Properties

Label 11.5.d.a.7.1
Level $11$
Weight $5$
Character 11.7
Analytic conductor $1.137$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [11,5,Mod(2,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 11.d (of order \(10\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.13706959392\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(3\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 115x^{10} + 5030x^{8} + 102975x^{6} + 953170x^{4} + 2910655x^{2} + 73205 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 7.1
Root \(6.10049i\) of defining polynomial
Character \(\chi\) \(=\) 11.7
Dual form 11.5.d.a.8.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.46775 + 3.39656i) q^{2} +(-2.26281 + 6.96422i) q^{3} +(-0.502581 - 1.54679i) q^{4} +(14.7329 - 10.7041i) q^{5} +(-18.0704 - 24.8717i) q^{6} +(47.9990 - 15.5958i) q^{7} +(-57.3923 - 18.6479i) q^{8} +(22.1503 + 16.0931i) q^{9} +O(q^{10})\) \(q+(-2.46775 + 3.39656i) q^{2} +(-2.26281 + 6.96422i) q^{3} +(-0.502581 - 1.54679i) q^{4} +(14.7329 - 10.7041i) q^{5} +(-18.0704 - 24.8717i) q^{6} +(47.9990 - 15.5958i) q^{7} +(-57.3923 - 18.6479i) q^{8} +(22.1503 + 16.0931i) q^{9} +76.4560i q^{10} +(-82.9397 + 88.1022i) q^{11} +11.9094 q^{12} +(125.766 - 173.103i) q^{13} +(-65.4772 + 201.518i) q^{14} +(41.2077 + 126.824i) q^{15} +(226.021 - 164.214i) q^{16} +(-255.614 - 351.822i) q^{17} +(-109.323 + 35.5210i) q^{18} +(-61.3806 - 19.9438i) q^{19} +(-23.9614 - 17.4089i) q^{20} +369.566i q^{21} +(-94.5704 - 499.124i) q^{22} +536.875 q^{23} +(259.736 - 357.496i) q^{24} +(-90.6549 + 279.007i) q^{25} +(277.594 + 854.346i) q^{26} +(-642.052 + 466.478i) q^{27} +(-48.2468 - 66.4060i) q^{28} +(-481.802 + 156.547i) q^{29} +(-532.457 - 173.006i) q^{30} +(192.037 + 139.523i) q^{31} +207.397i q^{32} +(-425.887 - 776.970i) q^{33} +1825.78 q^{34} +(540.225 - 743.556i) q^{35} +(13.7603 - 42.3498i) q^{36} +(-718.836 - 2212.35i) q^{37} +(219.212 - 159.267i) q^{38} +(920.939 + 1267.56i) q^{39} +(-1045.16 + 339.594i) q^{40} +(-100.981 - 32.8108i) q^{41} +(-1255.25 - 911.995i) q^{42} +2058.95i q^{43} +(177.959 + 84.0114i) q^{44} +498.599 q^{45} +(-1324.87 + 1823.53i) q^{46} +(17.8846 - 55.0431i) q^{47} +(632.178 + 1945.64i) q^{48} +(118.225 - 85.8952i) q^{49} +(-723.951 - 996.433i) q^{50} +(3028.58 - 984.044i) q^{51} +(-330.960 - 107.536i) q^{52} +(926.358 + 673.039i) q^{53} -3331.92i q^{54} +(-278.889 + 2185.79i) q^{55} -3045.60 q^{56} +(277.786 - 382.340i) q^{57} +(657.244 - 2022.79i) q^{58} +(-596.473 - 1835.75i) q^{59} +(175.460 - 127.479i) q^{60} +(-375.548 - 516.897i) q^{61} +(-947.795 + 307.957i) q^{62} +(1314.18 + 427.002i) q^{63} +(2911.90 + 2115.62i) q^{64} -3896.51i q^{65} +(3690.00 + 470.814i) q^{66} -8692.22 q^{67} +(-415.727 + 572.199i) q^{68} +(-1214.85 + 3738.92i) q^{69} +(1192.39 + 3669.81i) q^{70} +(1518.36 - 1103.16i) q^{71} +(-971.154 - 1336.68i) q^{72} +(2334.33 - 758.471i) q^{73} +(9288.28 + 3017.94i) q^{74} +(-1737.93 - 1262.68i) q^{75} +104.966i q^{76} +(-2607.00 + 5522.33i) q^{77} -6578.00 q^{78} +(-2255.51 + 3104.44i) q^{79} +(1572.18 - 4838.68i) q^{80} +(-1110.50 - 3417.77i) q^{81} +(360.640 - 262.020i) q^{82} +(4351.57 + 5989.42i) q^{83} +(571.640 - 185.737i) q^{84} +(-7531.86 - 2447.25i) q^{85} +(-6993.34 - 5080.96i) q^{86} -3709.62i q^{87} +(6403.03 - 3509.74i) q^{88} +11104.2 q^{89} +(-1230.42 + 1693.52i) q^{90} +(3336.98 - 10270.2i) q^{91} +(-269.823 - 830.430i) q^{92} +(-1406.21 + 1021.67i) q^{93} +(142.823 + 196.578i) q^{94} +(-1117.79 + 363.193i) q^{95} +(-1444.36 - 469.300i) q^{96} +(9943.57 + 7224.43i) q^{97} +613.524i q^{98} +(-3254.98 + 616.730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 5 q^{2} - 6 q^{3} + 7 q^{4} - 18 q^{5} + 75 q^{6} - 80 q^{7} - 245 q^{8} + q^{9} - 43 q^{11} + 594 q^{12} + 250 q^{13} + 610 q^{14} + 1134 q^{15} - 633 q^{16} - 1250 q^{17} - 3150 q^{18} - 1025 q^{19} + 752 q^{20} - 35 q^{22} + 1684 q^{23} + 5345 q^{24} + 197 q^{25} + 3490 q^{26} - 687 q^{27} - 3580 q^{28} - 2690 q^{29} - 6740 q^{30} - 1136 q^{31} + 5939 q^{33} + 2370 q^{34} + 3610 q^{35} - 514 q^{36} - 336 q^{37} + 1900 q^{38} - 6880 q^{39} - 2340 q^{40} - 4550 q^{41} + 1310 q^{42} - 6268 q^{44} + 5136 q^{45} + 4150 q^{46} + 24 q^{47} + 344 q^{48} + 827 q^{49} + 8895 q^{50} + 13155 q^{51} + 14070 q^{52} + 414 q^{53} - 2738 q^{55} - 21340 q^{56} - 26925 q^{57} + 2980 q^{58} - 10011 q^{59} - 6856 q^{60} + 9460 q^{61} - 6200 q^{62} + 9150 q^{63} - 2633 q^{64} - 3210 q^{66} + 12154 q^{67} - 9400 q^{68} - 9022 q^{69} - 9380 q^{70} + 17574 q^{71} + 43045 q^{72} + 27950 q^{73} + 43270 q^{74} - 1761 q^{75} + 4090 q^{77} - 42920 q^{78} - 41540 q^{79} - 2308 q^{80} - 21080 q^{81} - 28175 q^{82} - 18665 q^{83} + 26250 q^{84} - 4230 q^{85} - 10125 q^{86} - 15125 q^{88} + 5554 q^{89} + 18400 q^{90} + 7390 q^{91} + 3904 q^{92} + 36898 q^{93} + 18920 q^{94} + 14110 q^{95} - 21140 q^{96} + 20769 q^{97} - 3269 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.46775 + 3.39656i −0.616936 + 0.849140i −0.997125 0.0757688i \(-0.975859\pi\)
0.380189 + 0.924909i \(0.375859\pi\)
\(3\) −2.26281 + 6.96422i −0.251424 + 0.773803i 0.743090 + 0.669192i \(0.233360\pi\)
−0.994513 + 0.104611i \(0.966640\pi\)
\(4\) −0.502581 1.54679i −0.0314113 0.0966741i
\(5\) 14.7329 10.7041i 0.589315 0.428163i −0.252755 0.967530i \(-0.581337\pi\)
0.842070 + 0.539368i \(0.181337\pi\)
\(6\) −18.0704 24.8717i −0.501954 0.690881i
\(7\) 47.9990 15.5958i 0.979571 0.318282i 0.224898 0.974382i \(-0.427795\pi\)
0.754674 + 0.656100i \(0.227795\pi\)
\(8\) −57.3923 18.6479i −0.896755 0.291373i
\(9\) 22.1503 + 16.0931i 0.273460 + 0.198681i
\(10\) 76.4560i 0.764560i
\(11\) −82.9397 + 88.1022i −0.685452 + 0.728118i
\(12\) 11.9094 0.0827042
\(13\) 125.766 173.103i 0.744180 1.02428i −0.254188 0.967155i \(-0.581808\pi\)
0.998367 0.0571206i \(-0.0181919\pi\)
\(14\) −65.4772 + 201.518i −0.334067 + 1.02815i
\(15\) 41.2077 + 126.824i 0.183146 + 0.563664i
\(16\) 226.021 164.214i 0.882894 0.641460i
\(17\) −255.614 351.822i −0.884477 1.21738i −0.975161 0.221498i \(-0.928905\pi\)
0.0906838 0.995880i \(-0.471095\pi\)
\(18\) −109.323 + 35.5210i −0.337415 + 0.109633i
\(19\) −61.3806 19.9438i −0.170029 0.0552459i 0.222765 0.974872i \(-0.428492\pi\)
−0.392795 + 0.919626i \(0.628492\pi\)
\(20\) −23.9614 17.4089i −0.0599034 0.0435224i
\(21\) 369.566i 0.838019i
\(22\) −94.5704 499.124i −0.195393 1.03125i
\(23\) 536.875 1.01489 0.507443 0.861685i \(-0.330591\pi\)
0.507443 + 0.861685i \(0.330591\pi\)
\(24\) 259.736 357.496i 0.450931 0.620653i
\(25\) −90.6549 + 279.007i −0.145048 + 0.446411i
\(26\) 277.594 + 854.346i 0.410642 + 1.26383i
\(27\) −642.052 + 466.478i −0.880730 + 0.639888i
\(28\) −48.2468 66.4060i −0.0615393 0.0847015i
\(29\) −481.802 + 156.547i −0.572892 + 0.186144i −0.581114 0.813822i \(-0.697383\pi\)
0.00822167 + 0.999966i \(0.497383\pi\)
\(30\) −532.457 173.006i −0.591619 0.192229i
\(31\) 192.037 + 139.523i 0.199830 + 0.145185i 0.683200 0.730231i \(-0.260588\pi\)
−0.483370 + 0.875416i \(0.660588\pi\)
\(32\) 207.397i 0.202536i
\(33\) −425.887 776.970i −0.391080 0.713471i
\(34\) 1825.78 1.57939
\(35\) 540.225 743.556i 0.441000 0.606984i
\(36\) 13.7603 42.3498i 0.0106175 0.0326773i
\(37\) −718.836 2212.35i −0.525081 1.61603i −0.764156 0.645032i \(-0.776844\pi\)
0.239075 0.971001i \(-0.423156\pi\)
\(38\) 219.212 159.267i 0.151809 0.110296i
\(39\) 920.939 + 1267.56i 0.605483 + 0.833375i
\(40\) −1045.16 + 339.594i −0.653227 + 0.212246i
\(41\) −100.981 32.8108i −0.0600721 0.0195186i 0.278827 0.960341i \(-0.410054\pi\)
−0.338899 + 0.940823i \(0.610054\pi\)
\(42\) −1255.25 911.995i −0.711595 0.517004i
\(43\) 2058.95i 1.11355i 0.830664 + 0.556773i \(0.187961\pi\)
−0.830664 + 0.556773i \(0.812039\pi\)
\(44\) 177.959 + 84.0114i 0.0919211 + 0.0433943i
\(45\) 498.599 0.246222
\(46\) −1324.87 + 1823.53i −0.626120 + 0.861780i
\(47\) 17.8846 55.0431i 0.00809624 0.0249177i −0.946927 0.321449i \(-0.895830\pi\)
0.955023 + 0.296532i \(0.0958300\pi\)
\(48\) 632.178 + 1945.64i 0.274383 + 0.844464i
\(49\) 118.225 85.8952i 0.0492397 0.0357748i
\(50\) −723.951 996.433i −0.289580 0.398573i
\(51\) 3028.58 984.044i 1.16439 0.378333i
\(52\) −330.960 107.536i −0.122397 0.0397691i
\(53\) 926.358 + 673.039i 0.329782 + 0.239601i 0.740338 0.672235i \(-0.234665\pi\)
−0.410556 + 0.911835i \(0.634665\pi\)
\(54\) 3331.92i 1.14263i
\(55\) −278.889 + 2185.79i −0.0921948 + 0.722576i
\(56\) −3045.60 −0.971175
\(57\) 277.786 382.340i 0.0854989 0.117679i
\(58\) 657.244 2022.79i 0.195376 0.601305i
\(59\) −596.473 1835.75i −0.171351 0.527364i 0.828097 0.560585i \(-0.189424\pi\)
−0.999448 + 0.0332206i \(0.989424\pi\)
\(60\) 175.460 127.479i 0.0487389 0.0354108i
\(61\) −375.548 516.897i −0.100927 0.138913i 0.755567 0.655072i \(-0.227362\pi\)
−0.856493 + 0.516158i \(0.827362\pi\)
\(62\) −947.795 + 307.957i −0.246565 + 0.0801138i
\(63\) 1314.18 + 427.002i 0.331110 + 0.107584i
\(64\) 2911.90 + 2115.62i 0.710912 + 0.516508i
\(65\) 3896.51i 0.922251i
\(66\) 3690.00 + 470.814i 0.847108 + 0.108084i
\(67\) −8692.22 −1.93634 −0.968169 0.250298i \(-0.919471\pi\)
−0.968169 + 0.250298i \(0.919471\pi\)
\(68\) −415.727 + 572.199i −0.0899063 + 0.123745i
\(69\) −1214.85 + 3738.92i −0.255166 + 0.785322i
\(70\) 1192.39 + 3669.81i 0.243346 + 0.748941i
\(71\) 1518.36 1103.16i 0.301203 0.218837i −0.426910 0.904294i \(-0.640398\pi\)
0.728113 + 0.685457i \(0.240398\pi\)
\(72\) −971.154 1336.68i −0.187337 0.257847i
\(73\) 2334.33 758.471i 0.438043 0.142329i −0.0816893 0.996658i \(-0.526032\pi\)
0.519733 + 0.854329i \(0.326032\pi\)
\(74\) 9288.28 + 3017.94i 1.69618 + 0.551122i
\(75\) −1737.93 1262.68i −0.308966 0.224477i
\(76\) 104.966i 0.0181728i
\(77\) −2607.00 + 5522.33i −0.439703 + 0.931410i
\(78\) −6578.00 −1.08120
\(79\) −2255.51 + 3104.44i −0.361401 + 0.497426i −0.950539 0.310607i \(-0.899468\pi\)
0.589137 + 0.808033i \(0.299468\pi\)
\(80\) 1572.18 4838.68i 0.245654 0.756044i
\(81\) −1110.50 3417.77i −0.169258 0.520922i
\(82\) 360.640 262.020i 0.0536347 0.0389679i
\(83\) 4351.57 + 5989.42i 0.631669 + 0.869418i 0.998137 0.0610127i \(-0.0194330\pi\)
−0.366468 + 0.930431i \(0.619433\pi\)
\(84\) 571.640 185.737i 0.0810147 0.0263233i
\(85\) −7531.86 2447.25i −1.04247 0.338720i
\(86\) −6993.34 5080.96i −0.945557 0.686987i
\(87\) 3709.62i 0.490107i
\(88\) 6403.03 3509.74i 0.826837 0.453221i
\(89\) 11104.2 1.40187 0.700937 0.713223i \(-0.252765\pi\)
0.700937 + 0.713223i \(0.252765\pi\)
\(90\) −1230.42 + 1693.52i −0.151903 + 0.209077i
\(91\) 3336.98 10270.2i 0.402969 1.24021i
\(92\) −269.823 830.430i −0.0318789 0.0981132i
\(93\) −1406.21 + 1021.67i −0.162587 + 0.118126i
\(94\) 142.823 + 196.578i 0.0161637 + 0.0222475i
\(95\) −1117.79 + 363.193i −0.123855 + 0.0402430i
\(96\) −1444.36 469.300i −0.156723 0.0509223i
\(97\) 9943.57 + 7224.43i 1.05682 + 0.767821i 0.973497 0.228702i \(-0.0734481\pi\)
0.0833186 + 0.996523i \(0.473448\pi\)
\(98\) 613.524i 0.0638822i
\(99\) −3254.98 + 616.730i −0.332107 + 0.0629252i
\(100\) 477.125 0.0477125
\(101\) −4980.55 + 6855.14i −0.488241 + 0.672006i −0.980062 0.198690i \(-0.936331\pi\)
0.491821 + 0.870696i \(0.336331\pi\)
\(102\) −4131.39 + 12715.1i −0.397096 + 1.22214i
\(103\) −3982.66 12257.4i −0.375404 1.15537i −0.943206 0.332209i \(-0.892206\pi\)
0.567802 0.823165i \(-0.307794\pi\)
\(104\) −10446.0 + 7589.48i −0.965794 + 0.701690i
\(105\) 3955.86 + 5444.77i 0.358808 + 0.493857i
\(106\) −4572.03 + 1485.54i −0.406909 + 0.132213i
\(107\) −3063.72 995.464i −0.267597 0.0869477i 0.172145 0.985072i \(-0.444930\pi\)
−0.439742 + 0.898124i \(0.644930\pi\)
\(108\) 1044.22 + 758.674i 0.0895254 + 0.0650440i
\(109\) 14090.5i 1.18597i 0.805215 + 0.592983i \(0.202050\pi\)
−0.805215 + 0.592983i \(0.797950\pi\)
\(110\) −6735.94 6341.24i −0.556690 0.524069i
\(111\) 17033.9 1.38251
\(112\) 8287.72 11407.1i 0.660692 0.909365i
\(113\) 461.161 1419.31i 0.0361157 0.111153i −0.931373 0.364065i \(-0.881389\pi\)
0.967489 + 0.252913i \(0.0813885\pi\)
\(114\) 613.134 + 1887.03i 0.0471787 + 0.145201i
\(115\) 7909.71 5746.74i 0.598088 0.434536i
\(116\) 484.289 + 666.567i 0.0359906 + 0.0495368i
\(117\) 5571.52 1810.30i 0.407007 0.132245i
\(118\) 7707.19 + 2504.22i 0.553519 + 0.179849i
\(119\) −17756.2 12900.6i −1.25388 0.910996i
\(120\) 8047.19i 0.558832i
\(121\) −883.004 14614.3i −0.0603104 0.998180i
\(122\) 2682.43 0.180222
\(123\) 457.003 629.011i 0.0302071 0.0415765i
\(124\) 119.298 367.161i 0.00775871 0.0238788i
\(125\) 5168.06 + 15905.7i 0.330756 + 1.01796i
\(126\) −4693.39 + 3409.95i −0.295628 + 0.214786i
\(127\) −10211.8 14055.4i −0.633134 0.871435i 0.365092 0.930972i \(-0.381038\pi\)
−0.998226 + 0.0595368i \(0.981038\pi\)
\(128\) −17527.6 + 5695.05i −1.06980 + 0.347599i
\(129\) −14339.0 4659.02i −0.861665 0.279972i
\(130\) 13234.7 + 9615.60i 0.783120 + 0.568970i
\(131\) 18372.1i 1.07057i 0.844671 + 0.535285i \(0.179796\pi\)
−0.844671 + 0.535285i \(0.820204\pi\)
\(132\) −987.763 + 1049.25i −0.0566898 + 0.0602184i
\(133\) −3257.25 −0.184140
\(134\) 21450.2 29523.6i 1.19460 1.64422i
\(135\) −4466.06 + 13745.1i −0.245052 + 0.754191i
\(136\) 8109.53 + 24958.6i 0.438448 + 1.34940i
\(137\) 17181.8 12483.3i 0.915434 0.665102i −0.0269489 0.999637i \(-0.508579\pi\)
0.942383 + 0.334535i \(0.108579\pi\)
\(138\) −9701.52 13353.0i −0.509427 0.701165i
\(139\) −3870.52 + 1257.61i −0.200327 + 0.0650901i −0.407462 0.913222i \(-0.633586\pi\)
0.207135 + 0.978312i \(0.433586\pi\)
\(140\) −1421.63 461.915i −0.0725320 0.0235671i
\(141\) 342.863 + 249.105i 0.0172458 + 0.0125298i
\(142\) 7879.53i 0.390772i
\(143\) 4819.69 + 25437.4i 0.235693 + 1.24394i
\(144\) 7649.14 0.368882
\(145\) −5422.65 + 7463.63i −0.257914 + 0.354988i
\(146\) −3184.35 + 9800.42i −0.149388 + 0.459768i
\(147\) 330.673 + 1017.71i 0.0153026 + 0.0470965i
\(148\) −3060.76 + 2223.77i −0.139735 + 0.101523i
\(149\) −10578.8 14560.5i −0.476503 0.655850i 0.501325 0.865259i \(-0.332846\pi\)
−0.977828 + 0.209409i \(0.932846\pi\)
\(150\) 8577.55 2787.01i 0.381224 0.123867i
\(151\) −8398.18 2728.73i −0.368325 0.119676i 0.119006 0.992894i \(-0.462029\pi\)
−0.487331 + 0.873218i \(0.662029\pi\)
\(152\) 3150.87 + 2289.24i 0.136378 + 0.0990842i
\(153\) 11906.6i 0.508633i
\(154\) −12323.5 22482.5i −0.519629 0.947990i
\(155\) 4322.71 0.179926
\(156\) 1497.80 2061.55i 0.0615468 0.0847119i
\(157\) −5990.27 + 18436.1i −0.243023 + 0.747947i 0.752933 + 0.658098i \(0.228639\pi\)
−0.995955 + 0.0898493i \(0.971361\pi\)
\(158\) −4978.39 15321.9i −0.199423 0.613761i
\(159\) −6783.37 + 4928.40i −0.268319 + 0.194945i
\(160\) 2219.99 + 3055.55i 0.0867183 + 0.119357i
\(161\) 25769.5 8373.00i 0.994153 0.323020i
\(162\) 14349.1 + 4662.30i 0.546757 + 0.177652i
\(163\) 3687.37 + 2679.03i 0.138785 + 0.100833i 0.655011 0.755619i \(-0.272664\pi\)
−0.516227 + 0.856452i \(0.672664\pi\)
\(164\) 172.686i 0.00642052i
\(165\) −14591.3 6888.29i −0.535951 0.253013i
\(166\) −31082.0 −1.12796
\(167\) 7251.30 9980.56i 0.260006 0.357867i −0.658978 0.752162i \(-0.729011\pi\)
0.918984 + 0.394295i \(0.129011\pi\)
\(168\) 6891.63 21210.3i 0.244176 0.751498i
\(169\) −5321.48 16377.8i −0.186320 0.573434i
\(170\) 26898.9 19543.2i 0.930759 0.676236i
\(171\) −1038.64 1429.57i −0.0355200 0.0488891i
\(172\) 3184.75 1034.79i 0.107651 0.0349780i
\(173\) 653.072 + 212.196i 0.0218207 + 0.00708998i 0.319907 0.947449i \(-0.396348\pi\)
−0.298086 + 0.954539i \(0.596348\pi\)
\(174\) 12599.9 + 9154.39i 0.416169 + 0.302365i
\(175\) 14805.9i 0.483458i
\(176\) −4278.51 + 33532.8i −0.138123 + 1.08254i
\(177\) 14134.3 0.451158
\(178\) −27402.4 + 37716.2i −0.864867 + 1.19039i
\(179\) 4275.10 13157.4i 0.133426 0.410643i −0.861916 0.507051i \(-0.830736\pi\)
0.995342 + 0.0964086i \(0.0307355\pi\)
\(180\) −250.587 771.226i −0.00773415 0.0238033i
\(181\) −16520.5 + 12002.8i −0.504272 + 0.366375i −0.810647 0.585536i \(-0.800884\pi\)
0.306374 + 0.951911i \(0.400884\pi\)
\(182\) 26648.5 + 36678.5i 0.804506 + 1.10731i
\(183\) 4449.58 1445.76i 0.132867 0.0431711i
\(184\) −30812.5 10011.6i −0.910105 0.295711i
\(185\) −34271.6 24899.8i −1.00136 0.727533i
\(186\) 7297.51i 0.210935i
\(187\) 52196.9 + 6659.89i 1.49266 + 0.190451i
\(188\) −94.1283 −0.00266321
\(189\) −23542.7 + 32403.8i −0.659073 + 0.907136i
\(190\) 1524.82 4692.92i 0.0422388 0.129998i
\(191\) −2265.94 6973.85i −0.0621130 0.191164i 0.915185 0.403034i \(-0.132045\pi\)
−0.977298 + 0.211870i \(0.932045\pi\)
\(192\) −21322.7 + 15491.9i −0.578416 + 0.420244i
\(193\) 21150.0 + 29110.5i 0.567801 + 0.781511i 0.992292 0.123921i \(-0.0395470\pi\)
−0.424491 + 0.905432i \(0.639547\pi\)
\(194\) −49076.4 + 15945.9i −1.30398 + 0.423687i
\(195\) 27136.2 + 8817.08i 0.713640 + 0.231876i
\(196\) −192.279 139.699i −0.00500518 0.00363647i
\(197\) 39661.5i 1.02197i −0.859591 0.510983i \(-0.829282\pi\)
0.859591 0.510983i \(-0.170718\pi\)
\(198\) 5937.70 12577.7i 0.151456 0.320826i
\(199\) 8985.83 0.226909 0.113455 0.993543i \(-0.463808\pi\)
0.113455 + 0.993543i \(0.463808\pi\)
\(200\) 10405.8 14322.3i 0.260145 0.358058i
\(201\) 19668.9 60534.6i 0.486841 1.49834i
\(202\) −10993.2 33833.5i −0.269414 0.829170i
\(203\) −20684.6 + 15028.2i −0.501943 + 0.364683i
\(204\) −3044.21 4189.99i −0.0731500 0.100682i
\(205\) −1838.95 + 597.512i −0.0437586 + 0.0142180i
\(206\) 51461.1 + 16720.7i 1.21267 + 0.394022i
\(207\) 11891.9 + 8639.99i 0.277531 + 0.201638i
\(208\) 59777.3i 1.38169i
\(209\) 6847.99 3753.64i 0.156773 0.0859330i
\(210\) −28255.6 −0.640716
\(211\) 4141.35 5700.08i 0.0930202 0.128031i −0.759970 0.649958i \(-0.774787\pi\)
0.852990 + 0.521927i \(0.174787\pi\)
\(212\) 575.476 1771.13i 0.0128043 0.0394076i
\(213\) 4246.85 + 13070.5i 0.0936069 + 0.288093i
\(214\) 10941.6 7949.57i 0.238921 0.173586i
\(215\) 22039.1 + 30334.2i 0.476779 + 0.656230i
\(216\) 45547.7 14799.3i 0.976245 0.317201i
\(217\) 11393.5 + 3701.99i 0.241958 + 0.0786168i
\(218\) −47859.1 34771.7i −1.00705 0.731665i
\(219\) 17973.1i 0.374744i
\(220\) 3521.11 667.156i 0.0727503 0.0137842i
\(221\) −93049.0 −1.90514
\(222\) −42035.3 + 57856.6i −0.852920 + 1.17394i
\(223\) −3954.30 + 12170.1i −0.0795170 + 0.244728i −0.982910 0.184085i \(-0.941068\pi\)
0.903393 + 0.428813i \(0.141068\pi\)
\(224\) 3234.52 + 9954.83i 0.0644635 + 0.198398i
\(225\) −6498.12 + 4721.16i −0.128358 + 0.0932575i
\(226\) 3682.74 + 5068.85i 0.0721031 + 0.0992414i
\(227\) −53534.9 + 17394.5i −1.03893 + 0.337568i −0.778314 0.627876i \(-0.783925\pi\)
−0.260613 + 0.965443i \(0.583925\pi\)
\(228\) −731.007 237.519i −0.0140622 0.00456907i
\(229\) 72710.1 + 52827.0i 1.38651 + 1.00736i 0.996238 + 0.0866626i \(0.0276202\pi\)
0.390275 + 0.920698i \(0.372380\pi\)
\(230\) 41047.3i 0.775941i
\(231\) −32559.6 30651.7i −0.610176 0.574422i
\(232\) 30571.0 0.567982
\(233\) 14585.7 20075.5i 0.268668 0.369790i −0.653272 0.757124i \(-0.726604\pi\)
0.921939 + 0.387334i \(0.126604\pi\)
\(234\) −7600.31 + 23391.4i −0.138803 + 0.427193i
\(235\) −325.693 1002.38i −0.00589757 0.0181509i
\(236\) −2539.74 + 1845.23i −0.0456001 + 0.0331304i
\(237\) −16516.2 22732.6i −0.294045 0.404718i
\(238\) 87635.4 28474.5i 1.54713 0.502692i
\(239\) 31899.0 + 10364.6i 0.558445 + 0.181450i 0.574622 0.818419i \(-0.305149\pi\)
−0.0161762 + 0.999869i \(0.505149\pi\)
\(240\) 30140.1 + 21898.1i 0.523266 + 0.380175i
\(241\) 71818.0i 1.23651i −0.785976 0.618257i \(-0.787839\pi\)
0.785976 0.618257i \(-0.212161\pi\)
\(242\) 51817.5 + 33065.3i 0.884802 + 0.564601i
\(243\) −37968.2 −0.642996
\(244\) −610.786 + 840.674i −0.0102591 + 0.0141204i
\(245\) 822.361 2530.97i 0.0137003 0.0421652i
\(246\) 1008.71 + 3104.48i 0.0166684 + 0.0513001i
\(247\) −11171.9 + 8116.89i −0.183120 + 0.133044i
\(248\) −8419.63 11588.6i −0.136896 0.188421i
\(249\) −51558.5 + 16752.4i −0.831575 + 0.270195i
\(250\) −66778.0 21697.5i −1.06845 0.347160i
\(251\) −38944.7 28295.0i −0.618160 0.449120i 0.234118 0.972208i \(-0.424780\pi\)
−0.852278 + 0.523089i \(0.824780\pi\)
\(252\) 2247.35i 0.0353892i
\(253\) −44528.2 + 47299.9i −0.695656 + 0.738956i
\(254\) 72940.1 1.13057
\(255\) 34086.4 46915.9i 0.524204 0.721505i
\(256\) 6114.07 18817.2i 0.0932933 0.287127i
\(257\) 7798.62 + 24001.7i 0.118073 + 0.363392i 0.992576 0.121629i \(-0.0388119\pi\)
−0.874502 + 0.485021i \(0.838812\pi\)
\(258\) 51209.6 37205.9i 0.769328 0.558950i
\(259\) −69006.8 94979.7i −1.02871 1.41590i
\(260\) −6027.07 + 1958.31i −0.0891578 + 0.0289691i
\(261\) −13191.4 4286.14i −0.193646 0.0629196i
\(262\) −62401.8 45337.6i −0.909064 0.660474i
\(263\) 73780.1i 1.06666i 0.845906 + 0.533332i \(0.179060\pi\)
−0.845906 + 0.533332i \(0.820940\pi\)
\(264\) 9953.77 + 52534.0i 0.142817 + 0.753759i
\(265\) 20852.2 0.296934
\(266\) 8038.06 11063.4i 0.113603 0.156360i
\(267\) −25126.8 + 77332.4i −0.352464 + 1.08477i
\(268\) 4368.54 + 13445.0i 0.0608229 + 0.187194i
\(269\) 114414. 83127.0i 1.58116 1.14878i 0.665813 0.746119i \(-0.268085\pi\)
0.915348 0.402663i \(-0.131915\pi\)
\(270\) −35665.1 49088.7i −0.489233 0.673371i
\(271\) 96839.3 31465.0i 1.31860 0.428439i 0.436586 0.899663i \(-0.356187\pi\)
0.882014 + 0.471223i \(0.156187\pi\)
\(272\) −115548. 37543.8i −1.56180 0.507459i
\(273\) 63972.9 + 46479.0i 0.858362 + 0.623636i
\(274\) 89164.6i 1.18766i
\(275\) −17062.2 31127.7i −0.225616 0.411605i
\(276\) 6393.86 0.0839354
\(277\) 15920.1 21912.2i 0.207485 0.285579i −0.692574 0.721347i \(-0.743523\pi\)
0.900059 + 0.435768i \(0.143523\pi\)
\(278\) 5279.91 16249.9i 0.0683183 0.210262i
\(279\) 2008.31 + 6180.94i 0.0258001 + 0.0794047i
\(280\) −44870.5 + 32600.3i −0.572328 + 0.415821i
\(281\) 77971.9 + 107319.i 0.987474 + 1.35914i 0.932704 + 0.360642i \(0.117442\pi\)
0.0547693 + 0.998499i \(0.482558\pi\)
\(282\) −1692.20 + 549.828i −0.0212791 + 0.00691399i
\(283\) 80080.5 + 26019.7i 0.999894 + 0.324885i 0.762823 0.646607i \(-0.223813\pi\)
0.237071 + 0.971492i \(0.423813\pi\)
\(284\) −2469.45 1794.16i −0.0306170 0.0222446i
\(285\) 8606.40i 0.105958i
\(286\) −98293.3 46402.6i −1.20169 0.567297i
\(287\) −5358.71 −0.0650574
\(288\) −3337.66 + 4593.90i −0.0402399 + 0.0553855i
\(289\) −32631.1 + 100428.i −0.390693 + 1.20243i
\(290\) −11969.0 36836.7i −0.142318 0.438011i
\(291\) −72813.0 + 52901.7i −0.859850 + 0.624718i
\(292\) −2346.38 3229.52i −0.0275190 0.0378767i
\(293\) −114757. + 37286.9i −1.33673 + 0.434331i −0.888209 0.459440i \(-0.848050\pi\)
−0.448524 + 0.893771i \(0.648050\pi\)
\(294\) −4272.72 1388.29i −0.0494322 0.0160615i
\(295\) −28437.8 20661.3i −0.326777 0.237418i
\(296\) 140377.i 1.60218i
\(297\) 12153.9 95255.8i 0.137785 1.07989i
\(298\) 75561.6 0.850880
\(299\) 67520.8 92934.4i 0.755258 1.03952i
\(300\) −1079.65 + 3322.81i −0.0119961 + 0.0369201i
\(301\) 32111.0 + 98827.4i 0.354422 + 1.09080i
\(302\) 29992.9 21791.1i 0.328855 0.238927i
\(303\) −36470.7 50197.5i −0.397245 0.546761i
\(304\) −17148.3 + 5571.83i −0.185556 + 0.0602908i
\(305\) −11065.8 3595.50i −0.118955 0.0386508i
\(306\) 40441.4 + 29382.4i 0.431901 + 0.313794i
\(307\) 130584.i 1.38553i −0.721166 0.692763i \(-0.756393\pi\)
0.721166 0.692763i \(-0.243607\pi\)
\(308\) 9852.09 + 1257.05i 0.103855 + 0.0132510i
\(309\) 94375.0 0.988417
\(310\) −10667.4 + 14682.4i −0.111003 + 0.152782i
\(311\) 30522.3 93937.9i 0.315570 0.971225i −0.659949 0.751311i \(-0.729422\pi\)
0.975519 0.219915i \(-0.0705780\pi\)
\(312\) −29217.4 89922.0i −0.300146 0.923755i
\(313\) −50811.9 + 36917.0i −0.518653 + 0.376823i −0.816096 0.577916i \(-0.803866\pi\)
0.297443 + 0.954739i \(0.403866\pi\)
\(314\) −47837.0 65842.0i −0.485182 0.667796i
\(315\) 23932.3 7776.07i 0.241192 0.0783680i
\(316\) 5935.47 + 1928.55i 0.0594403 + 0.0193133i
\(317\) −15918.3 11565.4i −0.158409 0.115091i 0.505757 0.862676i \(-0.331213\pi\)
−0.664166 + 0.747585i \(0.731213\pi\)
\(318\) 35202.2i 0.348109i
\(319\) 26168.4 55431.8i 0.257156 0.544726i
\(320\) 65546.3 0.640101
\(321\) 13865.3 19083.9i 0.134561 0.185207i
\(322\) −35153.0 + 108190.i −0.339040 + 1.04346i
\(323\) 8673.08 + 26693.0i 0.0831320 + 0.255854i
\(324\) −4728.44 + 3435.41i −0.0450431 + 0.0327257i
\(325\) 36895.5 + 50782.3i 0.349306 + 0.480779i
\(326\) −18199.0 + 5913.21i −0.171243 + 0.0556401i
\(327\) −98129.1 31884.1i −0.917704 0.298180i
\(328\) 5183.70 + 3766.18i 0.0481828 + 0.0350068i
\(329\) 2920.94i 0.0269855i
\(330\) 59404.0 32561.6i 0.545491 0.299004i
\(331\) 28807.4 0.262935 0.131468 0.991320i \(-0.458031\pi\)
0.131468 + 0.991320i \(0.458031\pi\)
\(332\) 7077.33 9741.11i 0.0642086 0.0883756i
\(333\) 19681.2 60572.5i 0.177485 0.546244i
\(334\) 16005.2 + 49259.0i 0.143472 + 0.441563i
\(335\) −128061. + 93042.1i −1.14111 + 0.829067i
\(336\) 60687.8 + 83529.6i 0.537555 + 0.739881i
\(337\) −178804. + 58096.9i −1.57441 + 0.511556i −0.960608 0.277906i \(-0.910360\pi\)
−0.613800 + 0.789462i \(0.710360\pi\)
\(338\) 68760.4 + 22341.6i 0.601873 + 0.195560i
\(339\) 8840.86 + 6423.26i 0.0769299 + 0.0558928i
\(340\) 12880.1i 0.111420i
\(341\) −28219.7 + 5346.88i −0.242686 + 0.0459824i
\(342\) 7418.71 0.0634273
\(343\) −66890.6 + 92067.1i −0.568561 + 0.782557i
\(344\) 38395.1 118168.i 0.324458 0.998579i
\(345\) 22123.4 + 68088.8i 0.185872 + 0.572055i
\(346\) −2332.35 + 1694.55i −0.0194824 + 0.0141548i
\(347\) 17060.3 + 23481.5i 0.141687 + 0.195015i 0.873963 0.485993i \(-0.161542\pi\)
−0.732276 + 0.681008i \(0.761542\pi\)
\(348\) −5737.98 + 1864.38i −0.0473806 + 0.0153949i
\(349\) 90136.3 + 29287.0i 0.740029 + 0.240450i 0.654685 0.755902i \(-0.272801\pi\)
0.0853437 + 0.996352i \(0.472801\pi\)
\(350\) −50289.1 36537.2i −0.410523 0.298263i
\(351\) 169808.i 1.37830i
\(352\) −18272.1 17201.4i −0.147470 0.138829i
\(353\) −107013. −0.858793 −0.429397 0.903116i \(-0.641274\pi\)
−0.429397 + 0.903116i \(0.641274\pi\)
\(354\) −34879.9 + 48008.0i −0.278335 + 0.383096i
\(355\) 10561.6 32505.3i 0.0838058 0.257928i
\(356\) −5580.78 17175.9i −0.0440347 0.135525i
\(357\) 130022. 94466.2i 1.02019 0.741208i
\(358\) 34140.0 + 46989.7i 0.266378 + 0.366638i
\(359\) 64156.8 20845.8i 0.497799 0.161745i −0.0493475 0.998782i \(-0.515714\pi\)
0.547146 + 0.837037i \(0.315714\pi\)
\(360\) −28615.8 9297.83i −0.220801 0.0717425i
\(361\) −102062. 74152.4i −0.783159 0.568998i
\(362\) 85732.7i 0.654228i
\(363\) 103776. + 26920.1i 0.787558 + 0.204298i
\(364\) −17562.9 −0.132554
\(365\) 26272.7 36161.3i 0.197206 0.271430i
\(366\) −6069.83 + 18681.0i −0.0453121 + 0.139456i
\(367\) −50426.9 155198.i −0.374395 1.15227i −0.943886 0.330272i \(-0.892859\pi\)
0.569491 0.821998i \(-0.307141\pi\)
\(368\) 121345. 88162.2i 0.896037 0.651009i
\(369\) −1708.74 2351.87i −0.0125494 0.0172727i
\(370\) 169147. 54959.3i 1.23555 0.401456i
\(371\) 54960.9 + 17857.9i 0.399306 + 0.129742i
\(372\) 2287.04 + 1661.63i 0.0165268 + 0.0120074i
\(373\) 125734.i 0.903719i −0.892089 0.451860i \(-0.850761\pi\)
0.892089 0.451860i \(-0.149239\pi\)
\(374\) −151429. + 160855.i −1.08260 + 1.14998i
\(375\) −122465. −0.870862
\(376\) −2052.88 + 2825.54i −0.0145207 + 0.0199860i
\(377\) −33495.8 + 103090.i −0.235672 + 0.725324i
\(378\) −51964.0 159929.i −0.363680 1.11929i
\(379\) −78050.7 + 56707.2i −0.543373 + 0.394784i −0.825336 0.564641i \(-0.809014\pi\)
0.281963 + 0.959425i \(0.409014\pi\)
\(380\) 1123.56 + 1546.45i 0.00778091 + 0.0107095i
\(381\) 120992. 39312.8i 0.833504 0.270822i
\(382\) 29278.9 + 9513.29i 0.200645 + 0.0651934i
\(383\) 123692. + 89867.7i 0.843228 + 0.612641i 0.923270 0.384151i \(-0.125506\pi\)
−0.0800426 + 0.996791i \(0.525506\pi\)
\(384\) 134953.i 0.915207i
\(385\) 20702.8 + 109265.i 0.139672 + 0.737158i
\(386\) −151068. −1.01391
\(387\) −33134.9 + 45606.3i −0.221240 + 0.304511i
\(388\) 6177.19 19011.4i 0.0410325 0.126285i
\(389\) −10802.6 33246.9i −0.0713884 0.219711i 0.908996 0.416804i \(-0.136850\pi\)
−0.980385 + 0.197093i \(0.936850\pi\)
\(390\) −96912.9 + 70411.3i −0.637166 + 0.462928i
\(391\) −137233. 188884.i −0.897643 1.23550i
\(392\) −8386.95 + 2725.09i −0.0545798 + 0.0177341i
\(393\) −127947. 41572.5i −0.828410 0.269167i
\(394\) 134713. + 97874.4i 0.867792 + 0.630488i
\(395\) 69880.4i 0.447879i
\(396\) 2589.84 + 4724.80i 0.0165151 + 0.0301296i
\(397\) 20457.2 0.129797 0.0648986 0.997892i \(-0.479328\pi\)
0.0648986 + 0.997892i \(0.479328\pi\)
\(398\) −22174.7 + 30520.9i −0.139989 + 0.192678i
\(399\) 7370.55 22684.2i 0.0462971 0.142488i
\(400\) 25326.9 + 77948.1i 0.158293 + 0.487176i
\(401\) 153780. 111728.i 0.956338 0.694820i 0.00404091 0.999992i \(-0.498714\pi\)
0.952297 + 0.305171i \(0.0987137\pi\)
\(402\) 157072. + 216190.i 0.971953 + 1.33778i
\(403\) 48303.5 15694.8i 0.297419 0.0966373i
\(404\) 13106.6 + 4258.58i 0.0803019 + 0.0260917i
\(405\) −52944.9 38466.7i −0.322786 0.234517i
\(406\) 107342.i 0.651205i
\(407\) 254533. + 120161.i 1.53658 + 0.725393i
\(408\) −192167. −1.15441
\(409\) −110780. + 152476.i −0.662240 + 0.911495i −0.999553 0.0298979i \(-0.990482\pi\)
0.337313 + 0.941392i \(0.390482\pi\)
\(410\) 2508.58 7720.62i 0.0149232 0.0459288i
\(411\) 48057.3 + 147905.i 0.284496 + 0.875588i
\(412\) −16957.9 + 12320.6i −0.0999028 + 0.0725836i
\(413\) −57260.2 78811.9i −0.335701 0.462053i
\(414\) −58692.5 + 19070.3i −0.342438 + 0.111265i
\(415\) 128222. + 41661.9i 0.744504 + 0.241904i
\(416\) 35900.9 + 26083.5i 0.207452 + 0.150723i
\(417\) 29800.9i 0.171379i
\(418\) −4149.62 + 32522.6i −0.0237496 + 0.186137i
\(419\) −34335.6 −0.195577 −0.0977883 0.995207i \(-0.531177\pi\)
−0.0977883 + 0.995207i \(0.531177\pi\)
\(420\) 6433.76 8855.31i 0.0364725 0.0502002i
\(421\) 81293.7 250196.i 0.458662 1.41162i −0.408119 0.912929i \(-0.633815\pi\)
0.866781 0.498688i \(-0.166185\pi\)
\(422\) 9140.87 + 28132.7i 0.0513290 + 0.157974i
\(423\) 1281.96 931.402i 0.00716465 0.00520543i
\(424\) −40615.1 55901.9i −0.225921 0.310953i
\(425\) 121333. 39423.6i 0.671743 0.218262i
\(426\) −54874.8 17829.9i −0.302380 0.0982493i
\(427\) −26087.3 18953.6i −0.143078 0.103953i
\(428\) 5239.22i 0.0286009i
\(429\) −188058. 23994.6i −1.02182 0.130376i
\(430\) −157419. −0.851373
\(431\) −128666. + 177094.i −0.692643 + 0.953341i 0.307355 + 0.951595i \(0.400556\pi\)
−0.999998 + 0.00174659i \(0.999444\pi\)
\(432\) −68515.0 + 210867.i −0.367129 + 1.12991i
\(433\) 21470.6 + 66079.8i 0.114517 + 0.352446i 0.991846 0.127443i \(-0.0406769\pi\)
−0.877329 + 0.479889i \(0.840677\pi\)
\(434\) −40690.4 + 29563.3i −0.216029 + 0.156954i
\(435\) −39708.0 54653.3i −0.209845 0.288827i
\(436\) 21794.9 7081.60i 0.114652 0.0372527i
\(437\) −32953.7 10707.3i −0.172561 0.0560683i
\(438\) −61046.7 44353.0i −0.318210 0.231193i
\(439\) 72005.3i 0.373625i −0.982396 0.186812i \(-0.940184\pi\)
0.982396 0.186812i \(-0.0598156\pi\)
\(440\) 56766.5 120247.i 0.293216 0.621111i
\(441\) 4001.03 0.0205729
\(442\) 229621. 316046.i 1.17535 1.61773i
\(443\) −13800.0 + 42472.2i −0.0703190 + 0.216420i −0.980040 0.198800i \(-0.936295\pi\)
0.909721 + 0.415220i \(0.136295\pi\)
\(444\) −8560.91 26347.8i −0.0434264 0.133653i
\(445\) 163597. 118861.i 0.826146 0.600230i
\(446\) −31578.2 43463.7i −0.158752 0.218503i
\(447\) 125341. 40725.7i 0.627303 0.203823i
\(448\) 172763. + 56134.1i 0.860785 + 0.279686i
\(449\) −104641. 76026.2i −0.519050 0.377112i 0.297196 0.954817i \(-0.403949\pi\)
−0.816246 + 0.577704i \(0.803949\pi\)
\(450\) 33721.9i 0.166528i
\(451\) 11266.1 6175.35i 0.0553884 0.0303605i
\(452\) −2427.14 −0.0118800
\(453\) 38007.0 52312.2i 0.185211 0.254922i
\(454\) 73028.8 224760.i 0.354309 1.09045i
\(455\) −60769.3 187029.i −0.293536 0.903411i
\(456\) −23072.6 + 16763.2i −0.110960 + 0.0806173i
\(457\) 180382. + 248275.i 0.863697 + 1.18878i 0.980675 + 0.195642i \(0.0626791\pi\)
−0.116979 + 0.993134i \(0.537321\pi\)
\(458\) −358860. + 116601.i −1.71078 + 0.555866i
\(459\) 328235. + 106650.i 1.55797 + 0.506215i
\(460\) −12864.2 9346.42i −0.0607951 0.0441702i
\(461\) 22814.7i 0.107353i 0.998558 + 0.0536764i \(0.0170940\pi\)
−0.998558 + 0.0536764i \(0.982906\pi\)
\(462\) 184459. 34950.0i 0.864204 0.163743i
\(463\) 247942. 1.15661 0.578307 0.815819i \(-0.303713\pi\)
0.578307 + 0.815819i \(0.303713\pi\)
\(464\) −83190.2 + 114501.i −0.386399 + 0.531833i
\(465\) −9781.50 + 30104.4i −0.0452376 + 0.139227i
\(466\) 32193.8 + 99082.5i 0.148252 + 0.456273i
\(467\) −261318. + 189859.i −1.19822 + 0.870557i −0.994108 0.108390i \(-0.965430\pi\)
−0.204111 + 0.978948i \(0.565430\pi\)
\(468\) −5600.28 7708.13i −0.0255693 0.0351931i
\(469\) −417218. + 135562.i −1.89678 + 0.616301i
\(470\) 4208.38 + 1367.38i 0.0190511 + 0.00619006i
\(471\) −114839. 83435.1i −0.517662 0.376103i
\(472\) 116481.i 0.522844i
\(473\) −181398. 170769.i −0.810793 0.763283i
\(474\) 117970. 0.525069
\(475\) 11128.9 15317.6i 0.0493248 0.0678898i
\(476\) −11030.6 + 33948.6i −0.0486837 + 0.149833i
\(477\) 9687.80 + 29816.0i 0.0425783 + 0.131043i
\(478\) −113922. + 82769.5i −0.498602 + 0.362255i
\(479\) 58964.1 + 81157.2i 0.256990 + 0.353717i 0.917944 0.396710i \(-0.129848\pi\)
−0.660954 + 0.750427i \(0.729848\pi\)
\(480\) −26303.0 + 8546.35i −0.114162 + 0.0370935i
\(481\) −473369. 153807.i −2.04602 0.664791i
\(482\) 243934. + 177229.i 1.04997 + 0.762851i
\(483\) 198411.i 0.850493i
\(484\) −22161.5 + 8710.71i −0.0946037 + 0.0371846i
\(485\) 223828. 0.951549
\(486\) 93695.9 128961.i 0.396687 0.545993i
\(487\) −113517. + 349368.i −0.478632 + 1.47308i 0.362365 + 0.932036i \(0.381969\pi\)
−0.840997 + 0.541040i \(0.818031\pi\)
\(488\) 11914.5 + 36669.1i 0.0500307 + 0.153979i
\(489\) −27001.2 + 19617.5i −0.112919 + 0.0820402i
\(490\) 6567.20 + 9038.98i 0.0273520 + 0.0376467i
\(491\) 212925. 69183.6i 0.883210 0.286972i 0.167921 0.985801i \(-0.446295\pi\)
0.715290 + 0.698828i \(0.246295\pi\)
\(492\) −1202.63 390.757i −0.00496822 0.00161427i
\(493\) 178232. + 129493.i 0.733318 + 0.532786i
\(494\) 57976.6i 0.237574i
\(495\) −41353.7 + 43927.7i −0.168773 + 0.179278i
\(496\) 66315.8 0.269559
\(497\) 55675.4 76630.5i 0.225398 0.310234i
\(498\) 70332.8 216462.i 0.283595 0.872816i
\(499\) −128358. 395046.i −0.515492 1.58652i −0.782384 0.622796i \(-0.785997\pi\)
0.266892 0.963726i \(-0.414003\pi\)
\(500\) 22005.3 15987.8i 0.0880211 0.0639511i
\(501\) 53098.5 + 73083.9i 0.211547 + 0.291170i
\(502\) 192211. 62453.2i 0.762731 0.247826i
\(503\) −319477. 103805.i −1.26271 0.410280i −0.400252 0.916405i \(-0.631077\pi\)
−0.862460 + 0.506125i \(0.831077\pi\)
\(504\) −67461.0 49013.3i −0.265578 0.192954i
\(505\) 154308.i 0.605070i
\(506\) −50772.4 267967.i −0.198302 1.04660i
\(507\) 126100. 0.490570
\(508\) −16608.4 + 22859.5i −0.0643576 + 0.0885806i
\(509\) 69443.4 213725.i 0.268038 0.824935i −0.722940 0.690910i \(-0.757210\pi\)
0.990978 0.134024i \(-0.0427901\pi\)
\(510\) 75236.1 + 231553.i 0.289258 + 0.890245i
\(511\) 100217. 72811.7i 0.383794 0.278843i
\(512\) −124497. 171355.i −0.474917 0.653667i
\(513\) 48712.9 15827.8i 0.185101 0.0601430i
\(514\) −100768. 32741.5i −0.381414 0.123929i
\(515\) −189880. 137956.i −0.715919 0.520146i
\(516\) 24520.8i 0.0920950i
\(517\) 3366.08 + 6140.93i 0.0125934 + 0.0229749i
\(518\) 492895. 1.83694
\(519\) −2955.56 + 4067.98i −0.0109725 + 0.0151023i
\(520\) −72661.7 + 223630.i −0.268719 + 0.827033i
\(521\) 65350.4 + 201128.i 0.240754 + 0.740964i 0.996306 + 0.0858752i \(0.0273686\pi\)
−0.755552 + 0.655088i \(0.772631\pi\)
\(522\) 47111.1 34228.2i 0.172895 0.125616i
\(523\) −79321.4 109177.i −0.289993 0.399141i 0.639019 0.769191i \(-0.279340\pi\)
−0.929012 + 0.370050i \(0.879340\pi\)
\(524\) 28417.6 9233.45i 0.103496 0.0336280i
\(525\) −103112. 33503.0i −0.374101 0.121553i
\(526\) −250599. 182071.i −0.905748 0.658064i
\(527\) 103227.i 0.371682i
\(528\) −223848. 105675.i −0.802945 0.379057i
\(529\) 8393.49 0.0299938
\(530\) −51457.8 + 70825.7i −0.183189 + 0.252138i
\(531\) 16331.0 50261.6i 0.0579193 0.178257i
\(532\) 1637.03 + 5038.27i 0.00578407 + 0.0178015i
\(533\) −18379.7 + 13353.6i −0.0646969 + 0.0470050i
\(534\) −200658. 276182.i −0.703677 0.968528i
\(535\) −55793.0 + 18128.2i −0.194927 + 0.0633356i
\(536\) 498867. + 162092.i 1.73642 + 0.564197i
\(537\) 81957.3 + 59545.5i 0.284210 + 0.206491i
\(538\) 593752.i 2.05135i
\(539\) −2237.96 + 17540.0i −0.00770325 + 0.0603742i
\(540\) 23505.3 0.0806081
\(541\) −36527.6 + 50275.9i −0.124803 + 0.171777i −0.866847 0.498575i \(-0.833857\pi\)
0.742043 + 0.670352i \(0.233857\pi\)
\(542\) −132102. + 406568.i −0.449687 + 1.38400i
\(543\) −46207.6 142212.i −0.156716 0.482323i
\(544\) 72966.8 53013.5i 0.246563 0.179138i
\(545\) 150825. + 207593.i 0.507786 + 0.698908i
\(546\) −315737. + 102589.i −1.05911 + 0.344125i
\(547\) −338850. 110099.i −1.13249 0.367967i −0.317966 0.948102i \(-0.603000\pi\)
−0.814520 + 0.580135i \(0.803000\pi\)
\(548\) −27944.2 20302.7i −0.0930531 0.0676071i
\(549\) 17493.1i 0.0580395i
\(550\) 147832. + 18862.2i 0.488702 + 0.0623543i
\(551\) 32695.5 0.107692
\(552\) 139446. 191931.i 0.457644 0.629893i
\(553\) −59845.8 + 184186.i −0.195697 + 0.602292i
\(554\) 35139.2 + 108147.i 0.114491 + 0.352368i
\(555\) 250958. 182332.i 0.814733 0.591938i
\(556\) 3890.50 + 5354.81i 0.0125851 + 0.0173218i
\(557\) 376433. 122311.i 1.21333 0.394234i 0.368679 0.929557i \(-0.379810\pi\)
0.844647 + 0.535323i \(0.179810\pi\)
\(558\) −25949.9 8431.64i −0.0833427 0.0270797i
\(559\) 356409. + 258946.i 1.14058 + 0.828679i
\(560\) 256771.i 0.818786i
\(561\) −164493. + 348441.i −0.522662 + 1.10714i
\(562\) −556931. −1.76331
\(563\) 254804. 350707.i 0.803876 1.10644i −0.188363 0.982099i \(-0.560318\pi\)
0.992240 0.124341i \(-0.0396817\pi\)
\(564\) 212.995 655.531i 0.000669593 0.00206080i
\(565\) −8398.14 25846.8i −0.0263079 0.0809674i
\(566\) −285996. + 207788.i −0.892744 + 0.648617i
\(567\) −106606. 146730.i −0.331600 0.456409i
\(568\) −107714. + 34998.4i −0.333869 + 0.108481i
\(569\) 81414.7 + 26453.2i 0.251466 + 0.0817061i 0.432037 0.901856i \(-0.357795\pi\)
−0.180572 + 0.983562i \(0.557795\pi\)
\(570\) 29232.2 + 21238.4i 0.0899728 + 0.0653691i
\(571\) 474437.i 1.45514i 0.686031 + 0.727572i \(0.259351\pi\)
−0.686031 + 0.727572i \(0.740649\pi\)
\(572\) 36923.9 20239.4i 0.112854 0.0618593i
\(573\) 53694.9 0.163540
\(574\) 13223.9 18201.2i 0.0401362 0.0552428i
\(575\) −48670.3 + 149792.i −0.147207 + 0.453056i
\(576\) 30452.5 + 93723.0i 0.0917862 + 0.282489i
\(577\) 499816. 363138.i 1.50127 1.09074i 0.531396 0.847123i \(-0.321668\pi\)
0.969873 0.243612i \(-0.0783325\pi\)
\(578\) −260585. 358664.i −0.779998 1.07358i
\(579\) −250591. + 81421.8i −0.747494 + 0.242875i
\(580\) 14270.0 + 4636.59i 0.0424196 + 0.0137830i
\(581\) 302281. + 219620.i 0.895485 + 0.650608i
\(582\) 377862.i 1.11554i
\(583\) −136128. + 25792.6i −0.400507 + 0.0758853i
\(584\) −148117. −0.434289
\(585\) 62707.0 86308.8i 0.183233 0.252199i
\(586\) 156544. 481794.i 0.455871 1.40303i
\(587\) 52321.6 + 161029.i 0.151846 + 0.467335i 0.997828 0.0658772i \(-0.0209846\pi\)
−0.845981 + 0.533213i \(0.820985\pi\)
\(588\) 1407.98 1022.96i 0.00407233 0.00295872i
\(589\) −9004.72 12393.9i −0.0259561 0.0357255i
\(590\) 140354. 45603.9i 0.403202 0.131008i
\(591\) 276211. + 89746.5i 0.790800 + 0.256946i
\(592\) −525770. 381994.i −1.50021 1.08997i
\(593\) 519770.i 1.47809i −0.673654 0.739047i \(-0.735276\pi\)
0.673654 0.739047i \(-0.264724\pi\)
\(594\) 293549. + 276348.i 0.831971 + 0.783220i
\(595\) −399688. −1.12898
\(596\) −17205.3 + 23681.0i −0.0484361 + 0.0666666i
\(597\) −20333.3 + 62579.4i −0.0570504 + 0.175583i
\(598\) 149033. + 458677.i 0.416755 + 1.28264i
\(599\) −364603. + 264899.i −1.01617 + 0.738291i −0.965494 0.260425i \(-0.916137\pi\)
−0.0506757 + 0.998715i \(0.516137\pi\)
\(600\) 76197.6 + 104877.i 0.211660 + 0.291325i
\(601\) 18199.0 5913.22i 0.0503848 0.0163710i −0.283716 0.958908i \(-0.591567\pi\)
0.334101 + 0.942537i \(0.391567\pi\)
\(602\) −414915. 134814.i −1.14490 0.371999i
\(603\) −192535. 139885.i −0.529511 0.384713i
\(604\) 14361.6i 0.0393667i
\(605\) −169442. 205860.i −0.462925 0.562420i
\(606\) 260499. 0.709351
\(607\) 179595. 247192.i 0.487436 0.670898i −0.492477 0.870326i \(-0.663908\pi\)
0.979913 + 0.199428i \(0.0639083\pi\)
\(608\) 4136.27 12730.1i 0.0111893 0.0344371i
\(609\) −57854.5 178058.i −0.155992 0.480094i
\(610\) 39519.9 28712.9i 0.106208 0.0771644i
\(611\) −7278.82 10018.4i −0.0194975 0.0268360i
\(612\) −18416.9 + 5984.03i −0.0491716 + 0.0159768i
\(613\) 471453. + 153184.i 1.25463 + 0.407656i 0.859580 0.511002i \(-0.170725\pi\)
0.395055 + 0.918657i \(0.370725\pi\)
\(614\) 443538. + 322249.i 1.17650 + 0.854781i
\(615\) 14158.9i 0.0374352i
\(616\) 252602. 268325.i 0.665694 0.707129i
\(617\) −481904. −1.26587 −0.632937 0.774203i \(-0.718151\pi\)
−0.632937 + 0.774203i \(0.718151\pi\)
\(618\) −232894. + 320550.i −0.609790 + 0.839304i
\(619\) 172028. 529448.i 0.448971 1.38179i −0.429099 0.903257i \(-0.641169\pi\)
0.878070 0.478532i \(-0.158831\pi\)
\(620\) −2172.51 6686.31i −0.00565170 0.0173942i
\(621\) −344702. + 250440.i −0.893840 + 0.649413i
\(622\) 243745. + 335486.i 0.630020 + 0.867148i
\(623\) 532993. 173180.i 1.37324 0.446191i
\(624\) 416303. + 135265.i 1.06915 + 0.347389i
\(625\) 98059.8 + 71244.6i 0.251033 + 0.182386i
\(626\) 263687.i 0.672885i
\(627\) 10645.5 + 56184.7i 0.0270788 + 0.142917i
\(628\) 31527.3 0.0799407
\(629\) −594609. + 818409.i −1.50290 + 2.06857i
\(630\) −32646.9 + 100477.i −0.0822546 + 0.253154i
\(631\) −122608. 377349.i −0.307936 0.947730i −0.978565 0.205937i \(-0.933976\pi\)
0.670629 0.741793i \(-0.266024\pi\)
\(632\) 187340. 136110.i 0.469025 0.340767i
\(633\) 30325.5 + 41739.5i 0.0756835 + 0.104169i
\(634\) 78564.8 25527.3i 0.195456 0.0635076i
\(635\) −300899. 97768.1i −0.746232 0.242465i
\(636\) 11032.4 + 8015.49i 0.0272744 + 0.0198160i
\(637\) 31267.7i 0.0770579i
\(638\) 123701. + 225674.i 0.303900 + 0.554422i
\(639\) 51385.4 0.125846
\(640\) −197271. + 271521.i −0.481620 + 0.662893i
\(641\) −220138. + 677516.i −0.535771 + 1.64893i 0.206205 + 0.978509i \(0.433889\pi\)
−0.741976 + 0.670426i \(0.766111\pi\)
\(642\) 30603.7 + 94188.4i 0.0742512 + 0.228522i
\(643\) −93657.4 + 68046.1i −0.226527 + 0.164582i −0.695260 0.718758i \(-0.744711\pi\)
0.468733 + 0.883340i \(0.344711\pi\)
\(644\) −25902.5 35651.7i −0.0624553 0.0859624i
\(645\) −261125. + 84844.6i −0.627666 + 0.203941i
\(646\) −112067. 36412.9i −0.268543 0.0872549i
\(647\) −453337. 329369.i −1.08296 0.786817i −0.104764 0.994497i \(-0.533409\pi\)
−0.978197 + 0.207680i \(0.933409\pi\)
\(648\) 216862.i 0.516457i
\(649\) 211205. + 99706.4i 0.501436 + 0.236719i
\(650\) −263534. −0.623748
\(651\) −51562.9 + 70970.3i −0.121668 + 0.167461i
\(652\) 2290.69 7050.01i 0.00538853 0.0165842i
\(653\) −125501. 386251.i −0.294320 0.905823i −0.983449 0.181184i \(-0.942007\pi\)
0.689129 0.724638i \(-0.257993\pi\)
\(654\) 350454. 254620.i 0.819361 0.595301i
\(655\) 196656. + 270673.i 0.458378 + 0.630903i
\(656\) −28211.8 + 9166.58i −0.0655577 + 0.0213010i
\(657\) 63912.3 + 20766.4i 0.148065 + 0.0481094i
\(658\) 9921.15 + 7208.13i 0.0229145 + 0.0166483i
\(659\) 237251.i 0.546307i 0.961970 + 0.273154i \(0.0880667\pi\)
−0.961970 + 0.273154i \(0.911933\pi\)
\(660\) −3321.40 + 26031.5i −0.00762490 + 0.0597601i
\(661\) 202580. 0.463655 0.231827 0.972757i \(-0.425530\pi\)
0.231827 + 0.972757i \(0.425530\pi\)
\(662\) −71089.4 + 97846.2i −0.162214 + 0.223269i
\(663\) 210552. 648014.i 0.478998 1.47420i
\(664\) −138057. 424895.i −0.313127 0.963707i
\(665\) −47988.7 + 34865.8i −0.108516 + 0.0788418i
\(666\) 157170. + 216326.i 0.354341 + 0.487708i
\(667\) −258668. + 84046.2i −0.581420 + 0.188915i
\(668\) −19082.2 6200.17i −0.0427636 0.0138947i
\(669\) −75807.4 55077.3i −0.169379 0.123061i
\(670\) 664572.i 1.48045i
\(671\) 76687.6 + 9784.71i 0.170326 + 0.0217322i
\(672\) −76646.8 −0.169729
\(673\) 122108. 168067.i 0.269596 0.371066i −0.652658 0.757653i \(-0.726346\pi\)
0.922253 + 0.386587i \(0.126346\pi\)
\(674\) 243913. 750687.i 0.536927 1.65249i
\(675\) −71945.5 221425.i −0.157905 0.485982i
\(676\) −22658.5 + 16462.4i −0.0495836 + 0.0360246i
\(677\) 212149. + 291998.i 0.462875 + 0.637093i 0.975102 0.221758i \(-0.0711794\pi\)
−0.512227 + 0.858850i \(0.671179\pi\)
\(678\) −43634.0 + 14177.5i −0.0949217 + 0.0308419i
\(679\) 589952. + 191687.i 1.27961 + 0.415770i
\(680\) 386635. + 280907.i 0.836148 + 0.607497i
\(681\) 412189.i 0.888797i
\(682\) 51478.2 109045.i 0.110676 0.234442i
\(683\) 310133. 0.664824 0.332412 0.943134i \(-0.392138\pi\)
0.332412 + 0.943134i \(0.392138\pi\)
\(684\) −1689.23 + 2325.03i −0.00361058 + 0.00496954i
\(685\) 119515. 367830.i 0.254708 0.783910i
\(686\) −147642. 454396.i −0.313735 0.965576i
\(687\) −532429. + 386832.i −1.12810 + 0.819613i
\(688\) 338107. + 465365.i 0.714295 + 0.983143i
\(689\) 233009. 75709.3i 0.490834 0.159482i
\(690\) −285863. 92882.4i −0.600426 0.195090i
\(691\) 27576.4 + 20035.5i 0.0577540 + 0.0419607i 0.616288 0.787521i \(-0.288636\pi\)
−0.558534 + 0.829482i \(0.688636\pi\)
\(692\) 1116.81i 0.00233220i
\(693\) −146617. + 80366.5i −0.305294 + 0.167343i
\(694\) −121857. −0.253006
\(695\) −43562.3 + 59958.4i −0.0901865 + 0.124131i
\(696\) −69176.6 + 212904.i −0.142804 + 0.439506i
\(697\) 14268.6 + 43914.3i 0.0293709 + 0.0903943i
\(698\) −321909. + 233880.i −0.660726 + 0.480046i
\(699\) 106806. + 147005.i 0.218595 + 0.300870i
\(700\) 22901.5 7441.16i 0.0467378 0.0151860i
\(701\) −154914. 50334.5i −0.315249 0.102431i 0.147119 0.989119i \(-0.453000\pi\)
−0.462368 + 0.886688i \(0.653000\pi\)
\(702\) −576763. 419043.i −1.17037 0.850324i
\(703\) 150132.i 0.303782i
\(704\) −427903. + 81075.9i −0.863375 + 0.163586i
\(705\) 7717.79 0.0155280
\(706\) 264082. 363477.i 0.529821 0.729236i
\(707\) −132150. + 406715.i −0.264380 + 0.813677i
\(708\) −7103.64 21862.8i −0.0141715 0.0436152i
\(709\) −42019.7 + 30529.1i −0.0835912 + 0.0607326i −0.628796 0.777570i \(-0.716452\pi\)
0.545205 + 0.838303i \(0.316452\pi\)
\(710\) 84342.9 + 116088.i 0.167314 + 0.230288i
\(711\) −99920.2 + 32466.0i −0.197658 + 0.0642229i
\(712\) −637299. 207071.i −1.25714 0.408469i
\(713\) 103100. + 74906.3i 0.202805 + 0.147346i
\(714\) 674745.i 1.32356i
\(715\) 343291. + 323176.i 0.671507 + 0.632159i
\(716\) −22500.3 −0.0438896
\(717\) −144363. + 198698.i −0.280813 + 0.386506i
\(718\) −87518.6 + 269354.i −0.169766 + 0.522487i
\(719\) 298239. + 917885.i 0.576908 + 1.77554i 0.629589 + 0.776929i \(0.283223\pi\)
−0.0526809 + 0.998611i \(0.516777\pi\)
\(720\) 112694. 81876.8i 0.217388 0.157941i
\(721\) −382327. 526228.i −0.735470 1.01229i
\(722\) 503726. 163671.i 0.966319 0.313976i
\(723\) 500157. + 162511.i 0.956818 + 0.310889i
\(724\) 26868.7 + 19521.2i 0.0512589 + 0.0372417i
\(725\) 148618.i 0.282745i
\(726\) −347528. + 286048.i −0.659350 + 0.542708i
\(727\) −138074. −0.261241 −0.130621 0.991432i \(-0.541697\pi\)
−0.130621 + 0.991432i \(0.541697\pi\)
\(728\) −383035. + 527202.i −0.722729 + 0.994751i
\(729\) 175866. 541259.i 0.330922 1.01847i
\(730\) 57989.7 + 178474.i 0.108819 + 0.334911i
\(731\) 724384. 526296.i 1.35561 0.984906i
\(732\) −4472.55 6155.94i −0.00834705 0.0114887i
\(733\) −512975. + 166676.i −0.954746 + 0.310216i −0.744643 0.667463i \(-0.767380\pi\)
−0.210104 + 0.977679i \(0.567380\pi\)
\(734\) 651580. + 211711.i 1.20942 + 0.392963i
\(735\) 15765.4 + 11454.2i 0.0291830 + 0.0212027i
\(736\) 111346.i 0.205551i
\(737\) 720930. 765804.i 1.32727 1.40988i
\(738\) 12205.0 0.0224091
\(739\) 115460. 158917.i 0.211419 0.290993i −0.690117 0.723698i \(-0.742441\pi\)
0.901536 + 0.432705i \(0.142441\pi\)
\(740\) −21290.4 + 65525.0i −0.0388794 + 0.119659i
\(741\) −31247.8 96170.9i −0.0569093 0.175149i
\(742\) −196285. + 142609.i −0.356516 + 0.259024i
\(743\) −510591. 702769.i −0.924902 1.27302i −0.961815 0.273700i \(-0.911752\pi\)
0.0369131 0.999318i \(-0.488248\pi\)
\(744\) 99757.8 32413.3i 0.180219 0.0585568i
\(745\) −311714. 101282.i −0.561621 0.182482i
\(746\) 427062. + 310278.i 0.767384 + 0.557537i
\(747\) 202698.i 0.363252i
\(748\) −15931.7 84084.5i −0.0284747 0.150284i
\(749\) −162581. −0.289805
\(750\) 302212. 415960.i 0.537266 0.739484i
\(751\) −213891. + 658290.i −0.379239 + 1.16718i 0.561335 + 0.827589i \(0.310288\pi\)
−0.940574 + 0.339589i \(0.889712\pi\)
\(752\) −4996.54 15377.8i −0.00883556 0.0271931i
\(753\) 285177. 207193.i 0.502950 0.365415i
\(754\) −267491. 368169.i −0.470507 0.647597i
\(755\) −152938. + 49692.5i −0.268300 + 0.0871761i
\(756\) 61953.9 + 20130.0i 0.108399 + 0.0352209i
\(757\) −61422.9 44626.4i −0.107186 0.0778753i 0.532901 0.846178i \(-0.321102\pi\)
−0.640087 + 0.768302i \(0.721102\pi\)
\(758\) 405043.i 0.704957i
\(759\) −228648. 417135.i −0.396902 0.724092i
\(760\) 70925.6 0.122794
\(761\) 327846. 451241.i 0.566109 0.779182i −0.425978 0.904733i \(-0.640070\pi\)
0.992087 + 0.125551i \(0.0400700\pi\)
\(762\) −165050. + 507971.i −0.284253 + 0.874841i
\(763\) 219752. + 676328.i 0.377472 + 1.16174i
\(764\) −9648.24 + 7009.85i −0.0165296 + 0.0120094i
\(765\) −127449. 175418.i −0.217778 0.299745i
\(766\) −610482. + 198358.i −1.04044 + 0.338058i
\(767\) −392790. 127625.i −0.667682 0.216943i
\(768\) 117212. + 85159.5i 0.198724 + 0.144381i
\(769\) 113451.i 0.191848i −0.995389 0.0959239i \(-0.969419\pi\)
0.995389 0.0959239i \(-0.0305805\pi\)
\(770\) −422215. 199321.i −0.712119 0.336179i
\(771\) −184800. −0.310880
\(772\) 34398.1 47344.9i 0.0577165 0.0794399i
\(773\) −120125. + 369706.i −0.201036 + 0.618724i 0.798817 + 0.601574i \(0.205459\pi\)
−0.999853 + 0.0171505i \(0.994541\pi\)
\(774\) −73136.0 225089.i −0.122081 0.375728i
\(775\) −56336.9 + 40931.2i −0.0937971 + 0.0681476i
\(776\) −435965. 600054.i −0.723982 0.996476i
\(777\) 817609. 265657.i 1.35427 0.440028i
\(778\) 139583. + 45353.2i 0.230607 + 0.0749289i
\(779\) 5543.92 + 4027.90i 0.00913571 + 0.00663748i
\(780\) 46405.1i 0.0762740i
\(781\) −28742.2 + 225267.i −0.0471214 + 0.369313i
\(782\) 980213. 1.60290
\(783\) 236316. 325262.i 0.385452 0.530529i
\(784\) 12616.0 38828.2i 0.0205254 0.0631706i
\(785\) 109088. + 335738.i 0.177026 + 0.544830i
\(786\) 456945. 331990.i 0.739637 0.537377i
\(787\) 190393. + 262053.i 0.307398 + 0.423097i 0.934568 0.355786i \(-0.115787\pi\)
−0.627169 + 0.778883i \(0.715787\pi\)
\(788\) −61347.8 + 19933.1i −0.0987976 + 0.0321013i
\(789\) −513821. 166951.i −0.825388 0.268185i
\(790\) −237353. 172447.i −0.380312 0.276313i
\(791\) 75317.6i 0.120377i
\(792\) 198312. + 25302.9i 0.316153 + 0.0403386i
\(793\) −136707. −0.217393
\(794\) −50483.2 + 69484.2i −0.0800767 + 0.110216i
\(795\) −47184.6 + 145219.i −0.0746562 + 0.229768i
\(796\) −4516.11 13899.2i −0.00712752 0.0219362i
\(797\) −561981. + 408303.i −0.884718 + 0.642785i −0.934495 0.355975i \(-0.884149\pi\)
0.0497774 + 0.998760i \(0.484149\pi\)
\(798\) 58859.7 + 81013.4i 0.0924298 + 0.127219i
\(799\) −23936.9 + 7777.58i −0.0374952 + 0.0121829i
\(800\) −57865.1 18801.5i −0.0904142 0.0293774i
\(801\) 245962. + 178702.i 0.383357 + 0.278525i
\(802\) 798039.i 1.24073i
\(803\) −126786. + 268567.i −0.196626 + 0.416507i
\(804\) −103519. −0.160143
\(805\) 290033. 399196.i 0.447565 0.616020i
\(806\) −65892.6 + 202796.i −0.101430 + 0.312169i
\(807\) 320016. + 984909.i 0.491388 + 1.51234i
\(808\) 413679. 300556.i 0.633638 0.460365i
\(809\) −334920. 460978.i −0.511734 0.704341i 0.472477 0.881343i \(-0.343360\pi\)
−0.984211 + 0.177002i \(0.943360\pi\)
\(810\) 261309. 84904.5i 0.398276 0.129408i
\(811\) 115629. + 37570.0i 0.175802 + 0.0571215i 0.395595 0.918425i \(-0.370538\pi\)
−0.219793 + 0.975546i \(0.570538\pi\)
\(812\) 33641.1 + 24441.7i 0.0510220 + 0.0370697i
\(813\) 745610.i 1.12806i
\(814\) −1.03625e6 + 568011.i −1.56393 + 0.857250i
\(815\) 83002.2 0.124961
\(816\) 522928. 719748.i 0.785346 1.08094i
\(817\) 41063.2 126380.i 0.0615189 0.189336i
\(818\) −244516. 752542.i −0.365427 1.12467i
\(819\) 239194. 173785.i 0.356602 0.259086i
\(820\) 1848.45 + 2544.17i 0.00274903 + 0.00378371i
\(821\) −603167. + 195981.i −0.894853 + 0.290755i −0.720111 0.693859i \(-0.755909\pi\)
−0.174742 + 0.984614i \(0.555909\pi\)
\(822\) −620962. 201763.i −0.919013 0.298605i
\(823\) −87568.3 63622.1i −0.129285 0.0939309i 0.521264 0.853396i \(-0.325461\pi\)
−0.650548 + 0.759465i \(0.725461\pi\)
\(824\) 777747.i 1.14547i
\(825\) 255389. 48389.2i 0.375227 0.0710953i
\(826\) 408993. 0.599454
\(827\) 186226. 256318.i 0.272288 0.374773i −0.650872 0.759187i \(-0.725597\pi\)
0.923161 + 0.384414i \(0.125597\pi\)
\(828\) 7387.55 22736.6i 0.0107756 0.0331638i
\(829\) 251882. + 775214.i 0.366512 + 1.12801i 0.949029 + 0.315190i \(0.102068\pi\)
−0.582516 + 0.812819i \(0.697932\pi\)
\(830\) −457927. + 332704.i −0.664722 + 0.482949i
\(831\) 116577. + 160454.i 0.168815 + 0.232354i
\(832\) 732437. 237983.i 1.05809 0.343795i
\(833\) −60439.7 19638.0i −0.0871028 0.0283014i
\(834\) 101220. + 73540.9i 0.145524 + 0.105730i
\(835\) 224661.i 0.322222i
\(836\) −9247.74 8705.86i −0.0132319 0.0124566i
\(837\) −188382. −0.268898
\(838\) 84731.6 116623.i 0.120658 0.166072i
\(839\) 80718.2 248425.i 0.114669 0.352916i −0.877208 0.480110i \(-0.840597\pi\)
0.991878 + 0.127193i \(0.0405969\pi\)
\(840\) −125502. 386257.i −0.177866 0.547416i
\(841\) −364576. + 264880.i −0.515461 + 0.374504i
\(842\) 649195. + 893540.i 0.915695 + 1.26035i
\(843\) −923830. + 300171.i −1.29998 + 0.422389i
\(844\) −10898.2 3541.03i −0.0152992 0.00497101i
\(845\) −253710. 184331.i −0.355324 0.258158i
\(846\) 6652.73i 0.00929521i
\(847\) −270306. 687703.i −0.376781 0.958593i
\(848\) 319898. 0.444857
\(849\) −362415. + 498821.i −0.502794 + 0.692037i
\(850\) −165515. + 509404.i −0.229087 + 0.705057i
\(851\) −385925. 1.18775e6i −0.532897 1.64009i
\(852\) 18082.8 13137.9i 0.0249108 0.0180987i
\(853\) −494677. 680864.i −0.679866 0.935756i 0.320066 0.947395i \(-0.396295\pi\)
−0.999932 + 0.0116396i \(0.996295\pi\)
\(854\) 128754. 41834.7i 0.176541 0.0573615i
\(855\) −30604.3 9943.96i −0.0418650 0.0136028i
\(856\) 157271. + 114264.i 0.214635 + 0.155942i
\(857\) 93389.0i 0.127155i −0.997977 0.0635776i \(-0.979749\pi\)
0.997977 0.0635776i \(-0.0202510\pi\)
\(858\) 545578. 579536.i 0.741109 0.787238i
\(859\) 1.16761e6 1.58238 0.791190 0.611571i \(-0.209462\pi\)
0.791190 + 0.611571i \(0.209462\pi\)
\(860\) 35844.1 49335.2i 0.0484642 0.0667052i
\(861\) 12125.8 37319.3i 0.0163570 0.0503416i
\(862\) −283994. 874044.i −0.382204 1.17630i
\(863\) 763401. 554643.i 1.02502 0.744718i 0.0577115 0.998333i \(-0.481620\pi\)
0.967305 + 0.253615i \(0.0816197\pi\)
\(864\) −96746.0 133159.i −0.129600 0.178379i
\(865\) 11893.0 3864.27i 0.0158949 0.00516458i
\(866\) −277428. 90141.8i −0.369926 0.120196i
\(867\) −625566. 454500.i −0.832214 0.604639i
\(868\) 19483.9i 0.0258605i
\(869\) −86436.8 456196.i −0.114461 0.604105i
\(870\) 283622. 0.374716
\(871\) −1.09319e6 + 1.50465e6i −1.44098 + 1.98334i
\(872\) 262758. 808684.i 0.345559 1.06352i
\(873\) 103989. + 320046.i 0.136446 + 0.419937i
\(874\) 117689. 85506.4i 0.154069 0.111937i
\(875\) 496124. + 682856.i 0.647998 + 0.891893i
\(876\) 27800.5 9032.94i 0.0362280 0.0117712i
\(877\) 982991. + 319393.i 1.27806 + 0.415266i 0.867895 0.496747i \(-0.165472\pi\)
0.410162 + 0.912013i \(0.365472\pi\)
\(878\) 244570. + 177691.i 0.317260 + 0.230503i
\(879\) 883568.i 1.14357i
\(880\) 295902. + 539832.i 0.382105 + 0.697097i
\(881\) 609739. 0.785584 0.392792 0.919627i \(-0.371509\pi\)
0.392792 + 0.919627i \(0.371509\pi\)
\(882\) −9873.52 + 13589.7i −0.0126921 + 0.0174692i
\(883\) 96058.9 295639.i 0.123202 0.379175i −0.870368 0.492403i \(-0.836119\pi\)
0.993569 + 0.113227i \(0.0361188\pi\)
\(884\) 46764.6 + 143927.i 0.0598430 + 0.184178i
\(885\) 208239. 151295.i 0.265874 0.193169i
\(886\) −110204. 151683.i −0.140388 0.193228i
\(887\) −249889. + 81194.0i −0.317615 + 0.103199i −0.463486 0.886104i \(-0.653402\pi\)
0.145871 + 0.989304i \(0.453402\pi\)
\(888\) −977614. 317646.i −1.23977 0.402826i
\(889\) −709362. 515382.i −0.897562 0.652117i
\(890\) 848986.i 1.07182i
\(891\) 393218. + 185631.i 0.495311 + 0.233828i
\(892\) 20811.9 0.0261566
\(893\) −2195.54 + 3021.90i −0.00275320 + 0.00378945i
\(894\) −170982. + 526228.i −0.213932 + 0.658413i
\(895\) −77853.1 239607.i −0.0971919 0.299126i
\(896\) −752487. + 546714.i −0.937310 + 0.680995i
\(897\) 494429. + 680523.i 0.614496 + 0.845781i
\(898\) 516455. 167806.i 0.640442 0.208092i
\(899\) −114366. 37159.6i −0.141506 0.0459782i
\(900\) 10568.5 + 7678.44i 0.0130475 + 0.00947955i
\(901\) 497951.i 0.613391i
\(902\) −6826.81 + 53505.1i −0.00839082 + 0.0657630i
\(903\) −760918. −0.933173
\(904\) −52934.3 + 72857.8i −0.0647739 + 0.0891536i
\(905\) −114915. + 353672.i −0.140307 + 0.431821i
\(906\) 83889.8 + 258186.i 0.102200 + 0.314541i
\(907\) −228786. + 166222.i −0.278108 + 0.202058i −0.718092 0.695948i \(-0.754984\pi\)
0.439984 + 0.898006i \(0.354984\pi\)
\(908\) 53811.2 + 74064.8i 0.0652681 + 0.0898338i
\(909\) −220641. + 71690.6i −0.267029 + 0.0867630i
\(910\) 785217. + 255132.i 0.948215 + 0.308094i
\(911\) 1.12857e6 + 819956.i 1.35985 + 0.987992i 0.998454 + 0.0555816i \(0.0177013\pi\)
0.361401 + 0.932411i \(0.382299\pi\)
\(912\) 132033.i 0.158742i
\(913\) −888599. 113378.i −1.06602 0.136015i
\(914\) −1.28842e6 −1.54228
\(915\) 50079.7 68928.7i 0.0598163 0.0823300i
\(916\) 45169.3 139017.i 0.0538335 0.165682i
\(917\) 286527. + 881840.i 0.340743 + 1.04870i
\(918\) −1.17224e6 + 851684.i −1.39102 + 1.01063i
\(919\) −85147.5 117196.i −0.100819 0.138765i 0.755627 0.655002i \(-0.227332\pi\)
−0.856446 + 0.516237i \(0.827332\pi\)
\(920\) −561122. + 182319.i −0.662951 + 0.215406i
\(921\) 909419. + 295488.i 1.07212 + 0.348354i
\(922\) −77491.6 56301.0i −0.0911576 0.0662299i
\(923\) 401573.i 0.471369i
\(924\) −31047.8 + 65767.7i −0.0363653 + 0.0770316i
\(925\) 682427. 0.797577
\(926\) −611859. + 842151.i −0.713558 + 0.982128i
\(927\) 109042. 335597.i 0.126892 0.390534i
\(928\) −32467.3 99924.2i −0.0377008 0.116031i
\(929\) −562289. + 408527.i −0.651521 + 0.473358i −0.863789 0.503854i \(-0.831915\pi\)
0.212268 + 0.977211i \(0.431915\pi\)
\(930\) −78113.0 107513.i −0.0903145 0.124307i
\(931\) −8969.78 + 2914.46i −0.0103486 + 0.00336247i
\(932\) −38383.0 12471.4i −0.0441883 0.0143576i
\(933\) 585138. + 425128.i 0.672195 + 0.488378i
\(934\) 1.35611e6i 1.55453i
\(935\) 840298. 460599.i 0.961192 0.526866i
\(936\) −353521. −0.403518
\(937\) 647243. 890854.i 0.737205 1.01468i −0.261569 0.965185i \(-0.584240\pi\)
0.998775 0.0494911i \(-0.0157599\pi\)
\(938\) 569142. 1.75164e6i 0.646867 1.99085i
\(939\) −142120. 437402.i −0.161185 0.496077i
\(940\) −1386.78 + 1007.56i −0.00156947 + 0.00114028i
\(941\) 497946. + 685364.i 0.562345 + 0.774002i 0.991622 0.129171i \(-0.0412316\pi\)
−0.429277 + 0.903173i \(0.641232\pi\)
\(942\) 566785. 184160.i 0.638728 0.207535i
\(943\) −54214.3 17615.3i −0.0609664 0.0198092i
\(944\) −436271. 316970.i −0.489568 0.355692i
\(945\) 729405.i 0.816780i
\(946\) 1.02767e6 194715.i 1.14834 0.217580i
\(947\) −1.75534e6 −1.95732 −0.978660 0.205486i \(-0.934122\pi\)
−0.978660 + 0.205486i \(0.934122\pi\)
\(948\) −26861.7 + 36972.0i −0.0298894 + 0.0411393i
\(949\) 162287. 499469.i 0.180199 0.554595i
\(950\) 24563.9 + 75600.0i 0.0272177 + 0.0837673i
\(951\) 116564. 84688.7i 0.128885 0.0936406i
\(952\) 778499. + 1.07151e6i 0.858982 + 1.18229i
\(953\) 363486. 118104.i 0.400222 0.130040i −0.101988 0.994786i \(-0.532520\pi\)
0.502210 + 0.864746i \(0.332520\pi\)
\(954\) −125179. 40673.1i −0.137542 0.0446900i
\(955\) −108032. 78490.2i −0.118453 0.0860614i
\(956\) 54549.9i 0.0596868i
\(957\) 326825. + 307675.i 0.356855 + 0.335945i
\(958\) −421164. −0.458902
\(959\) 630021. 867150.i 0.685043 0.942881i
\(960\) −148319. + 456479.i −0.160937 + 0.495312i
\(961\) −267972. 824734.i −0.290164 0.893032i
\(962\) 1.69057e6 1.22827e6i 1.82676 1.32722i
\(963\) −51842.2 71354.7i −0.0559024 0.0769431i
\(964\) −111087. + 36094.4i −0.119539 + 0.0388405i
\(965\) 623201. + 202490.i 0.669227 + 0.217445i
\(966\) −673914. 489627.i −0.722188 0.524700i
\(967\) 1.17380e6i 1.25528i −0.778505 0.627639i \(-0.784021\pi\)
0.778505 0.627639i \(-0.215979\pi\)
\(968\) −221849. + 855218.i −0.236759 + 0.912696i
\(969\) −205521. −0.218882
\(970\) −552351. + 760246.i −0.587045 + 0.807999i
\(971\) 38552.4 118652.i 0.0408897 0.125845i −0.928528 0.371263i \(-0.878925\pi\)
0.969418 + 0.245417i \(0.0789250\pi\)
\(972\) 19082.1 + 58728.7i 0.0201973 + 0.0621610i
\(973\) −166167. + 120728.i −0.175517 + 0.127521i
\(974\) −906520. 1.24772e6i −0.955563 1.31522i
\(975\) −437147. + 142038.i −0.459852 + 0.149415i
\(976\) −169763. 55159.4i −0.178215 0.0579055i
\(977\) −326932. 237530.i −0.342506 0.248845i 0.403213 0.915106i \(-0.367894\pi\)
−0.745718 + 0.666261i \(0.767894\pi\)
\(978\) 140122.i 0.146497i
\(979\) −920983. + 978309.i −0.960918 + 1.02073i
\(980\) −4328.17 −0.00450663
\(981\) −226760. + 312108.i −0.235628 + 0.324315i
\(982\) −290459. + 893941.i −0.301205 + 0.927013i
\(983\) 136988. + 421605.i 0.141767 + 0.436314i 0.996581 0.0826204i \(-0.0263289\pi\)
−0.854814 + 0.518934i \(0.826329\pi\)
\(984\) −37958.2 + 27578.3i −0.0392027 + 0.0284824i
\(985\) −424539. 584328.i −0.437567 0.602260i
\(986\) −879663. + 285820.i −0.904821 + 0.293994i
\(987\) 20342.1 + 6609.54i 0.0208815 + 0.00678480i
\(988\) 18169.9 + 13201.2i 0.0186139 + 0.0135238i
\(989\) 1.10540e6i 1.13012i
\(990\) −47152.7 248863.i −0.0481101 0.253916i
\(991\) −790967. −0.805399 −0.402699 0.915332i \(-0.631928\pi\)
−0.402699 + 0.915332i \(0.631928\pi\)
\(992\) −28936.6 + 39827.8i −0.0294052 + 0.0404728i
\(993\) −65185.9 + 200621.i −0.0661081 + 0.203460i
\(994\) 122888. + 378209.i 0.124376 + 0.382789i
\(995\) 132387. 96184.9i 0.133721 0.0971541i
\(996\) 51824.6 + 71330.4i 0.0522417 + 0.0719045i
\(997\) 1.29408e6 420473.i 1.30188 0.423007i 0.425646 0.904890i \(-0.360047\pi\)
0.876236 + 0.481883i \(0.160047\pi\)
\(998\) 1.65855e6 + 538896.i 1.66521 + 0.541058i
\(999\) 1.49354e6 + 1.08512e6i 1.49653 + 1.08730i
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 11.5.d.a.7.1 12
3.2 odd 2 99.5.k.a.73.3 12
4.3 odd 2 176.5.n.a.161.2 12
11.2 odd 10 121.5.d.e.94.1 12
11.3 even 5 121.5.d.d.118.3 12
11.4 even 5 121.5.d.e.112.1 12
11.5 even 5 121.5.b.b.120.3 12
11.6 odd 10 121.5.b.b.120.10 12
11.7 odd 10 121.5.d.c.112.3 12
11.8 odd 10 inner 11.5.d.a.8.1 yes 12
11.9 even 5 121.5.d.c.94.3 12
11.10 odd 2 121.5.d.d.40.3 12
33.8 even 10 99.5.k.a.19.3 12
44.19 even 10 176.5.n.a.129.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.5.d.a.7.1 12 1.1 even 1 trivial
11.5.d.a.8.1 yes 12 11.8 odd 10 inner
99.5.k.a.19.3 12 33.8 even 10
99.5.k.a.73.3 12 3.2 odd 2
121.5.b.b.120.3 12 11.5 even 5
121.5.b.b.120.10 12 11.6 odd 10
121.5.d.c.94.3 12 11.9 even 5
121.5.d.c.112.3 12 11.7 odd 10
121.5.d.d.40.3 12 11.10 odd 2
121.5.d.d.118.3 12 11.3 even 5
121.5.d.e.94.1 12 11.2 odd 10
121.5.d.e.112.1 12 11.4 even 5
176.5.n.a.129.2 12 44.19 even 10
176.5.n.a.161.2 12 4.3 odd 2