Properties

Label 201.3.g.b.29.3
Level $201$
Weight $3$
Character 201.29
Analytic conductor $5.477$
Analytic rank $0$
Dimension $84$
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] = [201,3,Mod(29,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.29");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 201.g (of order \(6\), degree \(2\), 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: \(5.47685331364\)
Analytic rank: \(0\)
Dimension: \(84\)
Relative dimension: \(42\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 29.3
Character \(\chi\) \(=\) 201.29
Dual form 201.3.g.b.104.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.10861 - 1.79476i) q^{2} +(1.01703 + 2.82235i) q^{3} +(4.44231 + 7.69431i) q^{4} -6.24319i q^{5} +(1.90387 - 10.5989i) q^{6} +(0.163929 + 0.283933i) q^{7} -17.5334i q^{8} +(-6.93129 + 5.74084i) q^{9} +O(q^{10})\) \(q+(-3.10861 - 1.79476i) q^{2} +(1.01703 + 2.82235i) q^{3} +(4.44231 + 7.69431i) q^{4} -6.24319i q^{5} +(1.90387 - 10.5989i) q^{6} +(0.163929 + 0.283933i) q^{7} -17.5334i q^{8} +(-6.93129 + 5.74084i) q^{9} +(-11.2050 + 19.4077i) q^{10} +(-1.56125 + 0.901388i) q^{11} +(-17.1980 + 20.3631i) q^{12} +(3.90674 - 6.76667i) q^{13} -1.17685i q^{14} +(17.6205 - 6.34953i) q^{15} +(-13.6990 + 23.7274i) q^{16} +(17.3146 + 9.99660i) q^{17} +(31.8501 - 5.40607i) q^{18} +(13.3720 - 23.1610i) q^{19} +(48.0370 - 27.7342i) q^{20} +(-0.634637 + 0.751433i) q^{21} +6.47109 q^{22} +(-18.1296 - 10.4671i) q^{23} +(49.4854 - 17.8321i) q^{24} -13.9774 q^{25} +(-24.2891 + 14.0233i) q^{26} +(-23.2520 - 13.7239i) q^{27} +(-1.45645 + 2.52264i) q^{28} +(27.7448 - 16.0185i) q^{29} +(-66.1710 - 11.8862i) q^{30} +(3.65568 + 6.33183i) q^{31} +(24.4322 - 14.1059i) q^{32} +(-4.13187 - 3.48965i) q^{33} +(-35.8829 - 62.1511i) q^{34} +(1.77265 - 1.02344i) q^{35} +(-74.9627 - 27.8288i) q^{36} +(34.8705 - 60.3975i) q^{37} +(-83.1368 + 47.9990i) q^{38} +(23.0712 + 4.14424i) q^{39} -109.465 q^{40} +(40.6240 - 23.4543i) q^{41} +(3.32148 - 1.19690i) q^{42} -39.0020 q^{43} +(-13.8711 - 8.00849i) q^{44} +(35.8412 + 43.2733i) q^{45} +(37.5720 + 65.0766i) q^{46} +(55.1107 - 31.8182i) q^{47} +(-80.8992 - 14.5318i) q^{48} +(24.4463 - 42.3422i) q^{49} +(43.4504 + 25.0861i) q^{50} +(-10.6043 + 59.0347i) q^{51} +69.4198 q^{52} -52.5176i q^{53} +(47.6504 + 84.3939i) q^{54} +(5.62754 + 9.74718i) q^{55} +(4.97832 - 2.87423i) q^{56} +(78.9682 + 14.1849i) q^{57} -114.997 q^{58} +77.3415i q^{59} +(127.131 + 107.371i) q^{60} +(-44.0343 + 76.2696i) q^{61} -26.2443i q^{62} +(-2.76625 - 1.02693i) q^{63} +8.32506 q^{64} +(-42.2456 - 24.3905i) q^{65} +(6.58131 + 18.2637i) q^{66} +(-58.6622 + 32.3688i) q^{67} +177.632i q^{68} +(11.1035 - 61.8135i) q^{69} -7.34730 q^{70} +(2.38523 - 1.37711i) q^{71} +(100.657 + 121.529i) q^{72} +(28.8945 - 50.0467i) q^{73} +(-216.798 + 125.168i) q^{74} +(-14.2155 - 39.4492i) q^{75} +237.610 q^{76} +(-0.511868 - 0.295527i) q^{77} +(-64.2814 - 54.2900i) q^{78} +(70.1161 + 121.445i) q^{79} +(148.135 + 85.5255i) q^{80} +(15.0855 - 79.5828i) q^{81} -168.379 q^{82} +(-68.5120 - 39.5554i) q^{83} +(-8.60101 - 1.54499i) q^{84} +(62.4107 - 108.098i) q^{85} +(121.242 + 69.9991i) q^{86} +(73.4270 + 62.0141i) q^{87} +(15.8044 + 27.3740i) q^{88} +52.6293i q^{89} +(-33.7511 - 198.846i) q^{90} +2.56171 q^{91} -185.993i q^{92} +(-14.1527 + 16.7573i) q^{93} -228.424 q^{94} +(-144.599 - 83.4840i) q^{95} +(64.6602 + 54.6099i) q^{96} +(-23.0652 + 39.9500i) q^{97} +(-151.988 + 87.7502i) q^{98} +(5.64674 - 15.2107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 84 q - 6 q^{3} + 82 q^{4} + 3 q^{6} - 10 q^{7} + 2 q^{9} + 6 q^{10} - 58 q^{12} - 6 q^{13} + 78 q^{15} - 130 q^{16} + 11 q^{18} + 72 q^{19} - 36 q^{21} + 140 q^{22} + 72 q^{24} - 428 q^{25} + 138 q^{27} - 8 q^{28} + 29 q^{30} - 28 q^{31} - 30 q^{33} - 54 q^{34} + 105 q^{36} - 24 q^{37} - 103 q^{39} + 128 q^{40} + 252 q^{42} + 148 q^{43} + 276 q^{45} - 146 q^{46} + 137 q^{48} - 176 q^{49} + 15 q^{51} - 792 q^{52} + 72 q^{54} + 28 q^{55} - 205 q^{57} - 120 q^{58} - 64 q^{60} + 162 q^{61} - 106 q^{63} - 604 q^{64} - 462 q^{66} - 460 q^{67} + 101 q^{69} + 636 q^{70} + 212 q^{72} + 238 q^{73} + 628 q^{75} + 40 q^{76} + 96 q^{78} + 462 q^{79} - 726 q^{81} - 344 q^{82} + 385 q^{84} - 94 q^{85} - 91 q^{87} + 234 q^{88} + 482 q^{90} - 536 q^{91} + 281 q^{93} + 580 q^{94} + 40 q^{96} + 68 q^{97} + 379 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.10861 1.79476i −1.55431 0.897379i −0.997783 0.0665463i \(-0.978802\pi\)
−0.556522 0.830833i \(-0.687865\pi\)
\(3\) 1.01703 + 2.82235i 0.339011 + 0.940782i
\(4\) 4.44231 + 7.69431i 1.11058 + 1.92358i
\(5\) 6.24319i 1.24864i −0.781169 0.624319i \(-0.785376\pi\)
0.781169 0.624319i \(-0.214624\pi\)
\(6\) 1.90387 10.5989i 0.317311 1.76648i
\(7\) 0.163929 + 0.283933i 0.0234184 + 0.0405619i 0.877497 0.479582i \(-0.159212\pi\)
−0.854079 + 0.520144i \(0.825878\pi\)
\(8\) 17.5334i 2.19168i
\(9\) −6.93129 + 5.74084i −0.770143 + 0.637871i
\(10\) −11.2050 + 19.4077i −1.12050 + 1.94077i
\(11\) −1.56125 + 0.901388i −0.141932 + 0.0819443i −0.569284 0.822141i \(-0.692780\pi\)
0.427353 + 0.904085i \(0.359446\pi\)
\(12\) −17.1980 + 20.3631i −1.43317 + 1.69693i
\(13\) 3.90674 6.76667i 0.300518 0.520513i −0.675735 0.737145i \(-0.736174\pi\)
0.976253 + 0.216631i \(0.0695070\pi\)
\(14\) 1.17685i 0.0840607i
\(15\) 17.6205 6.34953i 1.17470 0.423302i
\(16\) −13.6990 + 23.7274i −0.856188 + 1.48296i
\(17\) 17.3146 + 9.99660i 1.01851 + 0.588035i 0.913671 0.406454i \(-0.133235\pi\)
0.104836 + 0.994490i \(0.466568\pi\)
\(18\) 31.8501 5.40607i 1.76945 0.300337i
\(19\) 13.3720 23.1610i 0.703790 1.21900i −0.263336 0.964704i \(-0.584823\pi\)
0.967126 0.254296i \(-0.0818438\pi\)
\(20\) 48.0370 27.7342i 2.40185 1.38671i
\(21\) −0.634637 + 0.751433i −0.0302208 + 0.0357825i
\(22\) 6.47109 0.294140
\(23\) −18.1296 10.4671i −0.788245 0.455093i 0.0510996 0.998694i \(-0.483727\pi\)
−0.839344 + 0.543600i \(0.817061\pi\)
\(24\) 49.4854 17.8321i 2.06189 0.743003i
\(25\) −13.9774 −0.559098
\(26\) −24.2891 + 14.0233i −0.934195 + 0.539358i
\(27\) −23.2520 13.7239i −0.861185 0.508291i
\(28\) −1.45645 + 2.52264i −0.0520159 + 0.0900942i
\(29\) 27.7448 16.0185i 0.956716 0.552360i 0.0615554 0.998104i \(-0.480394\pi\)
0.895161 + 0.445743i \(0.147061\pi\)
\(30\) −66.1710 11.8862i −2.20570 0.396207i
\(31\) 3.65568 + 6.33183i 0.117925 + 0.204253i 0.918945 0.394385i \(-0.129042\pi\)
−0.801020 + 0.598638i \(0.795709\pi\)
\(32\) 24.4322 14.1059i 0.763506 0.440811i
\(33\) −4.13187 3.48965i −0.125208 0.105747i
\(34\) −35.8829 62.1511i −1.05538 1.82797i
\(35\) 1.77265 1.02344i 0.0506471 0.0292411i
\(36\) −74.9627 27.8288i −2.08230 0.773023i
\(37\) 34.8705 60.3975i 0.942446 1.63236i 0.181661 0.983361i \(-0.441853\pi\)
0.760786 0.649003i \(-0.224814\pi\)
\(38\) −83.1368 + 47.9990i −2.18781 + 1.26313i
\(39\) 23.0712 + 4.14424i 0.591569 + 0.106263i
\(40\) −109.465 −2.73661
\(41\) 40.6240 23.4543i 0.990830 0.572056i 0.0853074 0.996355i \(-0.472813\pi\)
0.905522 + 0.424299i \(0.139479\pi\)
\(42\) 3.32148 1.19690i 0.0790828 0.0284975i
\(43\) −39.0020 −0.907023 −0.453512 0.891250i \(-0.649829\pi\)
−0.453512 + 0.891250i \(0.649829\pi\)
\(44\) −13.8711 8.00849i −0.315252 0.182011i
\(45\) 35.8412 + 43.2733i 0.796471 + 0.961630i
\(46\) 37.5720 + 65.0766i 0.816782 + 1.41471i
\(47\) 55.1107 31.8182i 1.17257 0.676982i 0.218284 0.975885i \(-0.429954\pi\)
0.954283 + 0.298903i \(0.0966207\pi\)
\(48\) −80.8992 14.5318i −1.68540 0.302746i
\(49\) 24.4463 42.3422i 0.498903 0.864126i
\(50\) 43.4504 + 25.0861i 0.869009 + 0.501722i
\(51\) −10.6043 + 59.0347i −0.207928 + 1.15754i
\(52\) 69.4198 1.33500
\(53\) 52.5176i 0.990898i −0.868637 0.495449i \(-0.835004\pi\)
0.868637 0.495449i \(-0.164996\pi\)
\(54\) 47.6504 + 84.3939i 0.882415 + 1.56285i
\(55\) 5.62754 + 9.74718i 0.102319 + 0.177221i
\(56\) 4.97832 2.87423i 0.0888985 0.0513256i
\(57\) 78.9682 + 14.1849i 1.38541 + 0.248859i
\(58\) −114.997 −1.98271
\(59\) 77.3415i 1.31087i 0.755250 + 0.655436i \(0.227515\pi\)
−0.755250 + 0.655436i \(0.772485\pi\)
\(60\) 127.131 + 107.371i 2.11885 + 1.78951i
\(61\) −44.0343 + 76.2696i −0.721873 + 1.25032i 0.238375 + 0.971173i \(0.423385\pi\)
−0.960248 + 0.279148i \(0.909948\pi\)
\(62\) 26.2443i 0.423295i
\(63\) −2.76625 1.02693i −0.0439088 0.0163005i
\(64\) 8.32506 0.130079
\(65\) −42.2456 24.3905i −0.649933 0.375239i
\(66\) 6.58131 + 18.2637i 0.0997169 + 0.276722i
\(67\) −58.6622 + 32.3688i −0.875556 + 0.483117i
\(68\) 177.632i 2.61224i
\(69\) 11.1035 61.8135i 0.160920 0.895848i
\(70\) −7.34730 −0.104961
\(71\) 2.38523 1.37711i 0.0335948 0.0193960i −0.483109 0.875560i \(-0.660492\pi\)
0.516703 + 0.856164i \(0.327159\pi\)
\(72\) 100.657 + 121.529i 1.39801 + 1.68791i
\(73\) 28.8945 50.0467i 0.395815 0.685571i −0.597390 0.801951i \(-0.703796\pi\)
0.993205 + 0.116380i \(0.0371290\pi\)
\(74\) −216.798 + 125.168i −2.92970 + 1.69146i
\(75\) −14.2155 39.4492i −0.189540 0.525989i
\(76\) 237.610 3.12645
\(77\) −0.511868 0.295527i −0.00664763 0.00383801i
\(78\) −64.2814 54.2900i −0.824121 0.696026i
\(79\) 70.1161 + 121.445i 0.887545 + 1.53727i 0.842768 + 0.538276i \(0.180924\pi\)
0.0447769 + 0.998997i \(0.485742\pi\)
\(80\) 148.135 + 85.5255i 1.85168 + 1.06907i
\(81\) 15.0855 79.5828i 0.186240 0.982504i
\(82\) −168.379 −2.05340
\(83\) −68.5120 39.5554i −0.825446 0.476572i 0.0268448 0.999640i \(-0.491454\pi\)
−0.852291 + 0.523068i \(0.824787\pi\)
\(84\) −8.60101 1.54499i −0.102393 0.0183927i
\(85\) 62.4107 108.098i 0.734243 1.27175i
\(86\) 121.242 + 69.9991i 1.40979 + 0.813943i
\(87\) 73.4270 + 62.0141i 0.843988 + 0.712805i
\(88\) 15.8044 + 27.3740i 0.179596 + 0.311069i
\(89\) 52.6293i 0.591341i 0.955290 + 0.295670i \(0.0955430\pi\)
−0.955290 + 0.295670i \(0.904457\pi\)
\(90\) −33.7511 198.846i −0.375012 2.20940i
\(91\) 2.56171 0.0281506
\(92\) 185.993i 2.02167i
\(93\) −14.1527 + 16.7573i −0.152179 + 0.180186i
\(94\) −228.424 −2.43004
\(95\) −144.599 83.4840i −1.52209 0.878779i
\(96\) 64.6602 + 54.6099i 0.673544 + 0.568854i
\(97\) −23.0652 + 39.9500i −0.237785 + 0.411856i −0.960078 0.279731i \(-0.909755\pi\)
0.722293 + 0.691587i \(0.243088\pi\)
\(98\) −151.988 + 87.7502i −1.55090 + 0.895410i
\(99\) 5.64674 15.2107i 0.0570378 0.153643i
\(100\) −62.0921 107.547i −0.620921 1.07547i
\(101\) −144.604 + 83.4872i −1.43172 + 0.826606i −0.997252 0.0740804i \(-0.976398\pi\)
−0.434471 + 0.900686i \(0.643065\pi\)
\(102\) 138.918 164.484i 1.36194 1.61259i
\(103\) 14.1555 + 24.5180i 0.137432 + 0.238039i 0.926524 0.376236i \(-0.122782\pi\)
−0.789092 + 0.614275i \(0.789448\pi\)
\(104\) −118.643 68.4985i −1.14080 0.658639i
\(105\) 4.69134 + 3.96216i 0.0446795 + 0.0377348i
\(106\) −94.2563 + 163.257i −0.889211 + 1.54016i
\(107\) 109.672i 1.02497i −0.858696 0.512485i \(-0.828725\pi\)
0.858696 0.512485i \(-0.171275\pi\)
\(108\) 2.30306 239.874i 0.0213246 2.22105i
\(109\) 0.710001 0.00651377 0.00325688 0.999995i \(-0.498963\pi\)
0.00325688 + 0.999995i \(0.498963\pi\)
\(110\) 40.4003i 0.367275i
\(111\) 205.927 + 36.9904i 1.85520 + 0.333247i
\(112\) −8.98265 −0.0802022
\(113\) 36.5402 21.0965i 0.323365 0.186695i −0.329526 0.944146i \(-0.606889\pi\)
0.652891 + 0.757451i \(0.273556\pi\)
\(114\) −220.023 185.824i −1.93002 1.63004i
\(115\) −65.3484 + 113.187i −0.568247 + 0.984232i
\(116\) 246.502 + 142.318i 2.12502 + 1.22688i
\(117\) 11.7677 + 69.3297i 0.100578 + 0.592562i
\(118\) 138.809 240.425i 1.17635 2.03750i
\(119\) 6.55492i 0.0550834i
\(120\) −111.329 308.947i −0.927742 2.57456i
\(121\) −58.8750 + 101.974i −0.486570 + 0.842764i
\(122\) 273.771 158.062i 2.24402 1.29559i
\(123\) 107.512 + 90.8013i 0.874082 + 0.738222i
\(124\) −32.4794 + 56.2559i −0.261930 + 0.453677i
\(125\) 68.8159i 0.550528i
\(126\) 6.75611 + 8.15709i 0.0536199 + 0.0647388i
\(127\) 38.5915 + 66.8424i 0.303870 + 0.526318i 0.977009 0.213198i \(-0.0683879\pi\)
−0.673139 + 0.739516i \(0.735055\pi\)
\(128\) −123.608 71.3652i −0.965689 0.557541i
\(129\) −39.6663 110.077i −0.307491 0.853311i
\(130\) 87.5501 + 151.641i 0.673463 + 1.16647i
\(131\) 22.6032i 0.172543i 0.996272 + 0.0862716i \(0.0274953\pi\)
−0.996272 + 0.0862716i \(0.972505\pi\)
\(132\) 8.49535 47.2940i 0.0643587 0.358288i
\(133\) 8.76823 0.0659266
\(134\) 240.452 + 4.66239i 1.79442 + 0.0347940i
\(135\) −85.6807 + 145.167i −0.634672 + 1.07531i
\(136\) 175.275 303.584i 1.28878 2.23224i
\(137\) 119.755i 0.874123i 0.899432 + 0.437061i \(0.143981\pi\)
−0.899432 + 0.437061i \(0.856019\pi\)
\(138\) −145.457 + 172.226i −1.05403 + 1.24802i
\(139\) −251.309 −1.80798 −0.903988 0.427559i \(-0.859374\pi\)
−0.903988 + 0.427559i \(0.859374\pi\)
\(140\) 15.7493 + 9.09287i 0.112495 + 0.0649491i
\(141\) 145.851 + 123.181i 1.03441 + 0.873626i
\(142\) −9.88635 −0.0696222
\(143\) 14.0859i 0.0985031i
\(144\) −41.2634 243.105i −0.286551 1.68823i
\(145\) −100.006 173.216i −0.689698 1.19459i
\(146\) −179.643 + 103.717i −1.23043 + 0.710391i
\(147\) 144.367 + 25.9324i 0.982088 + 0.176411i
\(148\) 619.622 4.18664
\(149\) 27.3970i 0.183873i 0.995765 + 0.0919364i \(0.0293056\pi\)
−0.995765 + 0.0919364i \(0.970694\pi\)
\(150\) −26.6112 + 148.146i −0.177408 + 0.987638i
\(151\) 2.98146 5.16405i 0.0197448 0.0341990i −0.855984 0.517002i \(-0.827048\pi\)
0.875729 + 0.482803i \(0.160381\pi\)
\(152\) −406.092 234.457i −2.67166 1.54248i
\(153\) −177.401 + 30.1112i −1.15949 + 0.196805i
\(154\) 1.06080 + 1.83736i 0.00688830 + 0.0119309i
\(155\) 39.5308 22.8231i 0.255038 0.147246i
\(156\) 70.6022 + 195.927i 0.452578 + 1.25594i
\(157\) 91.3470 158.218i 0.581828 1.00776i −0.413434 0.910534i \(-0.635671\pi\)
0.995263 0.0972222i \(-0.0309958\pi\)
\(158\) 503.365i 3.18586i
\(159\) 148.223 53.4121i 0.932219 0.335925i
\(160\) −88.0661 152.535i −0.550413 0.953343i
\(161\) 6.86347i 0.0426302i
\(162\) −189.727 + 220.317i −1.17115 + 1.35998i
\(163\) −68.1557 118.049i −0.418133 0.724228i 0.577619 0.816307i \(-0.303982\pi\)
−0.995752 + 0.0920791i \(0.970649\pi\)
\(164\) 360.929 + 208.382i 2.20079 + 1.27062i
\(165\) −21.7865 + 25.7961i −0.132040 + 0.156340i
\(166\) 141.985 + 245.925i 0.855330 + 1.48148i
\(167\) −145.747 + 84.1469i −0.872735 + 0.503874i −0.868256 0.496116i \(-0.834759\pi\)
−0.00447897 + 0.999990i \(0.501426\pi\)
\(168\) 13.1752 + 11.1274i 0.0784238 + 0.0662342i
\(169\) 53.9748 + 93.4871i 0.319377 + 0.553178i
\(170\) −388.021 + 224.024i −2.28248 + 1.31779i
\(171\) 40.2784 + 237.302i 0.235546 + 1.38773i
\(172\) −173.259 300.093i −1.00732 1.74473i
\(173\) 84.7667 + 48.9401i 0.489981 + 0.282891i 0.724567 0.689205i \(-0.242040\pi\)
−0.234586 + 0.972095i \(0.575373\pi\)
\(174\) −116.956 324.561i −0.672159 1.86529i
\(175\) −2.29131 3.96866i −0.0130932 0.0226780i
\(176\) 49.3925i 0.280639i
\(177\) −218.285 + 78.6589i −1.23325 + 0.444400i
\(178\) 94.4569 163.604i 0.530657 0.919125i
\(179\) 153.889i 0.859717i −0.902896 0.429858i \(-0.858564\pi\)
0.902896 0.429858i \(-0.141436\pi\)
\(180\) −173.741 + 468.007i −0.965227 + 2.60004i
\(181\) 3.73277 + 6.46535i 0.0206231 + 0.0357202i 0.876153 0.482034i \(-0.160102\pi\)
−0.855530 + 0.517754i \(0.826768\pi\)
\(182\) −7.96336 4.59765i −0.0437547 0.0252618i
\(183\) −260.044 46.7113i −1.42100 0.255253i
\(184\) −183.525 + 317.874i −0.997418 + 1.72758i
\(185\) −377.073 217.703i −2.03823 1.17677i
\(186\) 74.0704 26.6913i 0.398228 0.143502i
\(187\) −36.0432 −0.192745
\(188\) 489.637 + 282.692i 2.60445 + 1.50368i
\(189\) 0.0849868 8.85175i 0.000449666 0.0468346i
\(190\) 299.667 + 519.039i 1.57720 + 2.73178i
\(191\) 259.965 + 150.091i 1.36107 + 0.785816i 0.989767 0.142694i \(-0.0455765\pi\)
0.371307 + 0.928510i \(0.378910\pi\)
\(192\) 8.46686 + 23.4962i 0.0440982 + 0.122376i
\(193\) 194.090 1.00565 0.502823 0.864390i \(-0.332295\pi\)
0.502823 + 0.864390i \(0.332295\pi\)
\(194\) 143.401 82.7927i 0.739181 0.426767i
\(195\) 25.8733 144.038i 0.132684 0.738655i
\(196\) 434.391 2.21628
\(197\) 163.285 94.2724i 0.828856 0.478540i −0.0246051 0.999697i \(-0.507833\pi\)
0.853461 + 0.521157i \(0.174499\pi\)
\(198\) −44.8530 + 37.1495i −0.226530 + 0.187624i
\(199\) 89.6096 155.208i 0.450299 0.779941i −0.548105 0.836410i \(-0.684651\pi\)
0.998404 + 0.0564681i \(0.0179839\pi\)
\(200\) 245.072i 1.22536i
\(201\) −151.018 132.645i −0.751331 0.659926i
\(202\) 599.357 2.96711
\(203\) 9.09634 + 5.25177i 0.0448095 + 0.0258708i
\(204\) −501.339 + 180.658i −2.45754 + 0.885577i
\(205\) −146.430 253.623i −0.714291 1.23719i
\(206\) 101.623i 0.493314i
\(207\) 185.752 31.5285i 0.897352 0.152312i
\(208\) 107.037 + 185.393i 0.514600 + 0.891314i
\(209\) 48.2135i 0.230686i
\(210\) −7.47245 20.7366i −0.0355831 0.0987459i
\(211\) 1.38961 2.40687i 0.00658583 0.0114070i −0.862714 0.505693i \(-0.831237\pi\)
0.869300 + 0.494286i \(0.164570\pi\)
\(212\) 404.086 233.299i 1.90607 1.10047i
\(213\) 6.31256 + 5.33138i 0.0296364 + 0.0250300i
\(214\) −196.834 + 340.927i −0.919786 + 1.59312i
\(215\) 243.497i 1.13254i
\(216\) −240.626 + 407.687i −1.11401 + 1.88744i
\(217\) −1.19854 + 2.07594i −0.00552324 + 0.00956654i
\(218\) −2.20712 1.27428i −0.0101244 0.00584532i
\(219\) 170.636 + 30.6511i 0.779159 + 0.139959i
\(220\) −49.9985 + 86.6000i −0.227266 + 0.393636i
\(221\) 135.287 78.1082i 0.612160 0.353431i
\(222\) −573.759 484.578i −2.58450 2.18278i
\(223\) −123.261 −0.552740 −0.276370 0.961051i \(-0.589132\pi\)
−0.276370 + 0.961051i \(0.589132\pi\)
\(224\) 8.01028 + 4.62474i 0.0357602 + 0.0206462i
\(225\) 96.8816 80.2423i 0.430585 0.356632i
\(226\) −151.453 −0.670144
\(227\) −330.582 + 190.861i −1.45631 + 0.840800i −0.998827 0.0484202i \(-0.984581\pi\)
−0.457480 + 0.889220i \(0.651248\pi\)
\(228\) 241.658 + 670.619i 1.05990 + 2.94131i
\(229\) −26.9164 + 46.6206i −0.117539 + 0.203583i −0.918792 0.394742i \(-0.870834\pi\)
0.801253 + 0.598326i \(0.204167\pi\)
\(230\) 406.285 234.569i 1.76646 1.01987i
\(231\) 0.313493 1.74523i 0.00135711 0.00755510i
\(232\) −280.858 486.461i −1.21060 2.09681i
\(233\) −254.855 + 147.140i −1.09380 + 0.631504i −0.934585 0.355740i \(-0.884229\pi\)
−0.159212 + 0.987244i \(0.550895\pi\)
\(234\) 87.8489 236.639i 0.375423 1.01128i
\(235\) −198.647 344.067i −0.845306 1.46411i
\(236\) −595.089 + 343.575i −2.52156 + 1.45583i
\(237\) −271.448 + 321.405i −1.14535 + 1.35614i
\(238\) 11.7645 20.3767i 0.0494307 0.0856164i
\(239\) 368.056 212.497i 1.53998 0.889109i 0.541143 0.840931i \(-0.317992\pi\)
0.998839 0.0481777i \(-0.0153414\pi\)
\(240\) −90.7249 + 505.069i −0.378020 + 2.10446i
\(241\) 9.65970 0.0400817 0.0200409 0.999799i \(-0.493620\pi\)
0.0200409 + 0.999799i \(0.493620\pi\)
\(242\) 366.039 211.333i 1.51256 0.873276i
\(243\) 239.953 38.3620i 0.987460 0.157868i
\(244\) −782.455 −3.20678
\(245\) −264.350 152.623i −1.07898 0.622950i
\(246\) −171.247 475.224i −0.696126 1.93181i
\(247\) −104.482 180.968i −0.423004 0.732664i
\(248\) 111.019 64.0966i 0.447656 0.258454i
\(249\) 41.9602 233.594i 0.168515 0.938128i
\(250\) −123.508 + 213.922i −0.494032 + 0.855688i
\(251\) 123.217 + 71.1396i 0.490906 + 0.283425i 0.724950 0.688801i \(-0.241863\pi\)
−0.234044 + 0.972226i \(0.575196\pi\)
\(252\) −4.38702 25.8463i −0.0174088 0.102565i
\(253\) 37.7398 0.149169
\(254\) 277.049i 1.09075i
\(255\) 368.565 + 66.2049i 1.44535 + 0.259627i
\(256\) 239.516 + 414.855i 0.935611 + 1.62053i
\(257\) 23.2260 13.4096i 0.0903737 0.0521773i −0.454132 0.890934i \(-0.650051\pi\)
0.544506 + 0.838757i \(0.316717\pi\)
\(258\) −74.2546 + 413.379i −0.287809 + 1.60224i
\(259\) 22.8651 0.0882823
\(260\) 433.401i 1.66693i
\(261\) −100.348 + 270.307i −0.384473 + 1.03566i
\(262\) 40.5672 70.2645i 0.154837 0.268185i
\(263\) 298.676i 1.13565i −0.823149 0.567826i \(-0.807785\pi\)
0.823149 0.567826i \(-0.192215\pi\)
\(264\) −61.1854 + 72.4459i −0.231763 + 0.274416i
\(265\) −327.877 −1.23727
\(266\) −27.2570 15.7369i −0.102470 0.0591611i
\(267\) −148.538 + 53.5258i −0.556323 + 0.200471i
\(268\) −509.652 307.573i −1.90169 1.14766i
\(269\) 2.64942i 0.00984914i −0.999988 0.00492457i \(-0.998432\pi\)
0.999988 0.00492457i \(-0.00156755\pi\)
\(270\) 526.887 297.491i 1.95143 1.10182i
\(271\) 245.093 0.904400 0.452200 0.891916i \(-0.350639\pi\)
0.452200 + 0.891916i \(0.350639\pi\)
\(272\) −474.386 + 273.887i −1.74407 + 1.00694i
\(273\) 2.60534 + 7.23003i 0.00954338 + 0.0264836i
\(274\) 214.931 372.271i 0.784419 1.35865i
\(275\) 21.8223 12.5991i 0.0793537 0.0458149i
\(276\) 524.937 189.161i 1.90195 0.685367i
\(277\) −222.142 −0.801958 −0.400979 0.916087i \(-0.631330\pi\)
−0.400979 + 0.916087i \(0.631330\pi\)
\(278\) 781.221 + 451.038i 2.81015 + 1.62244i
\(279\) −61.6886 22.9010i −0.221106 0.0820825i
\(280\) −17.9444 31.0806i −0.0640871 0.111002i
\(281\) −142.102 82.0424i −0.505700 0.291966i 0.225364 0.974275i \(-0.427643\pi\)
−0.731064 + 0.682309i \(0.760976\pi\)
\(282\) −232.314 644.691i −0.823810 2.28614i
\(283\) 413.355 1.46062 0.730309 0.683117i \(-0.239376\pi\)
0.730309 + 0.683117i \(0.239376\pi\)
\(284\) 21.1919 + 12.2351i 0.0746193 + 0.0430815i
\(285\) 88.5593 493.013i 0.310734 1.72987i
\(286\) 25.2809 43.7877i 0.0883946 0.153104i
\(287\) 13.3189 + 7.68967i 0.0464073 + 0.0267933i
\(288\) −88.3666 + 238.034i −0.306829 + 0.826506i
\(289\) 55.3640 + 95.8932i 0.191571 + 0.331810i
\(290\) 717.948i 2.47568i
\(291\) −136.211 24.4674i −0.468079 0.0840803i
\(292\) 513.433 1.75833
\(293\) 470.012i 1.60414i 0.597232 + 0.802068i \(0.296267\pi\)
−0.597232 + 0.802068i \(0.703733\pi\)
\(294\) −402.238 339.717i −1.36816 1.15550i
\(295\) 482.858 1.63681
\(296\) −1058.97 611.399i −3.57762 2.06554i
\(297\) 48.6727 + 0.467313i 0.163881 + 0.00157344i
\(298\) 49.1711 85.1668i 0.165004 0.285795i
\(299\) −141.655 + 81.7848i −0.473764 + 0.273528i
\(300\) 240.384 284.624i 0.801281 0.948747i
\(301\) −6.39355 11.0740i −0.0212410 0.0367906i
\(302\) −18.5364 + 10.7020i −0.0613789 + 0.0354371i
\(303\) −382.697 323.213i −1.26303 1.06671i
\(304\) 366.366 + 634.565i 1.20515 + 2.08739i
\(305\) 476.166 + 274.914i 1.56120 + 0.901358i
\(306\) 605.515 + 224.789i 1.97881 + 0.734603i
\(307\) −271.865 + 470.884i −0.885554 + 1.53383i −0.0404776 + 0.999180i \(0.512888\pi\)
−0.845077 + 0.534645i \(0.820445\pi\)
\(308\) 5.25129i 0.0170496i
\(309\) −54.8018 + 64.8874i −0.177352 + 0.209992i
\(310\) −163.848 −0.528542
\(311\) 438.000i 1.40836i 0.710022 + 0.704180i \(0.248685\pi\)
−0.710022 + 0.704180i \(0.751315\pi\)
\(312\) 72.6628 404.517i 0.232894 1.29653i
\(313\) −196.687 −0.628392 −0.314196 0.949358i \(-0.601735\pi\)
−0.314196 + 0.949358i \(0.601735\pi\)
\(314\) −567.925 + 327.892i −1.80868 + 1.04424i
\(315\) −6.41133 + 17.2702i −0.0203534 + 0.0548262i
\(316\) −622.955 + 1078.99i −1.97138 + 3.41452i
\(317\) −242.844 140.206i −0.766069 0.442290i 0.0654013 0.997859i \(-0.479167\pi\)
−0.831471 + 0.555569i \(0.812501\pi\)
\(318\) −556.629 99.9865i −1.75041 0.314423i
\(319\) −28.8777 + 50.0176i −0.0905256 + 0.156795i
\(320\) 51.9749i 0.162422i
\(321\) 309.532 111.540i 0.964273 0.347476i
\(322\) −12.3183 + 21.3359i −0.0382555 + 0.0662604i
\(323\) 463.062 267.349i 1.43363 0.827707i
\(324\) 679.349 237.460i 2.09676 0.732900i
\(325\) −54.6062 + 94.5807i −0.168019 + 0.291018i
\(326\) 489.292i 1.50089i
\(327\) 0.722094 + 2.00387i 0.00220824 + 0.00612804i
\(328\) −411.234 712.278i −1.25376 2.17158i
\(329\) 18.0685 + 10.4318i 0.0549193 + 0.0317077i
\(330\) 114.024 41.0884i 0.345526 0.124510i
\(331\) 3.43848 + 5.95562i 0.0103882 + 0.0179928i 0.871173 0.490977i \(-0.163360\pi\)
−0.860785 + 0.508969i \(0.830027\pi\)
\(332\) 702.870i 2.11708i
\(333\) 105.035 + 618.818i 0.315420 + 1.85831i
\(334\) 604.093 1.80866
\(335\) 202.085 + 366.240i 0.603238 + 1.09325i
\(336\) −9.13565 25.3521i −0.0271894 0.0754528i
\(337\) 76.5731 132.629i 0.227220 0.393557i −0.729763 0.683700i \(-0.760370\pi\)
0.956983 + 0.290143i \(0.0937030\pi\)
\(338\) 387.487i 1.14641i
\(339\) 96.7043 + 81.6734i 0.285264 + 0.240924i
\(340\) 1108.99 3.26174
\(341\) −11.4149 6.59038i −0.0334747 0.0193266i
\(342\) 300.690 809.970i 0.879210 2.36833i
\(343\) 32.0948 0.0935709
\(344\) 683.839i 1.98790i
\(345\) −385.914 69.3211i −1.11859 0.200931i
\(346\) −175.671 304.271i −0.507720 0.879397i
\(347\) 52.4992 30.3104i 0.151295 0.0873500i −0.422442 0.906390i \(-0.638827\pi\)
0.573736 + 0.819040i \(0.305493\pi\)
\(348\) −150.970 + 840.456i −0.433822 + 2.41510i
\(349\) 255.090 0.730916 0.365458 0.930828i \(-0.380912\pi\)
0.365458 + 0.930828i \(0.380912\pi\)
\(350\) 16.4494i 0.0469982i
\(351\) −183.704 + 103.723i −0.523374 + 0.295507i
\(352\) −25.4298 + 44.0458i −0.0722439 + 0.125130i
\(353\) −343.251 198.176i −0.972383 0.561406i −0.0724210 0.997374i \(-0.523073\pi\)
−0.899962 + 0.435969i \(0.856406\pi\)
\(354\) 819.735 + 147.248i 2.31564 + 0.415955i
\(355\) −8.59759 14.8915i −0.0242186 0.0419478i
\(356\) −404.946 + 233.796i −1.13749 + 0.656730i
\(357\) −18.5003 + 6.66658i −0.0518215 + 0.0186739i
\(358\) −276.194 + 478.382i −0.771492 + 1.33626i
\(359\) 573.015i 1.59614i 0.602564 + 0.798070i \(0.294146\pi\)
−0.602564 + 0.798070i \(0.705854\pi\)
\(360\) 758.730 628.419i 2.10758 1.74561i
\(361\) −177.121 306.783i −0.490641 0.849815i
\(362\) 26.7977i 0.0740268i
\(363\) −347.685 62.4542i −0.957811 0.172050i
\(364\) 11.3799 + 19.7106i 0.0312635 + 0.0541499i
\(365\) −312.451 180.394i −0.856030 0.494229i
\(366\) 724.539 + 611.922i 1.97961 + 1.67192i
\(367\) −112.581 194.997i −0.306761 0.531326i 0.670891 0.741556i \(-0.265912\pi\)
−0.977652 + 0.210230i \(0.932579\pi\)
\(368\) 496.716 286.779i 1.34977 0.779290i
\(369\) −146.929 + 395.784i −0.398182 + 1.07259i
\(370\) 781.449 + 1353.51i 2.11202 + 3.65813i
\(371\) 14.9115 8.60914i 0.0401927 0.0232052i
\(372\) −191.806 34.4539i −0.515608 0.0926180i
\(373\) 6.33238 + 10.9680i 0.0169769 + 0.0294048i 0.874389 0.485226i \(-0.161262\pi\)
−0.857412 + 0.514630i \(0.827929\pi\)
\(374\) 112.044 + 64.6889i 0.299584 + 0.172965i
\(375\) 194.222 69.9881i 0.517927 0.186635i
\(376\) −557.881 966.279i −1.48373 2.56989i
\(377\) 250.320i 0.663978i
\(378\) −16.1509 + 27.3641i −0.0427273 + 0.0723918i
\(379\) −50.6066 + 87.6531i −0.133527 + 0.231275i −0.925034 0.379885i \(-0.875963\pi\)
0.791507 + 0.611160i \(0.209297\pi\)
\(380\) 1483.45i 3.90381i
\(381\) −149.404 + 176.899i −0.392135 + 0.464303i
\(382\) −538.754 933.149i −1.41035 2.44280i
\(383\) 245.824 + 141.926i 0.641838 + 0.370565i 0.785322 0.619087i \(-0.212497\pi\)
−0.143484 + 0.989653i \(0.545831\pi\)
\(384\) 75.7038 421.446i 0.197145 1.09752i
\(385\) −1.84503 + 3.19569i −0.00479229 + 0.00830049i
\(386\) −603.349 348.344i −1.56308 0.902445i
\(387\) 270.334 223.904i 0.698538 0.578564i
\(388\) −409.850 −1.05632
\(389\) 339.820 + 196.195i 0.873573 + 0.504358i 0.868534 0.495629i \(-0.165063\pi\)
0.00503929 + 0.999987i \(0.498396\pi\)
\(390\) −338.943 + 401.321i −0.869085 + 1.02903i
\(391\) −209.272 362.469i −0.535222 0.927031i
\(392\) −742.403 428.627i −1.89388 1.09343i
\(393\) −63.7940 + 22.9882i −0.162326 + 0.0584941i
\(394\) −676.784 −1.71773
\(395\) 758.202 437.748i 1.91950 1.10822i
\(396\) 142.120 24.1227i 0.358889 0.0609160i
\(397\) 713.608 1.79750 0.898751 0.438459i \(-0.144476\pi\)
0.898751 + 0.438459i \(0.144476\pi\)
\(398\) −557.123 + 321.655i −1.39981 + 0.808178i
\(399\) 8.91758 + 24.7470i 0.0223498 + 0.0620225i
\(400\) 191.477 331.648i 0.478693 0.829120i
\(401\) 96.6915i 0.241126i −0.992706 0.120563i \(-0.961530\pi\)
0.992706 0.120563i \(-0.0384700\pi\)
\(402\) 231.389 + 683.382i 0.575595 + 1.69995i
\(403\) 57.1272 0.141755
\(404\) −1284.75 741.752i −3.18008 1.83602i
\(405\) −496.851 94.1814i −1.22679 0.232547i
\(406\) −18.8513 32.6514i −0.0464318 0.0804223i
\(407\) 125.727i 0.308913i
\(408\) 1035.08 + 185.930i 2.53696 + 0.455711i
\(409\) −208.542 361.205i −0.509883 0.883143i −0.999934 0.0114496i \(-0.996355\pi\)
0.490052 0.871693i \(-0.336978\pi\)
\(410\) 1051.22i 2.56396i
\(411\) −337.990 + 121.795i −0.822359 + 0.296337i
\(412\) −125.766 + 217.833i −0.305258 + 0.528722i
\(413\) −21.9598 + 12.6785i −0.0531714 + 0.0306985i
\(414\) −634.016 235.370i −1.53144 0.568525i
\(415\) −246.952 + 427.734i −0.595065 + 1.03068i
\(416\) 220.433i 0.529887i
\(417\) −255.589 709.280i −0.612924 1.70091i
\(418\) 86.5315 149.877i 0.207013 0.358557i
\(419\) 13.0211 + 7.51772i 0.0310765 + 0.0179420i 0.515458 0.856915i \(-0.327622\pi\)
−0.484381 + 0.874857i \(0.660955\pi\)
\(420\) −9.64566 + 53.6978i −0.0229659 + 0.127852i
\(421\) 173.482 300.479i 0.412071 0.713728i −0.583045 0.812440i \(-0.698139\pi\)
0.995116 + 0.0987119i \(0.0314722\pi\)
\(422\) −8.63951 + 4.98802i −0.0204728 + 0.0118200i
\(423\) −199.325 + 536.923i −0.471217 + 1.26932i
\(424\) −920.813 −2.17173
\(425\) −242.014 139.727i −0.569445 0.328769i
\(426\) −10.0547 27.9027i −0.0236027 0.0654993i
\(427\) −28.8739 −0.0676205
\(428\) 843.848 487.196i 1.97161 1.13831i
\(429\) −39.7554 + 14.3259i −0.0926700 + 0.0333937i
\(430\) 437.018 756.937i 1.01632 1.76032i
\(431\) −308.725 + 178.242i −0.716298 + 0.413555i −0.813389 0.581721i \(-0.802380\pi\)
0.0970905 + 0.995276i \(0.469046\pi\)
\(432\) 644.160 363.705i 1.49111 0.841911i
\(433\) −336.614 583.032i −0.777399 1.34649i −0.933436 0.358743i \(-0.883205\pi\)
0.156038 0.987751i \(-0.450128\pi\)
\(434\) 7.45161 4.30219i 0.0171696 0.00991288i
\(435\) 387.166 458.419i 0.890036 1.05384i
\(436\) 3.15404 + 5.46296i 0.00723405 + 0.0125297i
\(437\) −484.859 + 279.934i −1.10952 + 0.640580i
\(438\) −475.429 401.532i −1.08545 0.916740i
\(439\) −196.308 + 340.015i −0.447171 + 0.774522i −0.998201 0.0599632i \(-0.980902\pi\)
0.551030 + 0.834485i \(0.314235\pi\)
\(440\) 170.901 98.6700i 0.388412 0.224250i
\(441\) 73.6356 + 433.828i 0.166974 + 0.983736i
\(442\) −560.741 −1.26865
\(443\) 400.981 231.507i 0.905150 0.522589i 0.0262825 0.999655i \(-0.491633\pi\)
0.878867 + 0.477066i \(0.158300\pi\)
\(444\) 630.177 + 1748.79i 1.41932 + 3.93872i
\(445\) 328.575 0.738371
\(446\) 383.171 + 221.224i 0.859128 + 0.496018i
\(447\) −77.3240 + 27.8637i −0.172984 + 0.0623349i
\(448\) 1.36472 + 2.36376i 0.00304624 + 0.00527625i
\(449\) 454.841 262.603i 1.01301 0.584861i 0.100938 0.994893i \(-0.467816\pi\)
0.912071 + 0.410032i \(0.134482\pi\)
\(450\) −445.183 + 75.5630i −0.989295 + 0.167918i
\(451\) −42.2828 + 73.2360i −0.0937535 + 0.162386i
\(452\) 324.646 + 187.435i 0.718244 + 0.414678i
\(453\) 17.6070 + 3.16272i 0.0388675 + 0.00698172i
\(454\) 1370.20 3.01806
\(455\) 15.9932i 0.0351500i
\(456\) 248.711 1384.58i 0.545418 3.03636i
\(457\) 4.44168 + 7.69322i 0.00971922 + 0.0168342i 0.870844 0.491559i \(-0.163573\pi\)
−0.861125 + 0.508393i \(0.830240\pi\)
\(458\) 167.345 96.6169i 0.365383 0.210954i
\(459\) −265.407 470.064i −0.578230 1.02411i
\(460\) −1161.19 −2.52433
\(461\) 752.593i 1.63252i −0.577683 0.816261i \(-0.696043\pi\)
0.577683 0.816261i \(-0.303957\pi\)
\(462\) −4.10679 + 4.86259i −0.00888916 + 0.0105251i
\(463\) −365.453 + 632.984i −0.789316 + 1.36714i 0.137071 + 0.990561i \(0.456231\pi\)
−0.926387 + 0.376574i \(0.877102\pi\)
\(464\) 877.747i 1.89170i
\(465\) 104.619 + 88.3578i 0.224987 + 0.190017i
\(466\) 1056.33 2.26679
\(467\) −65.3596 37.7354i −0.139956 0.0808038i 0.428387 0.903595i \(-0.359082\pi\)
−0.568343 + 0.822792i \(0.692415\pi\)
\(468\) −481.168 + 398.528i −1.02814 + 0.851556i
\(469\) −18.8070 11.3500i −0.0401002 0.0242004i
\(470\) 1426.09i 3.03424i
\(471\) 539.448 + 96.9004i 1.14533 + 0.205733i
\(472\) 1356.06 2.87301
\(473\) 60.8918 35.1559i 0.128735 0.0743254i
\(474\) 1420.67 511.939i 2.99720 1.08004i
\(475\) −186.906 + 323.732i −0.393487 + 0.681540i
\(476\) −50.4356 + 29.1190i −0.105957 + 0.0611744i
\(477\) 301.495 + 364.014i 0.632065 + 0.763133i
\(478\) −1525.52 −3.19147
\(479\) −25.6192 14.7913i −0.0534848 0.0308795i 0.473019 0.881052i \(-0.343164\pi\)
−0.526504 + 0.850173i \(0.676497\pi\)
\(480\) 340.940 403.686i 0.710292 0.841013i
\(481\) −272.460 471.914i −0.566445 0.981111i
\(482\) −30.0283 17.3368i −0.0622993 0.0359685i
\(483\) 19.3711 6.98037i 0.0401058 0.0144521i
\(484\) −1046.16 −2.16150
\(485\) 249.416 + 144.000i 0.514259 + 0.296908i
\(486\) −814.771 311.405i −1.67648 0.640750i
\(487\) −274.762 + 475.903i −0.564194 + 0.977213i 0.432930 + 0.901427i \(0.357480\pi\)
−0.997124 + 0.0757851i \(0.975854\pi\)
\(488\) 1337.27 + 772.071i 2.74030 + 1.58211i
\(489\) 263.859 312.419i 0.539589 0.638893i
\(490\) 547.841 + 948.889i 1.11804 + 1.93651i
\(491\) 446.874i 0.910130i 0.890458 + 0.455065i \(0.150384\pi\)
−0.890458 + 0.455065i \(0.849616\pi\)
\(492\) −221.051 + 1230.60i −0.449290 + 2.50122i
\(493\) 640.520 1.29923
\(494\) 750.079i 1.51838i
\(495\) −94.9631 35.2537i −0.191845 0.0712196i
\(496\) −200.317 −0.403865
\(497\) 0.782017 + 0.451498i 0.00157347 + 0.000908446i
\(498\) −549.682 + 650.844i −1.10378 + 1.30692i
\(499\) 188.341 326.216i 0.377436 0.653739i −0.613252 0.789887i \(-0.710139\pi\)
0.990688 + 0.136148i \(0.0434724\pi\)
\(500\) 529.491 305.702i 1.05898 0.611404i
\(501\) −385.721 325.768i −0.769903 0.650235i
\(502\) −255.357 442.290i −0.508678 0.881057i
\(503\) 186.865 107.887i 0.371501 0.214486i −0.302613 0.953114i \(-0.597859\pi\)
0.674114 + 0.738627i \(0.264526\pi\)
\(504\) −18.0056 + 48.5019i −0.0357255 + 0.0962339i
\(505\) 521.226 + 902.791i 1.03213 + 1.78770i
\(506\) −117.318 67.7338i −0.231855 0.133861i
\(507\) −208.959 + 247.415i −0.412148 + 0.487998i
\(508\) −342.871 + 593.869i −0.674942 + 1.16903i
\(509\) 130.472i 0.256331i −0.991753 0.128165i \(-0.959091\pi\)
0.991753 0.128165i \(-0.0409088\pi\)
\(510\) −1026.90 867.290i −2.01354 1.70057i
\(511\) 18.9465 0.0370774
\(512\) 1148.57i 2.24331i
\(513\) −628.785 + 355.024i −1.22570 + 0.692054i
\(514\) −96.2676 −0.187291
\(515\) 153.071 88.3755i 0.297225 0.171603i
\(516\) 670.757 794.202i 1.29992 1.53915i
\(517\) −57.3610 + 99.3522i −0.110950 + 0.192171i
\(518\) −71.0788 41.0374i −0.137218 0.0792227i
\(519\) −51.9153 + 289.015i −0.100030 + 0.556869i
\(520\) −427.649 + 740.710i −0.822402 + 1.42444i
\(521\) 116.822i 0.224226i 0.993695 + 0.112113i \(0.0357619\pi\)
−0.993695 + 0.112113i \(0.964238\pi\)
\(522\) 797.077 660.179i 1.52697 1.26471i
\(523\) −5.79925 + 10.0446i −0.0110884 + 0.0192057i −0.871516 0.490366i \(-0.836863\pi\)
0.860428 + 0.509572i \(0.170196\pi\)
\(524\) −173.916 + 100.410i −0.331900 + 0.191623i
\(525\) 8.87059 10.5031i 0.0168964 0.0200059i
\(526\) −536.052 + 928.469i −1.01911 + 1.76515i
\(527\) 146.178i 0.277377i
\(528\) 139.403 50.2338i 0.264020 0.0951397i
\(529\) −45.3778 78.5967i −0.0857804 0.148576i
\(530\) 1019.24 + 588.460i 1.92310 + 1.11030i
\(531\) −444.005 536.076i −0.836168 1.00956i
\(532\) 38.9512 + 67.4655i 0.0732166 + 0.126815i
\(533\) 366.519i 0.687653i
\(534\) 557.814 + 100.199i 1.04459 + 0.187639i
\(535\) −684.702 −1.27982
\(536\) 567.536 + 1028.55i 1.05884 + 1.91894i
\(537\) 434.329 156.511i 0.808806 0.291454i
\(538\) −4.75506 + 8.23601i −0.00883841 + 0.0153086i
\(539\) 88.1422i 0.163529i
\(540\) −1497.58 14.3784i −2.77329 0.0266267i
\(541\) 51.2806 0.0947886 0.0473943 0.998876i \(-0.484908\pi\)
0.0473943 + 0.998876i \(0.484908\pi\)
\(542\) −761.897 439.882i −1.40571 0.811590i
\(543\) −14.4511 + 17.1107i −0.0266135 + 0.0315113i
\(544\) 564.046 1.03685
\(545\) 4.43267i 0.00813334i
\(546\) 4.87715 27.1513i 0.00893252 0.0497277i
\(547\) 306.576 + 531.006i 0.560469 + 0.970760i 0.997455 + 0.0712924i \(0.0227124\pi\)
−0.436987 + 0.899468i \(0.643954\pi\)
\(548\) −921.430 + 531.988i −1.68144 + 0.970781i
\(549\) −132.638 781.440i −0.241598 1.42339i
\(550\) −90.4493 −0.164453
\(551\) 856.796i 1.55498i
\(552\) −1083.80 194.682i −1.96341 0.352685i
\(553\) −22.9881 + 39.8165i −0.0415698 + 0.0720010i
\(554\) 690.554 + 398.692i 1.24649 + 0.719660i
\(555\) 230.938 1285.64i 0.416105 2.31647i
\(556\) −1116.39 1933.65i −2.00790 3.47778i
\(557\) −631.412 + 364.546i −1.13360 + 0.654481i −0.944837 0.327542i \(-0.893780\pi\)
−0.188759 + 0.982024i \(0.560446\pi\)
\(558\) 150.664 + 181.906i 0.270007 + 0.325997i
\(559\) −152.371 + 263.914i −0.272577 + 0.472117i
\(560\) 56.0804i 0.100144i
\(561\) −36.6572 101.727i −0.0653426 0.181331i
\(562\) 294.493 + 510.076i 0.524008 + 0.907609i
\(563\) 417.193i 0.741019i −0.928829 0.370509i \(-0.879183\pi\)
0.928829 0.370509i \(-0.120817\pi\)
\(564\) −299.878 + 1669.43i −0.531699 + 2.95999i
\(565\) −131.710 228.128i −0.233114 0.403766i
\(566\) −1284.96 741.871i −2.27025 1.31073i
\(567\) 25.0691 8.76266i 0.0442137 0.0154544i
\(568\) −24.1455 41.8213i −0.0425097 0.0736290i
\(569\) −726.177 + 419.258i −1.27623 + 0.736834i −0.976154 0.217081i \(-0.930347\pi\)
−0.300079 + 0.953914i \(0.597013\pi\)
\(570\) −1160.14 + 1373.64i −2.03533 + 2.40990i
\(571\) 556.552 + 963.976i 0.974697 + 1.68822i 0.680932 + 0.732346i \(0.261575\pi\)
0.293764 + 0.955878i \(0.405092\pi\)
\(572\) −108.382 + 62.5741i −0.189478 + 0.109395i
\(573\) −159.215 + 886.359i −0.277863 + 1.54687i
\(574\) −27.6022 47.8084i −0.0480874 0.0832899i
\(575\) 253.406 + 146.304i 0.440706 + 0.254442i
\(576\) −57.7034 + 47.7929i −0.100179 + 0.0829737i
\(577\) 298.919 + 517.743i 0.518057 + 0.897302i 0.999780 + 0.0209780i \(0.00667799\pi\)
−0.481723 + 0.876324i \(0.659989\pi\)
\(578\) 397.460i 0.687647i
\(579\) 197.396 + 547.788i 0.340925 + 0.946093i
\(580\) 888.518 1538.96i 1.53193 2.65338i
\(581\) 25.9371i 0.0446422i
\(582\) 379.514 + 320.525i 0.652085 + 0.550730i
\(583\) 47.3387 + 81.9930i 0.0811985 + 0.140640i
\(584\) −877.490 506.619i −1.50255 0.867498i
\(585\) 432.839 73.4678i 0.739895 0.125586i
\(586\) 843.558 1461.08i 1.43952 2.49332i
\(587\) −56.2503 32.4761i −0.0958267 0.0553256i 0.451321 0.892362i \(-0.350953\pi\)
−0.547148 + 0.837036i \(0.684286\pi\)
\(588\) 441.791 + 1226.00i 0.751344 + 2.08504i
\(589\) 195.535 0.331978
\(590\) −1501.02 866.613i −2.54410 1.46883i
\(591\) 432.135 + 364.968i 0.731193 + 0.617542i
\(592\) 955.382 + 1654.77i 1.61382 + 2.79522i
\(593\) 966.846 + 558.209i 1.63043 + 0.941330i 0.983960 + 0.178392i \(0.0570895\pi\)
0.646472 + 0.762938i \(0.276244\pi\)
\(594\) −150.466 88.8084i −0.253309 0.149509i
\(595\) 40.9236 0.0687792
\(596\) −210.801 + 121.706i −0.353693 + 0.204205i
\(597\) 529.188 + 95.0573i 0.886412 + 0.159225i
\(598\) 587.136 0.981832
\(599\) −346.719 + 200.178i −0.578830 + 0.334188i −0.760668 0.649141i \(-0.775129\pi\)
0.181838 + 0.983328i \(0.441795\pi\)
\(600\) −691.679 + 249.247i −1.15280 + 0.415411i
\(601\) −163.982 + 284.025i −0.272849 + 0.472588i −0.969590 0.244735i \(-0.921299\pi\)
0.696741 + 0.717322i \(0.254632\pi\)
\(602\) 45.8995i 0.0762450i
\(603\) 220.780 561.128i 0.366137 0.930561i
\(604\) 52.9784 0.0877125
\(605\) 636.646 + 367.568i 1.05231 + 0.607550i
\(606\) 609.566 + 1691.59i 1.00588 + 2.79141i
\(607\) 101.026 + 174.983i 0.166435 + 0.288274i 0.937164 0.348889i \(-0.113441\pi\)
−0.770729 + 0.637163i \(0.780108\pi\)
\(608\) 754.499i 1.24095i
\(609\) −5.57105 + 31.0142i −0.00914786 + 0.0509265i
\(610\) −986.809 1709.20i −1.61772 2.80197i
\(611\) 497.221i 0.813782i
\(612\) −1019.76 1231.22i −1.66627 2.01179i
\(613\) −19.0228 + 32.9484i −0.0310323 + 0.0537495i −0.881124 0.472884i \(-0.843213\pi\)
0.850092 + 0.526634i \(0.176546\pi\)
\(614\) 1690.25 975.864i 2.75284 1.58936i
\(615\) 566.890 671.219i 0.921772 1.09141i
\(616\) −5.18160 + 8.97479i −0.00841168 + 0.0145695i
\(617\) 139.810i 0.226596i 0.993561 + 0.113298i \(0.0361414\pi\)
−0.993561 + 0.113298i \(0.963859\pi\)
\(618\) 286.815 103.354i 0.464101 0.167239i
\(619\) 462.300 800.728i 0.746850 1.29358i −0.202475 0.979287i \(-0.564899\pi\)
0.949325 0.314295i \(-0.101768\pi\)
\(620\) 351.216 + 202.775i 0.566478 + 0.327056i
\(621\) 277.900 + 492.191i 0.447505 + 0.792577i
\(622\) 786.104 1361.57i 1.26383 2.18902i
\(623\) −14.9432 + 8.62747i −0.0239859 + 0.0138483i
\(624\) −414.384 + 490.646i −0.664077 + 0.786292i
\(625\) −779.067 −1.24651
\(626\) 611.422 + 353.005i 0.976713 + 0.563905i
\(627\) −136.075 + 49.0347i −0.217026 + 0.0782053i
\(628\) 1623.17 2.58466
\(629\) 1207.54 697.173i 1.91978 1.10838i
\(630\) 50.9262 42.1797i 0.0808353 0.0669519i
\(631\) −257.740 + 446.419i −0.408463 + 0.707479i −0.994718 0.102648i \(-0.967268\pi\)
0.586255 + 0.810127i \(0.300602\pi\)
\(632\) 2129.34 1229.37i 3.36921 1.94521i
\(633\) 8.20631 + 1.47409i 0.0129642 + 0.00232873i
\(634\) 503.272 + 871.692i 0.793804 + 1.37491i
\(635\) 417.310 240.934i 0.657181 0.379424i
\(636\) 1069.42 + 903.199i 1.68148 + 1.42012i
\(637\) −191.010 330.839i −0.299859 0.519371i
\(638\) 179.539 103.657i 0.281409 0.162472i
\(639\) −8.62693 + 23.2384i −0.0135007 + 0.0363669i
\(640\) −445.547 + 771.710i −0.696167 + 1.20580i
\(641\) −151.797 + 87.6402i −0.236813 + 0.136724i −0.613711 0.789531i \(-0.710324\pi\)
0.376898 + 0.926255i \(0.376991\pi\)
\(642\) −1162.40 208.800i −1.81059 0.325234i
\(643\) 887.550 1.38033 0.690164 0.723653i \(-0.257539\pi\)
0.690164 + 0.723653i \(0.257539\pi\)
\(644\) 52.8096 30.4896i 0.0820025 0.0473442i
\(645\) −687.233 + 247.645i −1.06548 + 0.383945i
\(646\) −1919.31 −2.97107
\(647\) 666.232 + 384.649i 1.02973 + 0.594512i 0.916906 0.399103i \(-0.130678\pi\)
0.112819 + 0.993616i \(0.464012\pi\)
\(648\) −1395.36 264.500i −2.15333 0.408179i
\(649\) −69.7147 120.749i −0.107419 0.186054i
\(650\) 339.499 196.010i 0.522306 0.301554i
\(651\) −7.07798 1.27141i −0.0108725 0.00195301i
\(652\) 605.537 1048.82i 0.928738 1.60862i
\(653\) −360.543 208.159i −0.552133 0.318774i 0.197849 0.980233i \(-0.436604\pi\)
−0.749982 + 0.661458i \(0.769938\pi\)
\(654\) 1.35175 7.52523i 0.00206689 0.0115065i
\(655\) 141.116 0.215444
\(656\) 1285.20i 1.95915i
\(657\) 87.0343 + 512.766i 0.132472 + 0.780466i
\(658\) −37.4452 64.8570i −0.0569076 0.0985669i
\(659\) −573.877 + 331.328i −0.870831 + 0.502774i −0.867624 0.497221i \(-0.834354\pi\)
−0.00320640 + 0.999995i \(0.501021\pi\)
\(660\) −295.265 53.0381i −0.447372 0.0803608i
\(661\) −274.970 −0.415991 −0.207995 0.978130i \(-0.566694\pi\)
−0.207995 + 0.978130i \(0.566694\pi\)
\(662\) 24.6849i 0.0372884i
\(663\) 358.040 + 302.389i 0.540031 + 0.456092i
\(664\) −693.542 + 1201.25i −1.04449 + 1.80911i
\(665\) 54.7418i 0.0823184i
\(666\) 784.116 2112.18i 1.17735 3.17144i
\(667\) −670.670 −1.00550
\(668\) −1294.90 747.614i −1.93848 1.11918i
\(669\) −125.361 347.886i −0.187385 0.520008i
\(670\) 29.1082 1501.19i 0.0434451 2.24058i
\(671\) 158.768i 0.236614i
\(672\) −4.90589 + 27.3113i −0.00730044 + 0.0406418i
\(673\) 187.571 0.278709 0.139355 0.990243i \(-0.455497\pi\)
0.139355 + 0.990243i \(0.455497\pi\)
\(674\) −476.072 + 274.860i −0.706339 + 0.407805i
\(675\) 325.003 + 191.825i 0.481487 + 0.284185i
\(676\) −479.545 + 830.597i −0.709387 + 1.22869i
\(677\) 199.802 115.356i 0.295129 0.170393i −0.345124 0.938557i \(-0.612163\pi\)
0.640252 + 0.768165i \(0.278830\pi\)
\(678\) −154.032 427.452i −0.227186 0.630460i
\(679\) −15.1242 −0.0222742
\(680\) −1895.34 1094.27i −2.78726 1.60922i
\(681\) −874.890 738.904i −1.28471 1.08503i
\(682\) 23.6563 + 40.9738i 0.0346866 + 0.0600789i
\(683\) −617.809 356.692i −0.904553 0.522244i −0.0258782 0.999665i \(-0.508238\pi\)
−0.878674 + 0.477421i \(0.841572\pi\)
\(684\) −1646.95 + 1364.08i −2.40782 + 1.99428i
\(685\) 747.652 1.09146
\(686\) −99.7703 57.6024i −0.145438 0.0839685i
\(687\) −158.954 28.5528i −0.231375 0.0415615i
\(688\) 534.288 925.415i 0.776582 1.34508i
\(689\) −355.369 205.172i −0.515775 0.297783i
\(690\) 1075.24 + 908.114i 1.55832 + 1.31611i
\(691\) −43.4158 75.1983i −0.0628303 0.108825i 0.832899 0.553425i \(-0.186679\pi\)
−0.895730 + 0.444599i \(0.853346\pi\)
\(692\) 869.628i 1.25669i
\(693\) 5.24447 0.890170i 0.00756778 0.00128452i
\(694\) −217.600 −0.313544
\(695\) 1568.97i 2.25751i
\(696\) 1087.32 1287.43i 1.56224 1.84975i
\(697\) 937.852 1.34556
\(698\) −792.975 457.824i −1.13607 0.655908i
\(699\) −674.477 569.642i −0.964917 0.814938i
\(700\) 20.3574 35.2600i 0.0290820 0.0503715i
\(701\) −533.497 + 308.015i −0.761052 + 0.439394i −0.829673 0.558249i \(-0.811473\pi\)
0.0686213 + 0.997643i \(0.478140\pi\)
\(702\) 757.223 + 7.27020i 1.07867 + 0.0103564i
\(703\) −932.578 1615.27i −1.32657 2.29768i
\(704\) −12.9975 + 7.50411i −0.0184624 + 0.0106592i
\(705\) 769.045 910.578i 1.09084 1.29160i
\(706\) 711.356 + 1232.11i 1.00759 + 1.74519i
\(707\) −47.4095 27.3719i −0.0670573 0.0387156i
\(708\) −1574.91 1330.12i −2.22445 1.87870i
\(709\) 652.791 1130.67i 0.920720 1.59473i 0.122417 0.992479i \(-0.460935\pi\)
0.798303 0.602256i \(-0.205731\pi\)
\(710\) 61.7224i 0.0869329i
\(711\) −1183.19 439.242i −1.66412 0.617781i
\(712\) 922.773 1.29603
\(713\) 153.058i 0.214668i
\(714\) 69.4750 + 12.4797i 0.0973040 + 0.0174786i
\(715\) 87.9413 0.122995
\(716\) 1184.07 683.624i 1.65373 0.954782i
\(717\) 974.065 + 822.664i 1.35853 + 1.14737i
\(718\) 1028.42 1781.28i 1.43234 2.48089i
\(719\) −320.335 184.945i −0.445528 0.257226i 0.260411 0.965498i \(-0.416142\pi\)
−0.705940 + 0.708272i \(0.749475\pi\)
\(720\) −1517.75 + 257.615i −2.10799 + 0.357799i
\(721\) −4.64099 + 8.03843i −0.00643688 + 0.0111490i
\(722\) 1271.56i 1.76116i
\(723\) 9.82424 + 27.2630i 0.0135882 + 0.0377082i
\(724\) −33.1643 + 57.4422i −0.0458070 + 0.0793401i
\(725\) −387.801 + 223.897i −0.534898 + 0.308823i
\(726\) 968.728 + 818.157i 1.33434 + 1.12694i
\(727\) 292.373 506.405i 0.402164 0.696568i −0.591823 0.806068i \(-0.701592\pi\)
0.993987 + 0.109500i \(0.0349249\pi\)
\(728\) 44.9155i 0.0616971i
\(729\) 352.311 + 638.215i 0.483280 + 0.875466i
\(730\) 647.526 + 1121.55i 0.887022 + 1.53637i
\(731\) −675.305 389.887i −0.923809 0.533362i
\(732\) −795.783 2208.36i −1.08714 3.01689i
\(733\) 523.912 + 907.443i 0.714751 + 1.23798i 0.963056 + 0.269303i \(0.0867932\pi\)
−0.248305 + 0.968682i \(0.579874\pi\)
\(734\) 808.225i 1.10112i
\(735\) 161.901 901.310i 0.220274 1.22627i
\(736\) −590.596 −0.802440
\(737\) 62.4095 103.413i 0.0846805 0.140316i
\(738\) 1167.08 966.637i 1.58141 1.30981i
\(739\) 354.949 614.790i 0.480310 0.831921i −0.519435 0.854510i \(-0.673858\pi\)
0.999745 + 0.0225888i \(0.00719085\pi\)
\(740\) 3868.42i 5.22760i
\(741\) 404.493 478.935i 0.545874 0.646336i
\(742\) −61.8053 −0.0832956
\(743\) −863.539 498.564i −1.16223 0.671015i −0.210394 0.977617i \(-0.567475\pi\)
−0.951838 + 0.306601i \(0.900808\pi\)
\(744\) 293.813 + 248.145i 0.394909 + 0.333528i
\(745\) 171.045 0.229591
\(746\) 45.4604i 0.0609388i
\(747\) 701.958 119.147i 0.939703 0.159500i
\(748\) −160.115 277.328i −0.214058 0.370759i
\(749\) 31.1394 17.9784i 0.0415747 0.0240031i
\(750\) −729.374 131.016i −0.972499 0.174689i
\(751\) 51.1587 0.0681207 0.0340604 0.999420i \(-0.489156\pi\)
0.0340604 + 0.999420i \(0.489156\pi\)
\(752\) 1743.51i 2.31850i
\(753\) −75.4644 + 420.113i −0.100218 + 0.557919i
\(754\) −449.263 + 778.146i −0.595840 + 1.03202i
\(755\) −32.2401 18.6139i −0.0427022 0.0246541i
\(756\) 68.4856 38.6683i 0.0905894 0.0511485i
\(757\) −537.695 931.314i −0.710297 1.23027i −0.964746 0.263184i \(-0.915227\pi\)
0.254449 0.967086i \(-0.418106\pi\)
\(758\) 314.632 181.653i 0.415082 0.239648i
\(759\) 38.3827 + 106.515i 0.0505700 + 0.140336i
\(760\) −1463.76 + 2535.31i −1.92600 + 3.33593i
\(761\) 178.624i 0.234722i 0.993089 + 0.117361i \(0.0374435\pi\)
−0.993089 + 0.117361i \(0.962556\pi\)
\(762\) 781.929 281.768i 1.02615 0.369775i
\(763\) 0.116390 + 0.201593i 0.000152542 + 0.000264211i
\(764\) 2667.00i 3.49084i
\(765\) 187.990 + 1107.55i 0.245739 + 1.44778i
\(766\) −509.447 882.388i −0.665075 1.15194i
\(767\) 523.344 + 302.153i 0.682326 + 0.393941i
\(768\) −927.268 + 1097.92i −1.20738 + 1.42958i
\(769\) −579.131 1003.08i −0.753096 1.30440i −0.946315 0.323245i \(-0.895226\pi\)
0.193220 0.981156i \(-0.438107\pi\)
\(770\) 11.4710 6.62277i 0.0148974 0.00860100i
\(771\) 61.4681 + 51.9140i 0.0797251 + 0.0673333i
\(772\) 862.206 + 1493.38i 1.11685 + 1.93444i
\(773\) −340.404 + 196.532i −0.440367 + 0.254246i −0.703753 0.710444i \(-0.748494\pi\)
0.263386 + 0.964690i \(0.415161\pi\)
\(774\) −1242.22 + 210.847i −1.60493 + 0.272413i
\(775\) −51.0971 88.5028i −0.0659317 0.114197i
\(776\) 700.461 + 404.411i 0.902655 + 0.521148i
\(777\) 23.2546 + 64.5333i 0.0299287 + 0.0830545i
\(778\) −704.246 1219.79i −0.905200 1.56785i
\(779\) 1254.52i 1.61043i
\(780\) 1223.21 440.783i 1.56822 0.565107i
\(781\) −2.48263 + 4.30004i −0.00317878 + 0.00550581i
\(782\) 1502.37i 1.92119i
\(783\) −864.957 8.30456i −1.10467 0.0106061i
\(784\) 669.779 + 1160.09i 0.854309 + 1.47971i
\(785\) −987.783 570.297i −1.25832 0.726493i
\(786\) 239.569 + 43.0334i 0.304795 + 0.0547499i
\(787\) −393.633 + 681.792i −0.500169 + 0.866318i 0.499831 + 0.866123i \(0.333395\pi\)
−1.00000 0.000194969i \(0.999938\pi\)
\(788\) 1450.72 + 837.574i 1.84102 + 1.06291i
\(789\) 842.968 303.764i 1.06840 0.384999i
\(790\) −3142.61 −3.97798
\(791\) 11.9800 + 6.91666i 0.0151454 + 0.00874419i
\(792\) −266.695 99.0067i −0.336736 0.125008i
\(793\) 344.061 + 595.931i 0.433872 + 0.751489i
\(794\) −2218.33 1280.75i −2.79387 1.61304i
\(795\) −333.462 925.383i −0.419449 1.16400i
\(796\) 1592.29 2.00037
\(797\) −227.216 + 131.183i −0.285089 + 0.164596i −0.635725 0.771916i \(-0.719299\pi\)
0.350636 + 0.936512i \(0.385965\pi\)
\(798\) 16.6936 92.9337i 0.0209192 0.116458i
\(799\) 1272.29 1.59236
\(800\) −341.500 + 197.165i −0.426875 + 0.246456i
\(801\) −302.137 364.789i −0.377199 0.455417i
\(802\) −173.538 + 300.576i −0.216381 + 0.374783i
\(803\) 104.180i 0.129739i
\(804\) 349.745 1751.23i 0.435006 2.17814i
\(805\) −42.8499 −0.0532297
\(806\) −177.586 102.529i −0.220330 0.127208i
\(807\) 7.47758 2.69455i 0.00926590 0.00333897i
\(808\) 1463.82 + 2535.40i 1.81165 + 3.13788i
\(809\) 745.431i 0.921423i 0.887550 + 0.460711i \(0.152406\pi\)
−0.887550 + 0.460711i \(0.847594\pi\)
\(810\) 1375.48 + 1184.50i 1.69813 + 1.46235i
\(811\) 238.337 + 412.811i 0.293880 + 0.509015i 0.974724 0.223414i \(-0.0717200\pi\)
−0.680844 + 0.732429i \(0.738387\pi\)
\(812\) 93.3200i 0.114926i
\(813\) 249.267 + 691.736i 0.306602 + 0.850844i
\(814\) 225.650 390.838i 0.277212 0.480145i
\(815\) −737.003 + 425.509i −0.904298 + 0.522097i
\(816\) −1255.47 1060.33i −1.53857 1.29942i
\(817\) −521.535 + 903.325i −0.638354 + 1.10566i
\(818\) 1497.13i 1.83023i
\(819\) −17.7559 + 14.7064i −0.0216800 + 0.0179565i
\(820\) 1300.97 2253.35i 1.58655 2.74799i
\(821\) −37.5104 21.6566i −0.0456887 0.0263784i 0.476982 0.878913i \(-0.341731\pi\)
−0.522670 + 0.852535i \(0.675064\pi\)
\(822\) 1269.27 + 227.997i 1.54412 + 0.277369i
\(823\) −527.142 + 913.037i −0.640513 + 1.10940i 0.344805 + 0.938674i \(0.387945\pi\)
−0.985318 + 0.170727i \(0.945388\pi\)
\(824\) 429.885 248.194i 0.521705 0.301207i
\(825\) 57.7530 + 48.7763i 0.0700036 + 0.0591228i
\(826\) 91.0193 0.110193
\(827\) 87.2550 + 50.3767i 0.105508 + 0.0609150i 0.551825 0.833960i \(-0.313931\pi\)
−0.446318 + 0.894875i \(0.647265\pi\)
\(828\) 1067.76 + 1289.17i 1.28956 + 1.55697i
\(829\) −496.172 −0.598519 −0.299260 0.954172i \(-0.596740\pi\)
−0.299260 + 0.954172i \(0.596740\pi\)
\(830\) 1535.36 886.439i 1.84983 1.06800i
\(831\) −225.926 626.963i −0.271873 0.754468i
\(832\) 32.5238 56.3329i 0.0390911 0.0677079i
\(833\) 846.555 488.759i 1.01627 0.586745i
\(834\) −478.458 + 2663.60i −0.573691 + 3.19376i
\(835\) 525.345 + 909.925i 0.629156 + 1.08973i
\(836\) −370.969 + 214.179i −0.443743 + 0.256195i
\(837\) 1.89524 197.398i 0.00226433 0.235840i
\(838\) −26.9850 46.7393i −0.0322016 0.0557749i
\(839\) 861.500 497.387i 1.02682 0.592833i 0.110746 0.993849i \(-0.464676\pi\)
0.916071 + 0.401015i \(0.131343\pi\)
\(840\) 69.4702 82.2553i 0.0827026 0.0979230i
\(841\) 92.6816 160.529i 0.110204 0.190879i
\(842\) −1078.58 + 622.716i −1.28097 + 0.739568i
\(843\) 87.0301 484.500i 0.103239 0.574733i
\(844\) 24.6923 0.0292563
\(845\) 583.658 336.975i 0.690719 0.398787i
\(846\) 1583.27 1311.34i 1.87148 1.55005i
\(847\) −38.6052 −0.0455788
\(848\) 1246.10 + 719.438i 1.46946 + 0.848394i
\(849\) 420.395 + 1166.63i 0.495165 + 1.37412i
\(850\) 501.552 + 868.713i 0.590061 + 1.02202i
\(851\) −1264.38 + 729.989i −1.48576 + 0.857802i
\(852\) −12.9790 + 72.2544i −0.0152335 + 0.0848056i
\(853\) −741.602 + 1284.49i −0.869404 + 1.50585i −0.00679711 + 0.999977i \(0.502164\pi\)
−0.862607 + 0.505875i \(0.831170\pi\)
\(854\) 89.7579 + 51.8217i 0.105103 + 0.0606812i
\(855\) 1481.52 251.466i 1.73278 0.294112i
\(856\) −1922.92 −2.24640
\(857\) 373.684i 0.436038i 0.975945 + 0.218019i \(0.0699594\pi\)
−0.975945 + 0.218019i \(0.930041\pi\)
\(858\) 149.296 + 26.8178i 0.174004 + 0.0312561i
\(859\) −26.7737 46.3735i −0.0311685 0.0539854i 0.850020 0.526750i \(-0.176590\pi\)
−0.881189 + 0.472764i \(0.843256\pi\)
\(860\) −1873.54 + 1081.69i −2.17854 + 1.25778i
\(861\) −8.15715 + 45.4112i −0.00947404 + 0.0527424i
\(862\) 1279.61 1.48446
\(863\) 435.807i 0.504991i 0.967598 + 0.252496i \(0.0812513\pi\)
−0.967598 + 0.252496i \(0.918749\pi\)
\(864\) −761.686 7.31305i −0.881580 0.00846417i
\(865\) 305.542 529.215i 0.353228 0.611809i
\(866\) 2416.56i 2.79048i
\(867\) −214.337 + 253.783i −0.247217 + 0.292714i
\(868\) −21.2972 −0.0245360
\(869\) −218.937 126.404i −0.251942 0.145459i
\(870\) −2026.30 + 730.177i −2.32908 + 0.839284i
\(871\) −10.1489 + 523.405i −0.0116520 + 0.600924i
\(872\) 12.4487i 0.0142761i
\(873\) −69.4756 409.318i −0.0795826 0.468864i
\(874\) 2009.65 2.29937
\(875\) 19.5391 11.2809i 0.0223304 0.0128925i
\(876\) 522.178 + 1449.09i 0.596094 + 1.65421i
\(877\) 521.779 903.748i 0.594959 1.03050i −0.398593 0.917128i \(-0.630501\pi\)
0.993553 0.113372i \(-0.0361652\pi\)
\(878\) 1220.49 704.650i 1.39008 0.802563i
\(879\) −1326.54 + 478.018i −1.50914 + 0.543820i
\(880\) −308.367 −0.350417
\(881\) 1139.59 + 657.941i 1.29352 + 0.746812i 0.979276 0.202532i \(-0.0649169\pi\)
0.314240 + 0.949343i \(0.398250\pi\)
\(882\) 549.711 1480.76i 0.623255 1.67887i
\(883\) 408.052 + 706.767i 0.462120 + 0.800415i 0.999066 0.0432012i \(-0.0137556\pi\)
−0.536947 + 0.843616i \(0.680422\pi\)
\(884\) 1201.98 + 693.962i 1.35970 + 0.785025i
\(885\) 491.082 + 1362.79i 0.554895 + 1.53988i
\(886\) −1661.99 −1.87584
\(887\) −647.598 373.891i −0.730099 0.421523i 0.0883591 0.996089i \(-0.471838\pi\)
−0.818459 + 0.574566i \(0.805171\pi\)
\(888\) 648.569 3610.61i 0.730370 4.06600i
\(889\) −12.6525 + 21.9148i −0.0142323 + 0.0246511i
\(890\) −1021.41 589.713i −1.14765 0.662598i
\(891\) 48.1828 + 137.847i 0.0540773 + 0.154710i
\(892\) −547.564 948.409i −0.613861 1.06324i
\(893\) 1701.89i 1.90581i
\(894\) 290.379 + 52.1604i 0.324809 + 0.0583449i
\(895\) −960.760 −1.07348
\(896\) 46.7953i 0.0522269i
\(897\) −374.893 316.623i −0.417941 0.352980i
\(898\) −1885.23 −2.09937
\(899\) 202.852 + 117.117i 0.225642 + 0.130274i
\(900\) 1047.79 + 388.976i 1.16421 + 0.432196i
\(901\) 524.997 909.322i 0.582683 1.00924i
\(902\) 262.882 151.775i 0.291443 0.168265i
\(903\) 24.7521 29.3074i 0.0274110 0.0324556i
\(904\) −369.894 640.675i −0.409175 0.708712i
\(905\) 40.3644 23.3044i 0.0446016 0.0257507i
\(906\) −49.0570 41.4319i −0.0541468 0.0457306i
\(907\) 796.012 + 1378.73i 0.877632 + 1.52010i 0.853932 + 0.520384i \(0.174211\pi\)
0.0236995 + 0.999719i \(0.492456\pi\)
\(908\) −2937.09 1695.73i −3.23468 1.86755i
\(909\) 523.005 1408.82i 0.575363 1.54986i
\(910\) −28.7040 + 49.7168i −0.0315428 + 0.0546338i
\(911\) 191.983i 0.210739i 0.994433 + 0.105369i \(0.0336025\pi\)
−0.994433 + 0.105369i \(0.966398\pi\)
\(912\) −1418.36 + 1679.39i −1.55522 + 1.84143i
\(913\) 142.619 0.156209
\(914\) 31.8870i 0.0348873i
\(915\) −291.627 + 1623.50i −0.318718 + 1.77432i
\(916\) −478.284 −0.522145
\(917\) −6.41779 + 3.70531i −0.00699868 + 0.00404069i
\(918\) −18.6031 + 1937.59i −0.0202648 + 2.11066i
\(919\) −523.951 + 907.510i −0.570132 + 0.987497i 0.426420 + 0.904525i \(0.359774\pi\)
−0.996552 + 0.0829719i \(0.973559\pi\)
\(920\) 1984.55 + 1145.78i 2.15712 + 1.24541i
\(921\) −1605.50 288.393i −1.74321 0.313130i
\(922\) −1350.72 + 2339.52i −1.46499 + 2.53744i
\(923\) 21.5201i 0.0233154i
\(924\) 14.8210 5.34074i 0.0160400 0.00578002i
\(925\) −487.400 + 844.202i −0.526919 + 0.912651i
\(926\) 2272.10 1311.80i 2.45368 1.41663i
\(927\) −238.870 88.6771i −0.257681 0.0956603i
\(928\) 451.911 782.732i 0.486973 0.843461i
\(929\) 481.067i 0.517833i 0.965900 + 0.258917i \(0.0833655\pi\)
−0.965900 + 0.258917i \(0.916635\pi\)
\(930\) −166.639 462.436i −0.179182 0.497243i
\(931\) −653.791 1132.40i −0.702246 1.21633i
\(932\) −2264.29 1307.29i −2.42949 1.40267i
\(933\) −1236.19 + 445.460i −1.32496 + 0.477450i
\(934\) 135.452 + 234.609i 0.145023 + 0.251188i
\(935\) 225.025i 0.240668i
\(936\) 1215.59 206.327i 1.29870 0.220435i
\(937\) 662.767 0.707329 0.353664 0.935372i \(-0.384935\pi\)
0.353664 + 0.935372i \(0.384935\pi\)
\(938\) 38.0933 + 69.0367i 0.0406112 + 0.0735999i
\(939\) −200.037 555.118i −0.213032 0.591180i
\(940\) 1764.90 3056.90i 1.87756 3.25202i
\(941\) 674.729i 0.717034i 0.933523 + 0.358517i \(0.116718\pi\)
−0.933523 + 0.358517i \(0.883282\pi\)
\(942\) −1503.02 1269.40i −1.59557 1.34756i
\(943\) −981.997 −1.04135
\(944\) −1835.11 1059.50i −1.94397 1.12235i
\(945\) −55.2632 0.530589i −0.0584795 0.000561470i
\(946\) −252.385 −0.266792
\(947\) 1086.38i 1.14718i −0.819142 0.573590i \(-0.805550\pi\)
0.819142 0.573590i \(-0.194450\pi\)
\(948\) −3678.85 660.826i −3.88064 0.697074i
\(949\) −225.766 391.039i −0.237899 0.412053i
\(950\) 1162.04 670.904i 1.22320 0.706214i
\(951\) 148.730 827.984i 0.156393 0.870646i
\(952\) 114.930 0.120725
\(953\) 1432.08i 1.50271i 0.659899 + 0.751354i \(0.270599\pi\)
−0.659899 + 0.751354i \(0.729401\pi\)
\(954\) −283.914 1672.69i −0.297603 1.75334i
\(955\) 937.046 1623.01i 0.981200 1.69949i
\(956\) 3270.03 + 1887.95i 3.42054 + 1.97485i
\(957\) −170.537 30.6333i −0.178199 0.0320097i
\(958\) 53.0935 + 91.9606i 0.0554211 + 0.0959922i
\(959\) −34.0023 + 19.6313i −0.0354560 + 0.0204706i
\(960\) 146.691 52.8603i 0.152803 0.0550628i
\(961\) 453.772 785.956i 0.472187 0.817852i
\(962\) 1956.00i 2.03326i
\(963\) 629.608 + 760.166i 0.653799 + 0.789373i
\(964\) 42.9114 + 74.3247i 0.0445139 + 0.0771003i
\(965\) 1211.74i 1.25569i
\(966\) −72.7453 13.0671i −0.0753056 0.0135271i
\(967\) 19.7589 + 34.2234i 0.0204332 + 0.0353913i 0.876061 0.482200i \(-0.160162\pi\)
−0.855628 + 0.517591i \(0.826829\pi\)
\(968\) 1787.96 + 1032.28i 1.84707 + 1.06641i
\(969\) 1225.50 + 1035.02i 1.26471 + 1.06813i
\(970\) −516.891 895.281i −0.532877 0.922970i
\(971\) 442.524 255.491i 0.455740 0.263122i −0.254511 0.967070i \(-0.581915\pi\)
0.710251 + 0.703948i \(0.248581\pi\)
\(972\) 1361.11 + 1675.85i 1.40032 + 1.72413i
\(973\) −41.1967 71.3548i −0.0423399 0.0733349i
\(974\) 1708.26 986.264i 1.75386 1.01259i
\(975\) −322.476 57.9259i −0.330745 0.0594112i
\(976\) −1206.45 2089.63i −1.23612 2.14102i
\(977\) −554.112 319.917i −0.567156 0.327448i 0.188856 0.982005i \(-0.439522\pi\)
−0.756013 + 0.654557i \(0.772855\pi\)
\(978\) −1380.95 + 497.626i −1.41202 + 0.508820i
\(979\) −47.4394 82.1675i −0.0484570 0.0839301i
\(980\) 2711.99i 2.76734i
\(981\) −4.92122 + 4.07600i −0.00501653 + 0.00415495i
\(982\) 802.030 1389.16i 0.816731 1.41462i
\(983\) 170.206i 0.173149i −0.996245 0.0865745i \(-0.972408\pi\)
0.996245 0.0865745i \(-0.0275921\pi\)
\(984\) 1592.06 1885.06i 1.61794 1.91571i
\(985\) −588.561 1019.42i −0.597523 1.03494i
\(986\) −1991.13 1149.58i −2.01940 1.16590i
\(987\) −11.0660 + 61.6050i −0.0112118 + 0.0624164i
\(988\) 928.282 1607.83i 0.939557 1.62736i
\(989\) 707.092 + 408.240i 0.714956 + 0.412780i
\(990\) 231.932 + 280.026i 0.234274 + 0.282854i
\(991\) −453.646 −0.457766 −0.228883 0.973454i \(-0.573507\pi\)
−0.228883 + 0.973454i \(0.573507\pi\)
\(992\) 178.633 + 103.134i 0.180073 + 0.103965i
\(993\) −13.3118 + 15.7616i −0.0134056 + 0.0158728i
\(994\) −1.62066 2.80706i −0.00163044 0.00282401i
\(995\) −968.995 559.450i −0.973865 0.562261i
\(996\) 1983.74 714.842i 1.99171 0.717713i
\(997\) −163.788 −0.164281 −0.0821406 0.996621i \(-0.526176\pi\)
−0.0821406 + 0.996621i \(0.526176\pi\)
\(998\) −1170.96 + 676.052i −1.17330 + 0.677407i
\(999\) −1639.70 + 925.804i −1.64134 + 0.926731i
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 201.3.g.b.29.3 84
3.2 odd 2 inner 201.3.g.b.29.40 yes 84
67.37 even 3 inner 201.3.g.b.104.40 yes 84
201.104 odd 6 inner 201.3.g.b.104.3 yes 84
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.3.g.b.29.3 84 1.1 even 1 trivial
201.3.g.b.29.40 yes 84 3.2 odd 2 inner
201.3.g.b.104.3 yes 84 201.104 odd 6 inner
201.3.g.b.104.40 yes 84 67.37 even 3 inner