 0.0741713i
\(582\) −79.7642 + 554.772i −0.137052 + 0.953217i
\(583\) 346.741 + 1180.89i 0.594753 + 2.02554i
\(584\) 133.514 + 85.8041i 0.228619 + 0.146925i
\(585\) −40.1440 + 45.0825i −0.0686223 + 0.0770640i
\(586\) −1.74776 + 0.798176i −0.00298253 + 0.00136208i
\(587\) 134.389 61.3736i 0.228943 0.104555i −0.297641 0.954678i \(-0.596200\pi\)
0.526584 + 0.850123i \(0.323473\pi\)
\(588\) 10.8297 1.55708i 0.0184179 0.00264809i
\(589\) −141.908 + 220.813i −0.240930 + 0.374894i
\(590\) −300.778 199.095i −0.509793 0.337449i
\(591\) 135.656 943.509i 0.229537 1.59646i
\(592\) −70.4753 + 81.3328i −0.119046 + 0.137387i
\(593\) 307.280 + 478.137i 0.518179 + 0.806302i 0.997450 0.0713646i \(-0.0227354\pi\)
−0.479271 + 0.877667i \(0.659099\pi\)
\(594\) 496.789 430.470i 0.836345 0.724697i
\(595\) −247.264 + 108.906i −0.415569 + 0.183035i
\(596\) 75.0584 + 34.2780i 0.125937 + 0.0575134i
\(597\) −296.253 −0.496237
\(598\) −72.1486 534.892i −0.120650 0.894469i
\(599\) −374.061 −0.624476 −0.312238 0.950004i \(-0.601079\pi\)
−0.312238 + 0.950004i \(0.601079\pi\)
\(600\) −168.056 114.539i −0.280094 0.190899i
\(601\) 778.384 + 228.554i 1.29515 + 0.380290i 0.855464 0.517862i \(-0.173272\pi\)
0.439685 + 0.898152i \(0.355090\pi\)
\(602\) −564.421 + 489.074i −0.937577 + 0.812415i
\(603\) −18.3921 + 11.8199i −0.0305011 + 0.0196019i
\(604\) −112.470 + 129.798i −0.186209 + 0.214897i
\(605\) 410.155 + 657.594i 0.677943 + 1.08693i
\(606\) 561.247 164.797i 0.926151 0.271942i
\(607\) −204.984 + 318.961i −0.337699 + 0.525471i −0.968023 0.250862i \(-0.919286\pi\)
0.630323 + 0.776333i \(0.282922\pi\)
\(608\) −8.80796 61.2607i −0.0144868 0.100758i
\(609\) 816.266 372.776i 1.34034 0.612112i
\(610\) 731.006 + 345.858i 1.19837 + 0.566981i
\(611\) 31.0748 + 216.130i 0.0508589 + 0.353731i
\(612\) −9.63885 6.19451i −0.0157498 0.0101218i
\(613\) 524.902 154.125i 0.856285 0.251428i 0.176013 0.984388i \(-0.443680\pi\)
0.680272 + 0.732960i \(0.261862\pi\)
\(614\) 5.98443 41.6226i 0.00974663 0.0677893i
\(615\) −1007.36 13.6199i −1.63798 0.0221462i
\(616\) 271.288 174.346i 0.440403 0.283030i
\(617\) 502.369 + 579.764i 0.814212 + 0.939651i 0.999070 0.0431147i \(-0.0137281\pi\)
−0.184858 + 0.982765i \(0.559183\pi\)
\(618\) −72.2084 21.2023i −0.116842 0.0343079i
\(619\) 51.0793 + 23.3271i 0.0825190 + 0.0376852i 0.456247 0.889853i \(-0.349193\pi\)
−0.373728 + 0.927538i \(0.621921\pi\)
\(620\) −183.419 + 154.642i −0.295837 + 0.249422i
\(621\) −582.994 272.416i −0.938799 0.438674i
\(622\) 718.403i 1.15499i
\(623\) −568.007 259.400i −0.911729 0.416373i
\(624\) 183.171 + 53.7839i 0.293543 + 0.0861921i
\(625\) 228.525 + 581.723i 0.365640 + 0.930756i
\(626\) −80.5962 125.410i −0.128748 0.200336i
\(627\) 395.096 + 342.352i 0.630137 + 0.546017i
\(628\) −9.09284 + 63.2421i −0.0144790 + 0.100704i
\(629\) −203.263 + 59.6835i −0.323153 + 0.0948864i
\(630\) 4.55183 + 35.0127i 0.00722513 + 0.0555757i
\(631\) 296.687 42.6572i 0.470186 0.0676025i 0.0968505 0.995299i \(-0.469123\pi\)
0.373335 + 0.927696i \(0.378214\pi\)
\(632\) −102.045 223.448i −0.161464 0.353557i
\(633\) −482.819 + 220.496i −0.762747 + 0.348335i
\(634\) −66.9524 465.664i −0.105603 0.734486i
\(635\) −97.1474 747.258i −0.152988 1.17678i
\(636\) 120.059 + 408.883i 0.188772 + 0.642897i
\(637\) 31.2399 + 4.49162i 0.0490423 + 0.00705121i
\(638\) −699.472 + 807.234i −1.09635 + 1.26526i
\(639\) 37.2798 23.9583i 0.0583409 0.0374934i
\(640\) 8.80678 55.8788i 0.0137606 0.0873106i
\(641\) 169.016 575.616i 0.263676 0.897997i −0.716117 0.697980i \(-0.754082\pi\)
0.979793 0.200016i \(-0.0640995\pi\)
\(642\) −241.600 + 529.030i −0.376324 + 0.824035i
\(643\) 808.183 1.25689 0.628447 0.777852i \(-0.283691\pi\)
0.628447 + 0.777852i \(0.283691\pi\)
\(644\) −264.075 172.985i −0.410054 0.268610i
\(645\) −713.305 846.043i −1.10590 1.31169i
\(646\) 50.6101 110.821i 0.0783438 0.171549i
\(647\) 278.716 949.219i 0.430782 1.46711i −0.403095 0.915158i \(-0.632066\pi\)
0.833877 0.551950i \(-0.186116\pi\)
\(648\) 158.015 136.921i 0.243851 0.211298i
\(649\) 458.174 + 712.933i 0.705970 + 1.09851i
\(650\) −372.060 453.600i −0.572399 0.697846i
\(651\) −468.728 67.3930i −0.720013 0.103522i
\(652\) 23.4074 + 79.7182i 0.0359009 + 0.122267i
\(653\) −649.194 + 1010.16i −0.994171 + 1.54696i −0.166274 + 0.986080i \(0.553174\pi\)
−0.827897 + 0.560881i \(0.810463\pi\)
\(654\) 185.418 26.6591i 0.283514 0.0407632i
\(655\) 145.526 + 68.8523i 0.222178 + 0.105118i
\(656\) −116.407 254.897i −0.177450 0.388562i
\(657\) 40.4101 5.81009i 0.0615070 0.00884337i
\(658\) 107.439 + 69.0469i 0.163281 + 0.104934i
\(659\) −215.743 734.754i −0.327380 1.11495i −0.944617 0.328175i \(-0.893566\pi\)
0.617237 0.786777i \(-0.288252\pi\)
\(660\) 252.877 + 405.433i 0.383147 + 0.614292i
\(661\) 136.091 + 117.924i 0.205887 + 0.178402i 0.751701 0.659505i \(-0.229234\pi\)
−0.545814 + 0.837907i \(0.683779\pi\)
\(662\) −316.415 492.351i −0.477968 0.743733i
\(663\) 246.090 + 284.003i 0.371176 + 0.428360i
\(664\) 6.62087 22.5486i 0.00997118 0.0339587i
\(665\) −361.613 + 100.890i −0.543779 + 0.151714i
\(666\) 27.6835i 0.0415669i
\(667\) 1000.66 + 303.329i 1.50024 + 0.454766i
\(668\) 56.1827i 0.0841058i
\(669\) 182.870 400.429i 0.273348 0.598549i
\(670\) −85.6451 194.451i −0.127829 0.290226i
\(671\) −1244.25 1435.94i −1.85432 2.14000i
\(672\) 93.9333 60.3672i 0.139782 0.0898322i
\(673\) 17.3890 + 15.0676i 0.0258380 + 0.0223888i 0.667684 0.744445i \(-0.267286\pi\)
−0.641846 + 0.766834i \(0.721831\pi\)
\(674\) −297.804 42.8177i −0.441846 0.0635278i
\(675\) −694.776 + 80.7888i −1.02930 + 0.119687i
\(676\) 178.926 + 114.989i 0.264684 + 0.170102i
\(677\) −110.586 769.143i −0.163347 1.13611i −0.892268 0.451507i \(-0.850887\pi\)
0.728920 0.684599i \(-0.240022\pi\)
\(678\) −68.9798 151.045i −0.101740 0.222780i
\(679\) 392.835 + 860.188i 0.578549 + 1.26684i
\(680\) 74.0522 83.1620i 0.108900 0.122297i
\(681\) −212.321 + 330.377i −0.311778 + 0.485136i
\(682\) 540.831 158.802i 0.793007 0.232848i
\(683\) −471.147 67.7407i −0.689820 0.0991811i −0.211515 0.977375i \(-0.567840\pi\)
−0.478305 + 0.878194i \(0.658749\pi\)
\(684\) −12.0320 10.4258i −0.0175906 0.0152423i
\(685\) 175.010 567.531i 0.255489 0.828512i
\(686\) 373.361 323.519i 0.544258 0.471602i
\(687\) −696.450 204.496i −1.01376 0.297666i
\(688\) 127.865 279.985i 0.185850 0.406955i
\(689\) 1229.28i 1.78414i
\(690\) 261.584 387.788i 0.379107 0.562012i
\(691\) 358.460 0.518755 0.259378 0.965776i \(-0.416483\pi\)
0.259378 + 0.965776i \(0.416483\pi\)
\(692\) 346.002 + 158.014i 0.500003 + 0.228344i
\(693\) 23.3709 79.5939i 0.0337242 0.114854i
\(694\) −57.6315 66.5103i −0.0830425 0.0958361i
\(695\) −100.196 + 324.920i −0.144167 + 0.467510i
\(696\) −242.192 + 279.504i −0.347976 + 0.401586i
\(697\) 78.5015 545.990i 0.112628 0.783343i
\(698\) −100.786 343.246i −0.144393 0.491756i
\(699\) 138.397 + 88.9424i 0.197993 + 0.127242i
\(700\) −343.014 9.27708i −0.490021 0.0132530i
\(701\) −20.7816 + 9.49065i −0.0296457 + 0.0135387i −0.430183 0.902742i \(-0.641551\pi\)
0.400537 + 0.916281i \(0.368824\pi\)
\(702\) 597.228 272.745i 0.850753 0.388526i
\(703\) −291.363 + 41.8917i −0.414457 + 0.0595899i
\(704\) −71.8549 + 111.808i −0.102067 + 0.158819i
\(705\) −104.452 + 157.798i −0.148159 + 0.223828i
\(706\) 32.6048 226.771i 0.0461824 0.321205i
\(707\) 646.296 745.865i 0.914138 1.05497i
\(708\) 158.642 + 246.852i 0.224071 + 0.348662i
\(709\) 326.953 283.306i 0.461146 0.399586i −0.393066 0.919510i \(-0.628585\pi\)
0.854212 + 0.519925i \(0.174040\pi\)
\(710\) 173.598 + 394.142i 0.244504 + 0.555129i
\(711\) −57.4791 26.2498i −0.0808426 0.0369196i
\(712\) 257.355 0.361453
\(713\) −357.694 420.153i −0.501675 0.589274i
\(714\) 219.797 0.307839
\(715\) 370.417 + 1327.67i 0.518066 + 1.85688i
\(716\) −52.0143 15.2728i −0.0726457 0.0213307i
\(717\) 982.195 851.077i 1.36987 1.18700i
\(718\) −442.256 + 284.221i −0.615955 + 0.395850i
\(719\) −461.614 + 532.731i −0.642023 + 0.740934i −0.979731 0.200317i \(-0.935803\pi\)
0.337708 + 0.941251i \(0.390348\pi\)
\(720\) −7.70094 12.3468i −0.0106957 0.0171483i
\(721\) −121.831 + 35.7728i −0.168975 + 0.0496155i
\(722\) −184.492 + 287.075i −0.255529 + 0.397611i
\(723\) 53.5690 + 372.580i 0.0740926 + 0.515326i
\(724\) 460.345 210.233i 0.635836 0.290377i
\(725\) 1098.77 290.603i 1.51555 0.400832i
\(726\) −89.7274 624.068i −0.123591 0.859597i
\(727\) −480.300 308.670i −0.660660 0.424580i 0.166888 0.985976i \(-0.446628\pi\)
−0.827547 + 0.561396i \(0.810265\pi\)
\(728\) 309.049 90.7448i 0.424517 0.124649i
\(729\) 110.724 770.101i 0.151884 1.05638i
\(730\) −5.36400 + 396.734i −0.00734794 + 0.543471i
\(731\) 509.713 327.573i 0.697282 0.448116i
\(732\) −430.819 497.192i −0.588551 0.679224i
\(733\) 554.047 + 162.683i 0.755862 + 0.221941i 0.636888 0.770956i \(-0.280221\pi\)
0.118974 + 0.992897i \(0.462040\pi\)
\(734\) −35.8753 16.3837i −0.0488764 0.0223211i
\(735\) 17.6311 + 20.9121i 0.0239879 + 0.0284518i
\(736\) 128.617 + 19.6391i 0.174751 + 0.0266835i
\(737\) 499.212i 0.677356i
\(738\) −65.5689 29.9443i −0.0888467 0.0405749i
\(739\) 258.543 + 75.9150i 0.349855 + 0.102727i 0.451938 0.892049i \(-0.350733\pi\)
−0.102084 + 0.994776i \(0.532551\pi\)
\(740\) −265.766 41.8861i −0.359144 0.0566029i
\(741\) 282.302 + 439.271i 0.380975 + 0.592808i
\(742\) 543.381 + 470.842i 0.732319 + 0.634558i
\(743\) 133.250 926.774i 0.179340 1.24734i −0.678953 0.734182i \(-0.737566\pi\)
0.858294 0.513159i \(-0.171525\pi\)
\(744\) 187.262 54.9851i 0.251696 0.0739048i
\(745\) 26.5947 + 204.566i 0.0356975 + 0.274586i
\(746\) −227.693 + 32.7373i −0.305218 + 0.0438837i
\(747\) −2.51127 5.49892i −0.00336181 0.00736134i
\(748\) −237.981 + 108.682i −0.318157 + 0.145297i
\(749\) 139.648 + 971.273i 0.186446 + 1.29676i
\(750\) 20.6161 508.024i 0.0274881 0.677365i
\(751\) 347.315 + 1182.85i 0.462470 + 1.57503i 0.779366 + 0.626569i \(0.215541\pi\)
−0.316896 + 0.948460i \(0.602641\pi\)
\(752\) −52.0998 7.49082i −0.0692816 0.00996119i
\(753\) −446.496 + 515.284i −0.592956 + 0.684308i
\(754\) −897.489 + 576.781i −1.19030 + 0.764962i
\(755\) −424.133 66.8454i −0.561765 0.0885370i
\(756\) 108.191 368.463i 0.143109 0.487385i
\(757\) 206.287 451.705i 0.272506 0.596704i −0.723059 0.690787i \(-0.757264\pi\)
0.995564 + 0.0940822i \(0.0299917\pi\)
\(758\) 489.111 0.645265
\(759\) −929.695 + 586.082i −1.22490 + 0.772176i
\(760\) 118.294 99.7343i 0.155650 0.131229i
\(761\) −223.619 + 489.657i −0.293849 + 0.643439i −0.997763 0.0668454i \(-0.978707\pi\)
0.703914 + 0.710285i \(0.251434\pi\)
\(762\) −172.706 + 588.184i −0.226649 + 0.771895i
\(763\) 238.860 206.973i 0.313054 0.271263i
\(764\) 252.079 + 392.242i 0.329946 + 0.513406i
\(765\) 0.387247 28.6417i 0.000506205 0.0374401i
\(766\) −13.3918 1.92545i −0.0174827 0.00251364i
\(767\) 238.473 + 812.165i 0.310917 + 1.05889i
\(768\) −24.8797 + 38.7136i −0.0323954 + 0.0504083i
\(769\) −1354.35 + 194.726i −1.76118 + 0.253220i −0.945579 0.325394i \(-0.894503\pi\)
−0.815602 + 0.578613i \(0.803594\pi\)
\(770\) 728.753 + 344.792i 0.946432 + 0.447782i
\(771\) 72.4791 + 158.707i 0.0940066 + 0.205846i
\(772\) −334.999 + 48.1656i −0.433937 + 0.0623907i
\(773\) −327.614 210.545i −0.423821 0.272373i 0.311296 0.950313i \(-0.399237\pi\)
−0.735118 + 0.677939i \(0.762873\pi\)
\(774\) −22.3069 75.9705i −0.0288203 0.0981531i
\(775\) −570.699 184.472i −0.736386 0.238029i
\(776\) −294.543 255.223i −0.379566 0.328896i
\(777\) −287.114 446.758i −0.369516 0.574978i
\(778\) −392.547 453.023i −0.504559 0.582292i
\(779\) 215.936 735.411i 0.277197 0.944045i
\(780\) 128.257 + 459.704i 0.164432 + 0.589364i
\(781\) 1011.87i 1.29561i
\(782\) 192.087 + 169.401i 0.245636 + 0.216625i
\(783\) 1271.95i 1.62446i
\(784\) −3.16051 + 6.92054i −0.00403126 + 0.00882722i
\(785\) −146.180 + 64.3843i −0.186217 + 0.0820183i
\(786\) −85.7661 98.9794i −0.109117 0.125928i
\(787\) 301.515 193.772i 0.383120 0.246216i −0.334878 0.942261i \(-0.608695\pi\)
0.717998 + 0.696045i \(0.245059\pi\)
\(788\) 500.934 + 434.062i 0.635704 + 0.550840i
\(789\) 1091.42 + 156.923i 1.38330 + 0.198889i
\(790\) 338.970 512.091i 0.429076 0.648217i
\(791\) −235.687 151.467i −0.297961 0.191488i
\(792\) 4.86555 + 33.8406i 0.00614337 + 0.0427281i
\(793\) −788.353 1726.25i −0.994140 2.17686i
\(794\) 328.347 + 718.980i 0.413536 + 0.905517i
\(795\) −708.484 + 795.641i −0.891175 + 1.00081i
\(796\) 111.374 173.302i 0.139918 0.217716i
\(797\) −347.058 + 101.905i −0.435455 + 0.127861i −0.492111 0.870533i \(-0.663774\pi\)
0.0566556 + 0.998394i \(0.481956\pi\)
\(798\) 302.301 + 43.4643i 0.378823 + 0.0544666i
\(799\) −78.3045 67.8512i −0.0980031 0.0849202i
\(800\) 130.183 55.2492i 0.162728 0.0690614i
\(801\) 50.0315 43.3525i 0.0624613 0.0541230i
\(802\) −105.082 30.8548i −0.131025 0.0384723i
\(803\) 387.252 847.964i 0.482257 1.05600i
\(804\) 172.852i 0.214989i
\(805\) 17.5540 789.026i 0.0218062 0.980157i
\(806\) 562.990 0.698499
\(807\) −433.277 197.871i −0.536899 0.245193i
\(808\) −114.594 + 390.272i −0.141825 + 0.483010i
\(809\) 364.212 + 420.323i 0.450200 + 0.519558i 0.934799 0.355178i \(-0.115580\pi\)
−0.484599 + 0.874737i \(0.661034\pi\)
\(810\) 499.500 + 154.031i 0.616667 + 0.190162i
\(811\) −786.518 + 907.690i −0.969813 + 1.11922i 0.0230227 + 0.999735i \(0.492671\pi\)
−0.992836 + 0.119489i \(0.961874\pi\)
\(812\) −88.8035 + 617.642i −0.109364 + 0.760643i
\(813\) 121.079 + 412.359i 0.148929 + 0.507206i
\(814\) 531.775 + 341.751i 0.653286 + 0.419841i
\(815\) −138.130 + 155.123i −0.169485 + 0.190335i
\(816\) −82.4008 + 37.6312i −0.100981 + 0.0461167i
\(817\) 765.818 349.737i 0.937353 0.428075i
\(818\) 917.568 131.926i 1.12172 0.161279i
\(819\) 44.7948 69.7020i 0.0546945 0.0851063i
\(820\) 386.678 584.165i 0.471558 0.712396i
\(821\) 210.635 1465.00i 0.256559 1.78441i −0.300343 0.953831i \(-0.597101\pi\)
0.556902 0.830578i \(-0.311990\pi\)
\(822\) −316.392 + 365.136i −0.384905 + 0.444204i
\(823\) −68.5870 106.723i −0.0833378 0.129676i 0.797082 0.603871i \(-0.206376\pi\)
−0.880420 + 0.474195i \(0.842739\pi\)
\(824\) 39.5492 34.2695i 0.0479965 0.0415892i
\(825\) −525.442 + 1072.81i −0.636899 + 1.30038i
\(826\) 450.346 + 205.666i 0.545213 + 0.248990i
\(827\) 34.0401 0.0411609 0.0205804 0.999788i \(-0.493449\pi\)
0.0205804 + 0.999788i \(0.493449\pi\)
\(828\) 28.3123 17.8481i 0.0341936 0.0215557i
\(829\) 628.372 0.757987 0.378994 0.925399i \(-0.376270\pi\)
0.378994 + 0.925399i \(0.376270\pi\)
\(830\) 56.5901 15.7886i 0.0681809 0.0190224i
\(831\) 526.187 + 154.502i 0.633197 + 0.185924i
\(832\) −100.324 + 86.9316i −0.120582 + 0.104485i
\(833\) −12.5988 + 8.09679i −0.0151247 + 0.00972003i
\(834\) 181.139 209.045i 0.217193 0.250654i
\(835\) −119.176 + 74.3323i −0.142725 + 0.0890207i
\(836\) −348.803 + 102.418i −0.417228 + 0.122509i
\(837\) 362.891 564.670i 0.433562 0.674636i
\(838\) 70.4547 + 490.023i 0.0840748 + 0.584753i
\(839\) 710.803 324.613i 0.847202 0.386904i 0.0559793 0.998432i \(-0.482172\pi\)
0.791223 + 0.611528i \(0.209445\pi\)
\(840\) 252.330 + 119.384i 0.300393 + 0.142124i
\(841\) −174.449 1213.32i −0.207430 1.44271i
\(842\) −564.083 362.514i −0.669932 0.430539i
\(843\) 1060.26 311.322i 1.25773 0.369302i
\(844\) 52.5270 365.333i 0.0622357 0.432859i
\(845\) −7.18848 + 531.677i −0.00850708 + 0.629204i
\(846\) −11.3904 + 7.32018i −0.0134639 + 0.00865269i
\(847\) −696.616 803.938i −0.822451 0.949159i
\(848\) −284.323 83.4848i −0.335287 0.0984491i
\(849\) 160.250 + 73.1837i 0.188751 + 0.0861998i
\(850\) 274.379 + 47.0535i 0.322799 + 0.0553570i
\(851\) 93.4059 611.718i 0.109760 0.718822i
\(852\) 350.360i 0.411221i
\(853\) −121.995 55.7133i −0.143019 0.0653145i 0.342620 0.939474i \(-0.388686\pi\)
−0.485639 + 0.874160i \(0.661413\pi\)
\(854\) −1065.02 312.718i −1.24710 0.366181i
\(855\) 6.19643 39.3162i 0.00724728 0.0459838i
\(856\) −218.644 340.216i −0.255425 0.397449i
\(857\) −1057.08 915.963i −1.23346 1.06880i −0.995226 0.0975949i \(-0.968885\pi\)
−0.238237 0.971207i \(-0.576569\pi\)
\(858\) 159.580 1109.90i 0.185991 1.29359i
\(859\) 957.070 281.021i 1.11417 0.327149i 0.327701 0.944782i \(-0.393726\pi\)
0.786467 + 0.617632i \(0.211908\pi\)
\(860\) 763.080 99.2043i 0.887302 0.115354i
\(861\) 1368.71 196.791i 1.58968 0.228561i
\(862\) 474.293 + 1038.56i 0.550224 + 1.20482i
\(863\) −819.218 + 374.124i −0.949268 + 0.433516i −0.829014 0.559227i \(-0.811098\pi\)
−0.120253 + 0.992743i \(0.538371\pi\)
\(864\) 22.5240 + 156.658i 0.0260695 + 0.181317i
\(865\) 122.595 + 943.003i 0.141729 + 1.09018i
\(866\) 181.446 + 617.948i 0.209522 + 0.713566i
\(867\) 646.253 + 92.9171i 0.745390 + 0.107171i
\(868\) 215.639 248.860i 0.248432 0.286706i
\(869\) −1213.81 + 780.067i −1.39679 + 0.897661i
\(870\) −913.318 143.944i −1.04979 0.165452i
\(871\) −140.476 + 478.418i −0.161281 + 0.549274i
\(872\) −54.1118 + 118.488i −0.0620548 + 0.135881i
\(873\) −100.255 −0.114839
\(874\) 230.691 + 270.973i 0.263948 + 0.310037i
\(875\) −434.145 739.881i −0.496166 0.845578i
\(876\) 134.086 293.607i 0.153066 0.335168i
\(877\) −325.157 + 1107.38i −0.370761 + 1.26270i 0.537134 + 0.843497i \(0.319507\pi\)
−0.907895 + 0.419198i \(0.862311\pi\)
\(878\) 414.333 359.022i 0.471906 0.408909i
\(879\) 2.11265 + 3.28734i 0.00240346 + 0.00373986i
\(880\) −332.237 4.49198i −0.377542 0.00510452i
\(881\) 821.649 + 118.135i 0.932632 + 0.134092i 0.591848 0.806050i \(-0.298399\pi\)
0.340784 + 0.940142i \(0.389308\pi\)
\(882\) 0.551373 + 1.87780i 0.000625139 + 0.00212903i
\(883\) 191.147 297.431i 0.216475 0.336841i −0.715985 0.698116i \(-0.754022\pi\)
0.932459 + 0.361275i \(0.117658\pi\)
\(884\) −258.652 + 37.1885i −0.292592 + 0.0420684i
\(885\) −313.736 + 663.111i −0.354503 + 0.749279i
\(886\) −84.4382 184.894i −0.0953027 0.208684i
\(887\) 254.291 36.5616i 0.286687 0.0412194i 0.00252894 0.999997i \(-0.499195\pi\)
0.284158 + 0.958777i \(0.408286\pi\)
\(888\) 184.126 + 118.331i 0.207350 + 0.133255i
\(889\) 291.392 + 992.392i 0.327776 + 1.11630i
\(890\) 340.492 + 545.904i 0.382575 + 0.613375i
\(891\) −928.137 804.235i −1.04168 0.902621i
\(892\) 165.494 + 257.514i 0.185531 + 0.288693i
\(893\) −94.2797 108.805i −0.105576 0.121842i
\(894\) 47.2794 161.019i 0.0528852 0.180111i
\(895\) −36.4205 130.540i −0.0406933 0.145855i
\(896\) 77.6437i 0.0866559i
\(897\) −1055.89 + 300.057i −1.17714 + 0.334511i
\(898\) 577.597i 0.643204i
\(899\) −453.083 + 992.113i −0.503986 + 1.10357i
\(900\) 16.0014 32.6707i 0.0177794 0.0363008i
\(901\) −381.987 440.837i −0.423959 0.489275i
\(902\) −1384.64 + 889.856i −1.53508 + 0.986537i
\(903\) 1147.90 + 994.663i 1.27121 + 1.10151i
\(904\) 114.290 + 16.4325i 0.126428 + 0.0181775i
\(905\) 1055.01 + 698.343i 1.16575 + 0.771650i
\(906\) 293.845 + 188.842i 0.324332 + 0.208435i
\(907\) −1.05174 7.31501i −0.00115958 0.00806506i 0.989233 0.146346i \(-0.0467513\pi\)
−0.990393 + 0.138281i \(0.955842\pi\)
\(908\) −113.443 248.406i −0.124938 0.273575i
\(909\) 43.4652 + 95.1756i 0.0478165 + 0.104704i
\(910\) 601.375 + 535.498i 0.660851 + 0.588460i
\(911\) 156.342 243.273i 0.171616 0.267040i −0.744782 0.667308i \(-0.767447\pi\)
0.916398 + 0.400268i \(0.131083\pi\)
\(912\) −120.773 + 35.4620i −0.132426 + 0.0388838i
\(913\) −136.630 19.6445i −0.149650 0.0215164i
\(914\) −367.801 318.701i −0.402408 0.348688i
\(915\) 484.657 1571.67i 0.529680 1.71767i
\(916\) 381.452 330.530i 0.416432 0.360841i
\(917\) −212.021 62.2549i −0.231211 0.0678898i
\(918\) −129.422 + 283.394i −0.140982 + 0.308709i
\(919\) 1674.09i 1.82164i −0.412801 0.910821i \(-0.635450\pi\)
0.412801 0.910821i \(-0.364550\pi\)
\(920\) 128.507 + 298.807i 0.139682 + 0.324791i
\(921\) −85.5213 −0.0928570
\(922\) 395.243 + 180.501i 0.428680 + 0.195772i
\(923\) 284.737 969.725i 0.308491 1.05062i
\(924\) −429.491 495.659i −0.464817 0.536428i
\(925\) −262.772 619.165i −0.284077 0.669367i
\(926\) 836.985 965.933i 0.903872 1.04312i
\(927\) 1.91577 13.3245i 0.00206663 0.0143738i
\(928\) −72.4537 246.755i −0.0780751 0.265900i
\(929\) −1017.73 654.055i −1.09551 0.704042i −0.137421 0.990513i \(-0.543881\pi\)
−0.958089 + 0.286471i \(0.907518\pi\)
\(930\) 364.392 + 324.475i 0.391819 + 0.348898i
\(931\) −18.9291 + 8.64464i −0.0203320 + 0.00928532i
\(932\) −104.059 + 47.5221i −0.111651 + 0.0509894i
\(933\) −1446.19 + 207.931i −1.55005 + 0.222863i
\(934\) 350.928 546.055i 0.375726 0.584641i
\(935\) −545.399 361.018i −0.583315 0.386115i
\(936\) −4.85974 + 33.8002i −0.00519202 + 0.0361113i
\(937\) 57.0371 65.8244i 0.0608721 0.0702501i −0.724497 0.689278i \(-0.757928\pi\)
0.785369 + 0.619028i \(0.212473\pi\)
\(938\) 157.671 + 245.341i 0.168093 + 0.261557i
\(939\) −229.132 + 198.544i −0.244017 + 0.211442i
\(940\) −53.0408 120.425i −0.0564264 0.128112i
\(941\) −544.536 248.681i −0.578678 0.264273i 0.104501 0.994525i \(-0.466676\pi\)
−0.683178 + 0.730251i \(0.739403\pi\)
\(942\) 129.942 0.137943
\(943\) 1347.83 + 882.906i 1.42930 + 0.936274i
\(944\) −204.044 −0.216148
\(945\) 924.730 257.998i 0.978550 0.273014i
\(946\) −1734.70 509.353i −1.83372 0.538429i
\(947\) −102.013 + 88.3947i −0.107722 + 0.0933419i −0.707057 0.707157i \(-0.749977\pi\)
0.599334 + 0.800499i \(0.295432\pi\)
\(948\) −420.280 + 270.097i −0.443333 + 0.284913i
\(949\) 609.736 703.673i 0.642503 0.741489i
\(950\) 368.066 + 118.973i 0.387438 + 0.125235i
\(951\) −918.034 + 269.559i −0.965336 + 0.283448i
\(952\) −82.6313 + 128.577i −0.0867976 + 0.135060i
\(953\) 99.1806 + 689.816i 0.104072 + 0.723837i 0.973319 + 0.229458i \(0.0736953\pi\)
−0.869247 + 0.494379i \(0.835396\pi\)
\(954\) −69.3378 + 31.6655i −0.0726811 + 0.0331923i
\(955\) −498.518 + 1053.67i −0.522008 + 1.10332i
\(956\) 128.613 + 894.521i 0.134532 + 0.935691i
\(957\) 1827.47 + 1174.44i 1.90958 + 1.22721i
\(958\) −900.682 + 264.464i −0.940169 + 0.276059i
\(959\) −116.010 + 806.869i −0.120970 + 0.841365i
\(960\) −115.037 1.55534i −0.119830 0.00162015i
\(961\) −324.249 + 208.382i −0.337408 + 0.216839i
\(962\) 413.457 + 477.155i 0.429789 + 0.496003i
\(963\) −99.8169 29.3089i −0.103652 0.0304350i
\(964\) −238.091 108.732i −0.246982 0.112793i
\(965\) −545.389 646.879i −0.565170 0.670341i
\(966\) −271.797 + 581.669i −0.281363 + 0.602142i
\(967\) 343.640i 0.355367i −0.984088 0.177683i \(-0.943140\pi\)
0.984088 0.177683i \(-0.0568603\pi\)
\(968\) 398.799 + 182.125i 0.411983 + 0.188146i
\(969\) −237.738 69.8061i −0.245343 0.0720393i
\(970\) 151.689 962.462i 0.156380 0.992228i
\(971\) 539.791 + 839.931i 0.555912 + 0.865016i 0.999513 0.0312083i \(-0.00993552\pi\)
−0.443601 + 0.896225i \(0.646299\pi\)
\(972\) 59.2358 + 51.3282i 0.0609422 + 0.0528067i
\(973\) 66.4176 461.944i 0.0682606 0.474763i
\(974\) 519.807 152.629i 0.533682 0.156703i
\(975\) −805.440 + 880.269i −0.826093 + 0.902840i
\(976\) 452.811 65.1044i 0.463945 0.0667053i
\(977\) −405.712 888.385i −0.415263 0.909299i −0.995492 0.0948456i \(-0.969764\pi\)
0.580229 0.814453i \(-0.302963\pi\)
\(978\) 153.703 70.1939i 0.157161 0.0717729i
\(979\) −215.127 1496.24i −0.219742 1.52834i
\(980\) −18.8614 + 2.45209i −0.0192464 + 0.00250213i
\(981\) 9.44018 + 32.1503i 0.00962302 + 0.0327730i
\(982\) −778.102 111.874i −0.792364 0.113925i
\(983\) 898.265 1036.65i 0.913800 1.05458i −0.0845074 0.996423i \(-0.526932\pi\)
0.998307 0.0581585i \(-0.0185229\pi\)
\(984\) −479.431 + 308.112i −0.487227 + 0.313122i
\(985\) −257.980 + 1636.87i −0.261908 + 1.66180i
\(986\) 142.623 485.730i 0.144648 0.492627i
\(987\) 107.899 236.267i 0.109321 0.239379i
\(988\) −363.094 −0.367504
\(989\) 236.583 + 1753.97i 0.239215 + 1.77348i
\(990\) −65.3459 + 55.0936i −0.0660059 + 0.0556501i
\(991\) −238.395 + 522.013i −0.240560 + 0.526754i −0.990948 0.134244i \(-0.957139\pi\)
0.750388 + 0.660998i \(0.229867\pi\)
\(992\) −38.2348 + 130.216i −0.0385432 + 0.131266i
\(993\) −899.554 + 779.468i −0.905895 + 0.784963i
\(994\) −319.590 497.292i −0.321519 0.500293i
\(995\) 514.964 + 6.96252i 0.517552 + 0.00699751i
\(996\) −47.3082 6.80189i −0.0474981 0.00682920i
\(997\) 248.149 + 845.119i 0.248896 + 0.847662i 0.985258 + 0.171074i \(0.0547237\pi\)
−0.736362 + 0.676587i \(0.763458\pi\)
\(998\) 659.544 1026.27i 0.660865 1.02833i
\(999\) 745.085 107.127i 0.745831 0.107234i
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 230.3.i.a.109.21 yes 240
5.4 even 2 inner 230.3.i.a.109.4 yes 240
23.19 odd 22 inner 230.3.i.a.19.4 240
115.19 odd 22 inner 230.3.i.a.19.21 yes 240
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.3.i.a.19.4 240 23.19 odd 22 inner
230.3.i.a.19.21 yes 240 115.19 odd 22 inner
230.3.i.a.109.4 yes 240 5.4 even 2 inner
230.3.i.a.109.21 yes 240 1.1 even 1 trivial