Properties

Label 13.5.f.a.2.1
Level $13$
Weight $5$
Character 13.2
Analytic conductor $1.344$
Analytic rank $0$
Dimension $16$
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] = [13,5,Mod(2,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(12))
 
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("13.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 13.f (of order \(12\), 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: \(1.34380952009\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 152 x^{14} + 9190 x^{12} + 285720 x^{10} + 4862025 x^{8} + 43573680 x^{6} + 169417008 x^{4} + 100636992 x^{2} + 3779136 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{4}\cdot 3^{2}\cdot 13^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 2.1
Root \(-4.89748i\) of defining polynomial
Character \(\chi\) \(=\) 13.2
Dual form 13.5.f.a.7.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.34141 - 1.69918i) q^{2} +(7.28678 + 12.6211i) q^{3} +(23.4699 + 13.5504i) q^{4} +(-20.2793 + 20.2793i) q^{5} +(-24.7631 - 92.4170i) q^{6} +(21.3318 - 5.71584i) q^{7} +(-51.5321 - 51.5321i) q^{8} +(-65.6944 + 113.786i) q^{9} +O(q^{10})\) \(q+(-6.34141 - 1.69918i) q^{2} +(7.28678 + 12.6211i) q^{3} +(23.4699 + 13.5504i) q^{4} +(-20.2793 + 20.2793i) q^{5} +(-24.7631 - 92.4170i) q^{6} +(21.3318 - 5.71584i) q^{7} +(-51.5321 - 51.5321i) q^{8} +(-65.6944 + 113.786i) q^{9} +(163.058 - 94.1415i) q^{10} +(19.8619 - 74.1257i) q^{11} +394.954i q^{12} +(162.185 - 47.5081i) q^{13} -144.986 q^{14} +(-403.718 - 108.176i) q^{15} +(22.4185 + 38.8299i) q^{16} +(119.941 + 69.2480i) q^{17} +(609.938 - 609.938i) q^{18} +(57.8912 + 216.053i) q^{19} +(-750.746 + 201.162i) q^{20} +(227.580 + 227.580i) q^{21} +(-251.905 + 436.312i) q^{22} +(491.603 - 283.827i) q^{23} +(274.887 - 1025.89i) q^{24} -197.503i q^{25} +(-1109.21 + 25.6875i) q^{26} -734.346 q^{27} +(578.107 + 154.903i) q^{28} +(-406.589 - 704.232i) q^{29} +(2376.33 + 1371.98i) q^{30} +(-666.232 + 666.232i) q^{31} +(225.607 + 841.977i) q^{32} +(1080.28 - 289.459i) q^{33} +(-642.931 - 642.931i) q^{34} +(-316.681 + 548.508i) q^{35} +(-3083.68 + 1780.37i) q^{36} +(429.906 - 1604.43i) q^{37} -1468.45i q^{38} +(1781.41 + 1700.77i) q^{39} +2090.07 q^{40} +(907.358 + 243.126i) q^{41} +(-1056.48 - 1829.88i) q^{42} +(-2118.01 - 1222.83i) q^{43} +(1470.59 - 1470.59i) q^{44} +(-975.267 - 3639.75i) q^{45} +(-3599.73 + 964.545i) q^{46} +(908.134 + 908.134i) q^{47} +(-326.717 + 565.890i) q^{48} +(-1656.95 + 956.642i) q^{49} +(-335.593 + 1252.45i) q^{50} +2018.38i q^{51} +(4450.22 + 1082.65i) q^{52} +2101.44 q^{53} +(4656.79 + 1247.78i) q^{54} +(1100.43 + 1906.01i) q^{55} +(-1393.82 - 804.723i) q^{56} +(-2304.98 + 2304.98i) q^{57} +(1381.73 + 5156.69i) q^{58} +(-3417.07 + 915.600i) q^{59} +(-8009.41 - 8009.41i) q^{60} +(2816.09 - 4877.60i) q^{61} +(5356.90 - 3092.81i) q^{62} +(-750.998 + 2802.76i) q^{63} -6440.06i q^{64} +(-2325.57 + 4252.44i) q^{65} -7342.31 q^{66} +(-3279.23 - 878.668i) q^{67} +(1876.67 + 3250.49i) q^{68} +(7164.41 + 4136.38i) q^{69} +(2940.22 - 2940.22i) q^{70} +(-1904.53 - 7107.80i) q^{71} +(9249.01 - 2478.26i) q^{72} +(4192.40 + 4192.40i) q^{73} +(-5452.42 + 9443.87i) q^{74} +(2492.71 - 1439.16i) q^{75} +(-1568.89 + 5855.19i) q^{76} -1694.76i q^{77} +(-8406.75 - 13812.2i) q^{78} -3957.00 q^{79} +(-1242.08 - 332.813i) q^{80} +(-29.7681 - 51.5598i) q^{81} +(-5340.82 - 3083.52i) q^{82} +(1386.98 - 1386.98i) q^{83} +(2257.49 + 8425.08i) q^{84} +(-3836.63 + 1028.02i) q^{85} +(11353.4 + 11353.4i) q^{86} +(5925.45 - 10263.2i) q^{87} +(-4843.38 + 2796.32i) q^{88} +(2395.70 - 8940.86i) q^{89} +24738.3i q^{90} +(3188.15 - 1940.46i) q^{91} +15383.8 q^{92} +(-13263.3 - 3553.88i) q^{93} +(-4215.77 - 7301.93i) q^{94} +(-5555.41 - 3207.42i) q^{95} +(-8982.71 + 8982.71i) q^{96} +(751.041 + 2802.92i) q^{97} +(12132.9 - 3251.01i) q^{98} +(7129.65 + 7129.65i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 4 q^{2} - 2 q^{3} - 6 q^{4} + 8 q^{5} - 38 q^{6} + 56 q^{7} + 90 q^{8} - 164 q^{9} - 486 q^{10} - 100 q^{11} + 294 q^{13} + 808 q^{14} + 346 q^{15} + 230 q^{16} + 984 q^{17} + 2434 q^{18} - 1498 q^{19} - 3962 q^{20} - 1076 q^{21} - 1524 q^{22} - 1014 q^{23} - 2142 q^{24} + 614 q^{26} + 3352 q^{27} + 5764 q^{28} + 814 q^{29} + 9162 q^{30} + 4060 q^{31} - 4996 q^{32} - 5636 q^{33} - 2502 q^{34} - 4892 q^{35} - 15750 q^{36} - 1790 q^{37} + 6982 q^{39} + 18816 q^{40} + 4280 q^{41} - 1204 q^{42} - 1368 q^{43} + 10736 q^{44} - 6806 q^{45} - 15246 q^{46} + 1484 q^{47} - 3002 q^{48} - 11820 q^{49} - 13574 q^{50} + 1432 q^{52} + 7204 q^{53} + 13240 q^{54} + 6936 q^{55} + 8124 q^{56} + 12736 q^{57} + 3030 q^{58} - 2380 q^{59} - 6472 q^{60} - 162 q^{61} + 19614 q^{62} + 12004 q^{63} - 5248 q^{65} - 23872 q^{66} - 14854 q^{67} - 6444 q^{68} + 2412 q^{69} - 34524 q^{70} - 8050 q^{71} + 15420 q^{72} - 15448 q^{73} - 2882 q^{74} + 8280 q^{75} + 10622 q^{76} - 11672 q^{78} - 17064 q^{79} + 2564 q^{80} + 2128 q^{81} - 5346 q^{82} + 12788 q^{83} + 25948 q^{84} + 35382 q^{85} + 67260 q^{86} + 29342 q^{87} + 40836 q^{88} + 20492 q^{89} + 8996 q^{91} - 49884 q^{92} - 78920 q^{93} - 30606 q^{94} - 98574 q^{95} - 94664 q^{96} + 50944 q^{97} + 61484 q^{98} - 21632 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{12}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.34141 1.69918i −1.58535 0.424794i −0.644775 0.764372i \(-0.723049\pi\)
−0.940578 + 0.339578i \(0.889716\pi\)
\(3\) 7.28678 + 12.6211i 0.809643 + 1.40234i 0.913112 + 0.407710i \(0.133672\pi\)
−0.103469 + 0.994633i \(0.532994\pi\)
\(4\) 23.4699 + 13.5504i 1.46687 + 0.846897i
\(5\) −20.2793 + 20.2793i −0.811174 + 0.811174i −0.984810 0.173636i \(-0.944448\pi\)
0.173636 + 0.984810i \(0.444448\pi\)
\(6\) −24.7631 92.4170i −0.687863 2.56714i
\(7\) 21.3318 5.71584i 0.435343 0.116650i −0.0344902 0.999405i \(-0.510981\pi\)
0.469833 + 0.882755i \(0.344314\pi\)
\(8\) −51.5321 51.5321i −0.805189 0.805189i
\(9\) −65.6944 + 113.786i −0.811042 + 1.40477i
\(10\) 163.058 94.1415i 1.63058 0.941415i
\(11\) 19.8619 74.1257i 0.164148 0.612609i −0.833999 0.551765i \(-0.813954\pi\)
0.998147 0.0608433i \(-0.0193790\pi\)
\(12\) 394.954i 2.74274i
\(13\) 162.185 47.5081i 0.959675 0.281113i
\(14\) −144.986 −0.739724
\(15\) −403.718 108.176i −1.79430 0.480782i
\(16\) 22.4185 + 38.8299i 0.0875721 + 0.151679i
\(17\) 119.941 + 69.2480i 0.415021 + 0.239612i 0.692945 0.720991i \(-0.256313\pi\)
−0.277924 + 0.960603i \(0.589646\pi\)
\(18\) 609.938 609.938i 1.88252 1.88252i
\(19\) 57.8912 + 216.053i 0.160364 + 0.598485i 0.998586 + 0.0531568i \(0.0169283\pi\)
−0.838223 + 0.545328i \(0.816405\pi\)
\(20\) −750.746 + 201.162i −1.87687 + 0.502905i
\(21\) 227.580 + 227.580i 0.516055 + 0.516055i
\(22\) −251.905 + 436.312i −0.520465 + 0.901472i
\(23\) 491.603 283.827i 0.929307 0.536535i 0.0427144 0.999087i \(-0.486399\pi\)
0.886592 + 0.462552i \(0.153066\pi\)
\(24\) 274.887 1025.89i 0.477235 1.78107i
\(25\) 197.503i 0.316005i
\(26\) −1109.21 + 25.6875i −1.64084 + 0.0379993i
\(27\) −734.346 −1.00733
\(28\) 578.107 + 154.903i 0.737381 + 0.197581i
\(29\) −406.589 704.232i −0.483458 0.837375i 0.516361 0.856371i \(-0.327286\pi\)
−0.999820 + 0.0189964i \(0.993953\pi\)
\(30\) 2376.33 + 1371.98i 2.64037 + 1.52442i
\(31\) −666.232 + 666.232i −0.693270 + 0.693270i −0.962950 0.269680i \(-0.913082\pi\)
0.269680 + 0.962950i \(0.413082\pi\)
\(32\) 225.607 + 841.977i 0.220319 + 0.822243i
\(33\) 1080.28 289.459i 0.991988 0.265802i
\(34\) −642.931 642.931i −0.556169 0.556169i
\(35\) −316.681 + 548.508i −0.258515 + 0.447762i
\(36\) −3083.68 + 1780.37i −2.37939 + 1.37374i
\(37\) 429.906 1604.43i 0.314029 1.17197i −0.610861 0.791738i \(-0.709177\pi\)
0.924890 0.380235i \(-0.124157\pi\)
\(38\) 1468.45i 1.01693i
\(39\) 1781.41 + 1700.77i 1.17121 + 1.11819i
\(40\) 2090.07 1.30630
\(41\) 907.358 + 243.126i 0.539773 + 0.144632i 0.518397 0.855140i \(-0.326529\pi\)
0.0213753 + 0.999772i \(0.493195\pi\)
\(42\) −1056.48 1829.88i −0.598912 1.03735i
\(43\) −2118.01 1222.83i −1.14549 0.661349i −0.197706 0.980261i \(-0.563349\pi\)
−0.947784 + 0.318912i \(0.896683\pi\)
\(44\) 1470.59 1470.59i 0.759600 0.759600i
\(45\) −975.267 3639.75i −0.481613 1.79741i
\(46\) −3599.73 + 964.545i −1.70120 + 0.455834i
\(47\) 908.134 + 908.134i 0.411106 + 0.411106i 0.882124 0.471018i \(-0.156113\pi\)
−0.471018 + 0.882124i \(0.656113\pi\)
\(48\) −326.717 + 565.890i −0.141804 + 0.245612i
\(49\) −1656.95 + 956.642i −0.690109 + 0.398435i
\(50\) −335.593 + 1252.45i −0.134237 + 0.500980i
\(51\) 2018.38i 0.776002i
\(52\) 4450.22 + 1082.65i 1.64579 + 0.400390i
\(53\) 2101.44 0.748110 0.374055 0.927407i \(-0.377967\pi\)
0.374055 + 0.927407i \(0.377967\pi\)
\(54\) 4656.79 + 1247.78i 1.59698 + 0.427909i
\(55\) 1100.43 + 1906.01i 0.363780 + 0.630085i
\(56\) −1393.82 804.723i −0.444458 0.256608i
\(57\) −2304.98 + 2304.98i −0.709444 + 0.709444i
\(58\) 1381.73 + 5156.69i 0.410741 + 1.53290i
\(59\) −3417.07 + 915.600i −0.981634 + 0.263028i −0.713733 0.700418i \(-0.752997\pi\)
−0.267901 + 0.963446i \(0.586330\pi\)
\(60\) −8009.41 8009.41i −2.22483 2.22483i
\(61\) 2816.09 4877.60i 0.756809 1.31083i −0.187661 0.982234i \(-0.560091\pi\)
0.944470 0.328598i \(-0.106576\pi\)
\(62\) 5356.90 3092.81i 1.39357 0.804580i
\(63\) −750.998 + 2802.76i −0.189216 + 0.706163i
\(64\) 6440.06i 1.57228i
\(65\) −2325.57 + 4252.44i −0.550431 + 1.00649i
\(66\) −7342.31 −1.68556
\(67\) −3279.23 878.668i −0.730504 0.195738i −0.125650 0.992075i \(-0.540102\pi\)
−0.604854 + 0.796337i \(0.706768\pi\)
\(68\) 1876.67 + 3250.49i 0.405854 + 0.702960i
\(69\) 7164.41 + 4136.38i 1.50481 + 0.868804i
\(70\) 2940.22 2940.22i 0.600045 0.600045i
\(71\) −1904.53 7107.80i −0.377808 1.41000i −0.849198 0.528074i \(-0.822914\pi\)
0.471390 0.881925i \(-0.343752\pi\)
\(72\) 9249.01 2478.26i 1.78414 0.478060i
\(73\) 4192.40 + 4192.40i 0.786714 + 0.786714i 0.980954 0.194240i \(-0.0622240\pi\)
−0.194240 + 0.980954i \(0.562224\pi\)
\(74\) −5452.42 + 9443.87i −0.995694 + 1.72459i
\(75\) 2492.71 1439.16i 0.443148 0.255851i
\(76\) −1568.89 + 5855.19i −0.271623 + 1.01371i
\(77\) 1694.76i 0.285843i
\(78\) −8406.75 13812.2i −1.38178 2.27025i
\(79\) −3957.00 −0.634033 −0.317016 0.948420i \(-0.602681\pi\)
−0.317016 + 0.948420i \(0.602681\pi\)
\(80\) −1242.08 332.813i −0.194074 0.0520021i
\(81\) −29.7681 51.5598i −0.00453713 0.00785853i
\(82\) −5340.82 3083.52i −0.794292 0.458584i
\(83\) 1386.98 1386.98i 0.201333 0.201333i −0.599238 0.800571i \(-0.704530\pi\)
0.800571 + 0.599238i \(0.204530\pi\)
\(84\) 2257.49 + 8425.08i 0.319940 + 1.19403i
\(85\) −3836.63 + 1028.02i −0.531021 + 0.142287i
\(86\) 11353.4 + 11353.4i 1.53507 + 1.53507i
\(87\) 5925.45 10263.2i 0.782857 1.35595i
\(88\) −4843.38 + 2796.32i −0.625436 + 0.361096i
\(89\) 2395.70 8940.86i 0.302449 1.12875i −0.632670 0.774421i \(-0.718041\pi\)
0.935119 0.354333i \(-0.115292\pi\)
\(90\) 24738.3i 3.05411i
\(91\) 3188.15 1940.46i 0.384996 0.234326i
\(92\) 15383.8 1.81756
\(93\) −13263.3 3553.88i −1.53350 0.410901i
\(94\) −4215.77 7301.93i −0.477113 0.826384i
\(95\) −5555.41 3207.42i −0.615558 0.355393i
\(96\) −8982.71 + 8982.71i −0.974686 + 0.974686i
\(97\) 751.041 + 2802.92i 0.0798215 + 0.297898i 0.994283 0.106774i \(-0.0340522\pi\)
−0.914462 + 0.404672i \(0.867386\pi\)
\(98\) 12132.9 3251.01i 1.26332 0.338505i
\(99\) 7129.65 + 7129.65i 0.727441 + 0.727441i
\(100\) 2676.24 4635.38i 0.267624 0.463538i
\(101\) 2484.93 1434.67i 0.243596 0.140640i −0.373232 0.927738i \(-0.621751\pi\)
0.616829 + 0.787098i \(0.288417\pi\)
\(102\) 3429.58 12799.4i 0.329641 1.23024i
\(103\) 5465.63i 0.515188i 0.966253 + 0.257594i \(0.0829298\pi\)
−0.966253 + 0.257594i \(0.917070\pi\)
\(104\) −10805.9 5909.54i −0.999068 0.546370i
\(105\) −9230.36 −0.837221
\(106\) −13326.1 3570.72i −1.18602 0.317793i
\(107\) −293.203 507.843i −0.0256095 0.0443570i 0.852937 0.522015i \(-0.174819\pi\)
−0.878546 + 0.477658i \(0.841486\pi\)
\(108\) −17235.0 9950.64i −1.47762 0.853107i
\(109\) 5258.17 5258.17i 0.442570 0.442570i −0.450305 0.892875i \(-0.648685\pi\)
0.892875 + 0.450305i \(0.148685\pi\)
\(110\) −3739.66 13956.6i −0.309063 1.15344i
\(111\) 23382.3 6265.26i 1.89776 0.508503i
\(112\) 700.172 + 700.172i 0.0558173 + 0.0558173i
\(113\) −10187.3 + 17645.0i −0.797818 + 1.38186i 0.123217 + 0.992380i \(0.460679\pi\)
−0.921034 + 0.389481i \(0.872654\pi\)
\(114\) 18533.4 10700.3i 1.42609 0.823351i
\(115\) −4213.56 + 15725.2i −0.318606 + 1.18905i
\(116\) 22037.7i 1.63776i
\(117\) −5248.89 + 21575.4i −0.383439 + 1.57611i
\(118\) 23224.8 1.66797
\(119\) 2954.37 + 791.621i 0.208627 + 0.0559015i
\(120\) 15229.9 + 26379.0i 1.05763 + 1.83187i
\(121\) 7579.36 + 4375.95i 0.517681 + 0.298883i
\(122\) −26145.9 + 26145.9i −1.75664 + 1.75664i
\(123\) 3543.21 + 13223.4i 0.234200 + 0.874046i
\(124\) −24664.1 + 6608.72i −1.60406 + 0.429808i
\(125\) −8669.35 8669.35i −0.554838 0.554838i
\(126\) 9524.77 16497.4i 0.599948 1.03914i
\(127\) −3968.07 + 2290.97i −0.246021 + 0.142040i −0.617941 0.786225i \(-0.712033\pi\)
0.371920 + 0.928265i \(0.378700\pi\)
\(128\) −7333.08 + 27367.4i −0.447576 + 1.67038i
\(129\) 35642.1i 2.14183i
\(130\) 21973.1 23014.9i 1.30018 1.36183i
\(131\) −28273.1 −1.64752 −0.823759 0.566940i \(-0.808127\pi\)
−0.823759 + 0.566940i \(0.808127\pi\)
\(132\) 29276.2 + 7844.54i 1.68022 + 0.450215i
\(133\) 2469.85 + 4277.90i 0.139626 + 0.241840i
\(134\) 19301.9 + 11144.0i 1.07496 + 0.620627i
\(135\) 14892.0 14892.0i 0.817122 0.817122i
\(136\) −2612.32 9749.30i −0.141237 0.527103i
\(137\) −7065.68 + 1893.24i −0.376455 + 0.100871i −0.442085 0.896973i \(-0.645761\pi\)
0.0656300 + 0.997844i \(0.479094\pi\)
\(138\) −38404.1 38404.1i −2.01660 2.01660i
\(139\) 10399.9 18013.2i 0.538269 0.932310i −0.460728 0.887541i \(-0.652412\pi\)
0.998997 0.0447683i \(-0.0142550\pi\)
\(140\) −14865.0 + 8582.29i −0.758417 + 0.437872i
\(141\) −4844.25 + 18079.0i −0.243662 + 0.909361i
\(142\) 48309.6i 2.39584i
\(143\) −300.265 12965.7i −0.0146836 0.634049i
\(144\) −5891.07 −0.284099
\(145\) 22526.7 + 6036.01i 1.07142 + 0.287087i
\(146\) −19462.1 33709.4i −0.913028 1.58141i
\(147\) −24147.7 13941.7i −1.11748 0.645179i
\(148\) 31830.4 31830.4i 1.45318 1.45318i
\(149\) 56.0657 + 209.240i 0.00252537 + 0.00942480i 0.967177 0.254104i \(-0.0817804\pi\)
−0.964652 + 0.263528i \(0.915114\pi\)
\(150\) −18252.7 + 4890.79i −0.811230 + 0.217368i
\(151\) 21275.9 + 21275.9i 0.933114 + 0.933114i 0.997899 0.0647854i \(-0.0206363\pi\)
−0.0647854 + 0.997899i \(0.520636\pi\)
\(152\) 8150.41 14116.9i 0.352770 0.611016i
\(153\) −15758.9 + 9098.41i −0.673199 + 0.388672i
\(154\) −2879.70 + 10747.2i −0.121424 + 0.453162i
\(155\) 27021.5i 1.12472i
\(156\) 18763.5 + 64055.6i 0.771019 + 2.63213i
\(157\) −15748.9 −0.638926 −0.319463 0.947599i \(-0.603502\pi\)
−0.319463 + 0.947599i \(0.603502\pi\)
\(158\) 25093.0 + 6723.64i 1.00517 + 0.269333i
\(159\) 15312.7 + 26522.5i 0.605702 + 1.04911i
\(160\) −21649.9 12499.6i −0.845699 0.488265i
\(161\) 8864.47 8864.47i 0.341980 0.341980i
\(162\) 101.162 + 377.543i 0.00385469 + 0.0143859i
\(163\) 2761.28 739.883i 0.103929 0.0278476i −0.206480 0.978451i \(-0.566201\pi\)
0.310409 + 0.950603i \(0.399534\pi\)
\(164\) 18001.2 + 18001.2i 0.669288 + 0.669288i
\(165\) −16037.2 + 27777.3i −0.589063 + 1.02029i
\(166\) −11152.2 + 6438.70i −0.404709 + 0.233659i
\(167\) 6856.78 25589.9i 0.245860 0.917561i −0.727090 0.686543i \(-0.759127\pi\)
0.972949 0.231019i \(-0.0742058\pi\)
\(168\) 23455.4i 0.831044i
\(169\) 24047.0 15410.2i 0.841951 0.539554i
\(170\) 26076.4 0.902299
\(171\) −28387.0 7606.27i −0.970793 0.260123i
\(172\) −33139.7 57399.6i −1.12019 1.94023i
\(173\) 45826.6 + 26458.0i 1.53118 + 0.884026i 0.999308 + 0.0371990i \(0.0118436\pi\)
0.531869 + 0.846826i \(0.321490\pi\)
\(174\) −55014.6 + 55014.6i −1.81710 + 1.81710i
\(175\) −1128.90 4213.10i −0.0368620 0.137571i
\(176\) 3323.57 890.547i 0.107295 0.0287496i
\(177\) −36455.3 36455.3i −1.16363 1.16363i
\(178\) −30384.2 + 52627.0i −0.958976 + 1.66100i
\(179\) −33039.9 + 19075.6i −1.03118 + 0.595349i −0.917321 0.398148i \(-0.869653\pi\)
−0.113854 + 0.993497i \(0.536320\pi\)
\(180\) 26430.4 98639.7i 0.815754 3.04444i
\(181\) 23773.2i 0.725656i 0.931856 + 0.362828i \(0.118189\pi\)
−0.931856 + 0.362828i \(0.881811\pi\)
\(182\) −23514.6 + 6888.01i −0.709895 + 0.207946i
\(183\) 82080.9 2.45098
\(184\) −39959.6 10707.1i −1.18028 0.316255i
\(185\) 23818.6 + 41255.0i 0.695941 + 1.20541i
\(186\) 78069.1 + 45073.2i 2.25659 + 1.30285i
\(187\) 7515.31 7515.31i 0.214913 0.214913i
\(188\) 9008.27 + 33619.3i 0.254874 + 0.951204i
\(189\) −15664.9 + 4197.40i −0.438535 + 0.117505i
\(190\) 29779.2 + 29779.2i 0.824908 + 0.824908i
\(191\) 7556.32 13087.9i 0.207130 0.358760i −0.743679 0.668537i \(-0.766921\pi\)
0.950809 + 0.309777i \(0.100254\pi\)
\(192\) 81280.5 46927.3i 2.20487 1.27298i
\(193\) 15078.6 56274.0i 0.404805 1.51075i −0.399610 0.916685i \(-0.630855\pi\)
0.804415 0.594067i \(-0.202479\pi\)
\(194\) 19050.6i 0.506181i
\(195\) −70616.3 + 1635.36i −1.85710 + 0.0430076i
\(196\) −51851.3 −1.34973
\(197\) −24810.2 6647.88i −0.639291 0.171297i −0.0754087 0.997153i \(-0.524026\pi\)
−0.563882 + 0.825855i \(0.690693\pi\)
\(198\) −33097.5 57326.6i −0.844239 1.46226i
\(199\) −57761.4 33348.6i −1.45859 0.842115i −0.459644 0.888103i \(-0.652023\pi\)
−0.998942 + 0.0459886i \(0.985356\pi\)
\(200\) −10177.8 + 10177.8i −0.254444 + 0.254444i
\(201\) −12805.3 47790.1i −0.316956 1.18289i
\(202\) −18195.7 + 4875.52i −0.445929 + 0.119486i
\(203\) −12698.5 12698.5i −0.308150 0.308150i
\(204\) −27349.8 + 47371.2i −0.657193 + 1.13829i
\(205\) −23331.1 + 13470.2i −0.555171 + 0.320528i
\(206\) 9287.08 34659.8i 0.218849 0.816756i
\(207\) 74583.5i 1.74061i
\(208\) 5480.67 + 5232.57i 0.126680 + 0.120945i
\(209\) 17164.9 0.392960
\(210\) 58533.5 + 15684.0i 1.32729 + 0.355646i
\(211\) 14547.1 + 25196.3i 0.326747 + 0.565942i 0.981864 0.189585i \(-0.0607142\pi\)
−0.655117 + 0.755527i \(0.727381\pi\)
\(212\) 49320.6 + 28475.3i 1.09738 + 0.633572i
\(213\) 75830.3 75830.3i 1.67141 1.67141i
\(214\) 996.408 + 3718.65i 0.0217575 + 0.0812002i
\(215\) 67750.2 18153.6i 1.46566 0.392723i
\(216\) 37842.4 + 37842.4i 0.811093 + 0.811093i
\(217\) −10403.9 + 18020.0i −0.220940 + 0.382680i
\(218\) −42278.8 + 24409.7i −0.889631 + 0.513628i
\(219\) −22363.5 + 83461.7i −0.466285 + 1.74020i
\(220\) 59645.0i 1.23234i
\(221\) 22742.5 + 5532.81i 0.465643 + 0.113282i
\(222\) −158922. −3.22462
\(223\) −20898.8 5599.80i −0.420253 0.112606i 0.0424944 0.999097i \(-0.486470\pi\)
−0.462747 + 0.886490i \(0.653136\pi\)
\(224\) 9625.21 + 16671.4i 0.191829 + 0.332257i
\(225\) 22473.1 + 12974.9i 0.443914 + 0.256294i
\(226\) 94584.0 94584.0i 1.85183 1.85183i
\(227\) 18887.8 + 70490.2i 0.366547 + 1.36797i 0.865312 + 0.501234i \(0.167120\pi\)
−0.498765 + 0.866737i \(0.666213\pi\)
\(228\) −85331.0 + 22864.4i −1.64149 + 0.439835i
\(229\) 13183.8 + 13183.8i 0.251403 + 0.251403i 0.821546 0.570143i \(-0.193112\pi\)
−0.570143 + 0.821546i \(0.693112\pi\)
\(230\) 53439.8 92560.5i 1.01020 1.74973i
\(231\) 21389.7 12349.4i 0.400849 0.231430i
\(232\) −15338.2 + 57242.9i −0.284969 + 1.06352i
\(233\) 2695.47i 0.0496503i −0.999692 0.0248251i \(-0.992097\pi\)
0.999692 0.0248251i \(-0.00790290\pi\)
\(234\) 69945.8 127900.i 1.27741 2.33581i
\(235\) −36832.7 −0.666957
\(236\) −92604.9 24813.4i −1.66269 0.445515i
\(237\) −28833.8 49941.6i −0.513340 0.889131i
\(238\) −17389.8 10040.0i −0.307001 0.177247i
\(239\) −60150.4 + 60150.4i −1.05303 + 1.05303i −0.0545214 + 0.998513i \(0.517363\pi\)
−0.998513 + 0.0545214i \(0.982637\pi\)
\(240\) −4850.28 18101.5i −0.0842062 0.314262i
\(241\) −50325.8 + 13484.7i −0.866475 + 0.232171i −0.664563 0.747232i \(-0.731382\pi\)
−0.201912 + 0.979404i \(0.564716\pi\)
\(242\) −40628.3 40628.3i −0.693743 0.693743i
\(243\) −29307.2 + 50761.5i −0.496319 + 0.859651i
\(244\) 132187. 76317.9i 2.22028 1.28188i
\(245\) 14201.8 53002.0i 0.236599 0.882998i
\(246\) 89875.8i 1.48516i
\(247\) 19653.4 + 32290.3i 0.322139 + 0.529271i
\(248\) 68664.7 1.11643
\(249\) 27611.9 + 7398.58i 0.445346 + 0.119330i
\(250\) 40245.2 + 69706.7i 0.643923 + 1.11531i
\(251\) −32906.3 18998.4i −0.522313 0.301558i 0.215567 0.976489i \(-0.430840\pi\)
−0.737881 + 0.674931i \(0.764173\pi\)
\(252\) −55604.2 + 55604.2i −0.875602 + 0.875602i
\(253\) −11274.7 42077.8i −0.176142 0.657373i
\(254\) 29055.9 7785.51i 0.450368 0.120676i
\(255\) −40931.4 40931.4i −0.629472 0.629472i
\(256\) 41483.7 71851.9i 0.632991 1.09637i
\(257\) 3349.07 1933.59i 0.0507058 0.0292750i −0.474433 0.880292i \(-0.657347\pi\)
0.525139 + 0.851017i \(0.324013\pi\)
\(258\) −60562.3 + 226021.i −0.909835 + 3.39555i
\(259\) 36682.7i 0.546841i
\(260\) −112203. + 68292.0i −1.65981 + 1.01024i
\(261\) 106842. 1.56842
\(262\) 179291. + 48040.9i 2.61190 + 0.699856i
\(263\) −1730.83 2997.89i −0.0250232 0.0433415i 0.853243 0.521514i \(-0.174633\pi\)
−0.878266 + 0.478173i \(0.841299\pi\)
\(264\) −70585.3 40752.4i −1.01276 0.584717i
\(265\) −42615.8 + 42615.8i −0.606847 + 0.606847i
\(266\) −8393.42 31324.7i −0.118625 0.442714i
\(267\) 130300. 34913.9i 1.82778 0.489751i
\(268\) −65057.0 65057.0i −0.905783 0.905783i
\(269\) −35350.0 + 61227.9i −0.488522 + 0.846146i −0.999913 0.0132029i \(-0.995797\pi\)
0.511390 + 0.859348i \(0.329131\pi\)
\(270\) −119741. + 69132.4i −1.64253 + 0.948318i
\(271\) −3225.01 + 12035.9i −0.0439129 + 0.163885i −0.984400 0.175944i \(-0.943702\pi\)
0.940487 + 0.339829i \(0.110369\pi\)
\(272\) 6209.73i 0.0839334i
\(273\) 47722.0 + 26098.2i 0.640315 + 0.350175i
\(274\) 48023.3 0.639663
\(275\) −14640.1 3922.79i −0.193588 0.0518717i
\(276\) 112099. + 194161.i 1.47157 + 2.54884i
\(277\) −49200.6 28406.0i −0.641225 0.370212i 0.143861 0.989598i \(-0.454048\pi\)
−0.785086 + 0.619386i \(0.787381\pi\)
\(278\) −96557.6 + 96557.6i −1.24939 + 1.24939i
\(279\) −32040.2 119576.i −0.411611 1.53615i
\(280\) 44585.0 11946.5i 0.568687 0.152379i
\(281\) 28752.4 + 28752.4i 0.364135 + 0.364135i 0.865333 0.501198i \(-0.167107\pi\)
−0.501198 + 0.865333i \(0.667107\pi\)
\(282\) 61438.8 106415.i 0.772582 1.33815i
\(283\) 35550.4 20525.0i 0.443886 0.256278i −0.261358 0.965242i \(-0.584170\pi\)
0.705245 + 0.708964i \(0.250837\pi\)
\(284\) 51614.1 192626.i 0.639929 2.38825i
\(285\) 93487.0i 1.15096i
\(286\) −20126.9 + 82730.9i −0.246062 + 1.01143i
\(287\) 20745.2 0.251857
\(288\) −110626. 29642.3i −1.33375 0.357377i
\(289\) −32169.9 55720.0i −0.385172 0.667137i
\(290\) −132595. 76553.7i −1.57663 0.910270i
\(291\) −29903.2 + 29903.2i −0.353128 + 0.353128i
\(292\) 41586.7 + 155204.i 0.487741 + 1.82027i
\(293\) −16479.2 + 4415.59i −0.191956 + 0.0514344i −0.353516 0.935428i \(-0.615014\pi\)
0.161560 + 0.986863i \(0.448347\pi\)
\(294\) 129441. + 129441.i 1.49754 + 1.49754i
\(295\) 50728.1 87863.7i 0.582914 1.00964i
\(296\) −104834. + 60525.7i −1.19651 + 0.690806i
\(297\) −14585.5 + 54433.8i −0.165352 + 0.617101i
\(298\) 1422.14i 0.0160144i
\(299\) 66246.6 69387.7i 0.741005 0.776140i
\(300\) 78004.7 0.866719
\(301\) −52170.5 13979.1i −0.575827 0.154293i
\(302\) −98767.9 171071.i −1.08293 1.87570i
\(303\) 36214.2 + 20908.3i 0.394452 + 0.227737i
\(304\) −7091.49 + 7091.49i −0.0767344 + 0.0767344i
\(305\) 41806.2 + 156023.i 0.449409 + 1.67722i
\(306\) 115394. 30919.6i 1.23236 0.330211i
\(307\) −33947.8 33947.8i −0.360193 0.360193i 0.503691 0.863884i \(-0.331975\pi\)
−0.863884 + 0.503691i \(0.831975\pi\)
\(308\) 22964.6 39775.9i 0.242079 0.419294i
\(309\) −68982.2 + 39826.9i −0.722471 + 0.417119i
\(310\) −45914.3 + 171354.i −0.477776 + 1.78308i
\(311\) 30532.2i 0.315673i 0.987465 + 0.157836i \(0.0504518\pi\)
−0.987465 + 0.157836i \(0.949548\pi\)
\(312\) −4155.64 179444.i −0.0426903 1.84340i
\(313\) −10587.5 −0.108070 −0.0540350 0.998539i \(-0.517208\pi\)
−0.0540350 + 0.998539i \(0.517208\pi\)
\(314\) 99870.1 + 26760.1i 1.01292 + 0.271412i
\(315\) −41608.4 72067.9i −0.419334 0.726308i
\(316\) −92870.3 53618.7i −0.930043 0.536960i
\(317\) 14491.7 14491.7i 0.144212 0.144212i −0.631315 0.775527i \(-0.717484\pi\)
0.775527 + 0.631315i \(0.217484\pi\)
\(318\) −52038.1 194209.i −0.514597 1.92050i
\(319\) −60277.3 + 16151.3i −0.592342 + 0.158717i
\(320\) 130600. + 130600.i 1.27539 + 1.27539i
\(321\) 4273.02 7401.09i 0.0414691 0.0718266i
\(322\) −71275.6 + 41151.0i −0.687431 + 0.396888i
\(323\) −8017.70 + 29922.5i −0.0768502 + 0.286809i
\(324\) 1613.47i 0.0153699i
\(325\) −9383.01 32032.1i −0.0888332 0.303262i
\(326\) −18767.6 −0.176593
\(327\) 104679. + 28048.7i 0.978958 + 0.262311i
\(328\) −34229.3 59286.8i −0.318163 0.551075i
\(329\) 24562.9 + 14181.4i 0.226928 + 0.131017i
\(330\) 148897. 148897.i 1.36728 1.36728i
\(331\) 9079.85 + 33886.5i 0.0828749 + 0.309293i 0.994903 0.100834i \(-0.0321510\pi\)
−0.912028 + 0.410127i \(0.865484\pi\)
\(332\) 51346.5 13758.2i 0.465838 0.124821i
\(333\) 154319. + 154319.i 1.39166 + 1.39166i
\(334\) −86963.4 + 150625.i −0.779549 + 1.35022i
\(335\) 84319.5 48681.9i 0.751343 0.433788i
\(336\) −3734.92 + 13938.9i −0.0330829 + 0.123467i
\(337\) 68997.6i 0.607539i 0.952746 + 0.303769i \(0.0982452\pi\)
−0.952746 + 0.303769i \(0.901755\pi\)
\(338\) −178676. + 56862.4i −1.56399 + 0.497728i
\(339\) −296932. −2.58379
\(340\) −103975. 27860.1i −0.899440 0.241004i
\(341\) 36152.3 + 62617.5i 0.310904 + 0.538502i
\(342\) 167089. + 96468.9i 1.42855 + 0.824774i
\(343\) −67371.7 + 67371.7i −0.572650 + 0.572650i
\(344\) 46130.4 + 172161.i 0.389825 + 1.45485i
\(345\) −229173. + 61406.6i −1.92542 + 0.515913i
\(346\) −245649. 245649.i −2.05193 2.05193i
\(347\) 67786.7 117410.i 0.562971 0.975094i −0.434265 0.900785i \(-0.642992\pi\)
0.997235 0.0743084i \(-0.0236749\pi\)
\(348\) 278139. 160584.i 2.29670 1.32600i
\(349\) 35819.2 133679.i 0.294080 1.09752i −0.647865 0.761755i \(-0.724338\pi\)
0.941945 0.335767i \(-0.108995\pi\)
\(350\) 28635.2i 0.233757i
\(351\) −119100. + 34887.4i −0.966712 + 0.283174i
\(352\) 66893.1 0.539878
\(353\) 38151.7 + 10222.7i 0.306171 + 0.0820383i 0.408633 0.912699i \(-0.366005\pi\)
−0.102462 + 0.994737i \(0.532672\pi\)
\(354\) 169234. + 293122.i 1.35046 + 2.33906i
\(355\) 182764. + 105519.i 1.45022 + 0.837286i
\(356\) 177379. 177379.i 1.39959 1.39959i
\(357\) 11536.7 + 43055.7i 0.0905204 + 0.337827i
\(358\) 241932. 64825.6i 1.88768 0.505802i
\(359\) −17939.3 17939.3i −0.139193 0.139193i 0.634077 0.773270i \(-0.281380\pi\)
−0.773270 + 0.634077i \(0.781380\pi\)
\(360\) −137306. + 237821.i −1.05946 + 1.83504i
\(361\) 69533.8 40145.3i 0.533558 0.308050i
\(362\) 40394.9 150756.i 0.308255 1.15042i
\(363\) 127546.i 0.967954i
\(364\) 101119. 2341.77i 0.763189 0.0176743i
\(365\) −170038. −1.27632
\(366\) −520508. 139470.i −3.88567 1.04116i
\(367\) 109265. + 189253.i 0.811242 + 1.40511i 0.911995 + 0.410201i \(0.134541\pi\)
−0.100753 + 0.994911i \(0.532125\pi\)
\(368\) 22042.0 + 12725.9i 0.162763 + 0.0939711i
\(369\) −87272.7 + 87272.7i −0.640952 + 0.640952i
\(370\) −80943.9 302087.i −0.591263 2.20662i
\(371\) 44827.5 12011.5i 0.325684 0.0872669i
\(372\) −263131. 263131.i −1.90146 1.90146i
\(373\) 97162.0 168290.i 0.698359 1.20959i −0.270676 0.962671i \(-0.587247\pi\)
0.969035 0.246923i \(-0.0794195\pi\)
\(374\) −60427.5 + 34887.8i −0.432008 + 0.249420i
\(375\) 46244.9 172588.i 0.328852 1.22729i
\(376\) 93596.0i 0.662036i
\(377\) −99399.3 94899.6i −0.699360 0.667701i
\(378\) 106470. 0.745149
\(379\) 188740. + 50572.7i 1.31397 + 0.352077i 0.846715 0.532047i \(-0.178577\pi\)
0.467254 + 0.884123i \(0.345244\pi\)
\(380\) −86923.3 150556.i −0.601962 1.04263i
\(381\) −57829.0 33387.6i −0.398378 0.230004i
\(382\) −70156.4 + 70156.4i −0.480774 + 0.480774i
\(383\) −31354.7 117017.i −0.213749 0.797723i −0.986603 0.163139i \(-0.947838\pi\)
0.772854 0.634584i \(-0.218829\pi\)
\(384\) −398841. + 106869.i −2.70481 + 0.724753i
\(385\) 34368.6 + 34368.6i 0.231868 + 0.231868i
\(386\) −191239. + 331236.i −1.28352 + 2.22312i
\(387\) 278283. 160667.i 1.85808 1.07276i
\(388\) −20353.7 + 75961.2i −0.135201 + 0.504578i
\(389\) 3999.65i 0.0264316i 0.999913 + 0.0132158i \(0.00420684\pi\)
−0.999913 + 0.0132158i \(0.995793\pi\)
\(390\) 450586. + 109619.i 2.96243 + 0.720704i
\(391\) 78617.8 0.514242
\(392\) 134684. + 36088.5i 0.876483 + 0.234853i
\(393\) −206020. 356837.i −1.33390 2.31038i
\(394\) 146036. + 84313.9i 0.940736 + 0.543134i
\(395\) 80245.3 80245.3i 0.514311 0.514311i
\(396\) 70722.9 + 263942.i 0.450993 + 1.68313i
\(397\) −177669. + 47606.1i −1.12727 + 0.302052i −0.773824 0.633401i \(-0.781658\pi\)
−0.353450 + 0.935453i \(0.614992\pi\)
\(398\) 309624. + 309624.i 1.95465 + 1.95465i
\(399\) −35994.5 + 62344.3i −0.226095 + 0.391608i
\(400\) 7669.04 4427.72i 0.0479315 0.0276733i
\(401\) −80819.4 + 301622.i −0.502605 + 1.87575i −0.0202056 + 0.999796i \(0.506432\pi\)
−0.482399 + 0.875951i \(0.660235\pi\)
\(402\) 324815.i 2.00995i
\(403\) −76401.4 + 139704.i −0.470426 + 0.860200i
\(404\) 77761.3 0.476432
\(405\) 1649.28 + 441.922i 0.0100550 + 0.00269424i
\(406\) 58949.6 + 102104.i 0.357626 + 0.619426i
\(407\) −110391. 63734.1i −0.666413 0.384754i
\(408\) 104011. 104011.i 0.624828 0.624828i
\(409\) −42559.5 158834.i −0.254419 0.949505i −0.968413 0.249353i \(-0.919782\pi\)
0.713994 0.700152i \(-0.246885\pi\)
\(410\) 170840. 45776.4i 1.01630 0.272317i
\(411\) −75380.9 75380.9i −0.446249 0.446249i
\(412\) −74061.3 + 128278.i −0.436312 + 0.755714i
\(413\) −67658.8 + 39062.8i −0.396665 + 0.229015i
\(414\) 126730. 472965.i 0.739402 2.75948i
\(415\) 56254.2i 0.326632i
\(416\) 76590.8 + 125838.i 0.442578 + 0.727151i
\(417\) 303127. 1.74322
\(418\) −108850. 29166.2i −0.622981 0.166927i
\(419\) −133921. 231958.i −0.762817 1.32124i −0.941393 0.337311i \(-0.890483\pi\)
0.178577 0.983926i \(-0.442851\pi\)
\(420\) −216636. 125075.i −1.22809 0.709040i
\(421\) −10736.2 + 10736.2i −0.0605743 + 0.0605743i −0.736745 0.676171i \(-0.763638\pi\)
0.676171 + 0.736745i \(0.263638\pi\)
\(422\) −49436.2 184498.i −0.277600 1.03602i
\(423\) −162992. + 43673.7i −0.910933 + 0.244084i
\(424\) −108292. 108292.i −0.602370 0.602370i
\(425\) 13676.7 23688.8i 0.0757188 0.131149i
\(426\) −609720. + 352022.i −3.35978 + 1.93977i
\(427\) 32192.6 120144.i 0.176563 0.658943i
\(428\) 15892.0i 0.0867545i
\(429\) 161453. 98267.7i 0.877266 0.533945i
\(430\) −460478. −2.49042
\(431\) 73459.2 + 19683.3i 0.395450 + 0.105960i 0.451063 0.892492i \(-0.351045\pi\)
−0.0556136 + 0.998452i \(0.517711\pi\)
\(432\) −16462.9 28514.6i −0.0882142 0.152792i
\(433\) 287163. + 165794.i 1.53163 + 0.884286i 0.999287 + 0.0377562i \(0.0120210\pi\)
0.532341 + 0.846530i \(0.321312\pi\)
\(434\) 96594.3 96594.3i 0.512828 0.512828i
\(435\) 87966.3 + 328295.i 0.464876 + 1.73494i
\(436\) 194659. 52158.7i 1.02400 0.274381i
\(437\) 89781.3 + 89781.3i 0.470135 + 0.470135i
\(438\) 283632. 491266.i 1.47845 2.56076i
\(439\) −230242. + 132931.i −1.19469 + 0.689756i −0.959367 0.282160i \(-0.908949\pi\)
−0.235326 + 0.971917i \(0.575616\pi\)
\(440\) 41512.9 154928.i 0.214426 0.800248i
\(441\) 251384.i 1.29259i
\(442\) −134818. 73729.3i −0.690087 0.377395i
\(443\) 422.417 0.00215246 0.00107623 0.999999i \(-0.499657\pi\)
0.00107623 + 0.999999i \(0.499657\pi\)
\(444\) 633676. + 169793.i 3.21441 + 0.861299i
\(445\) 132732. + 229898.i 0.670277 + 1.16095i
\(446\) 123013. + 71021.3i 0.618415 + 0.357042i
\(447\) −2232.30 + 2232.30i −0.0111722 + 0.0111722i
\(448\) −36810.3 137378.i −0.183406 0.684481i
\(449\) 136854. 36669.8i 0.678834 0.181893i 0.0971032 0.995274i \(-0.469042\pi\)
0.581731 + 0.813381i \(0.302376\pi\)
\(450\) −120465. 120465.i −0.594888 0.594888i
\(451\) 36043.7 62429.6i 0.177205 0.306928i
\(452\) −478191. + 276084.i −2.34059 + 1.35134i
\(453\) −113492. + 423558.i −0.553056 + 2.06403i
\(454\) 479101.i 2.32442i
\(455\) −25302.4 + 104005.i −0.122219 + 0.502378i
\(456\) 237561. 1.14247
\(457\) −134308. 35987.8i −0.643088 0.172315i −0.0774862 0.996993i \(-0.524689\pi\)
−0.565602 + 0.824679i \(0.691356\pi\)
\(458\) −61202.4 106006.i −0.291768 0.505357i
\(459\) −88078.1 50851.9i −0.418064 0.241369i
\(460\) −311974. + 311974.i −1.47436 + 1.47436i
\(461\) 4115.18 + 15358.1i 0.0193636 + 0.0722660i 0.974932 0.222505i \(-0.0714233\pi\)
−0.955568 + 0.294771i \(0.904757\pi\)
\(462\) −156625. + 41967.5i −0.733798 + 0.196621i
\(463\) −146640. 146640.i −0.684055 0.684055i 0.276856 0.960911i \(-0.410707\pi\)
−0.960911 + 0.276856i \(0.910707\pi\)
\(464\) 18230.2 31575.6i 0.0846749 0.146661i
\(465\) 341040. 196900.i 1.57725 0.910625i
\(466\) −4580.07 + 17093.1i −0.0210912 + 0.0787132i
\(467\) 229929.i 1.05429i −0.849775 0.527146i \(-0.823262\pi\)
0.849775 0.527146i \(-0.176738\pi\)
\(468\) −415545. + 435249.i −1.89726 + 1.98722i
\(469\) −74974.3 −0.340852
\(470\) 233571. + 62585.3i 1.05736 + 0.283319i
\(471\) −114759. 198768.i −0.517301 0.895992i
\(472\) 223271. + 128906.i 1.00219 + 0.578613i
\(473\) −132711. + 132711.i −0.593178 + 0.593178i
\(474\) 97987.4 + 365694.i 0.436127 + 1.62765i
\(475\) 42671.2 11433.7i 0.189124 0.0506758i
\(476\) 58612.0 + 58612.0i 0.258686 + 0.258686i
\(477\) −138053. + 239115.i −0.606749 + 1.05092i
\(478\) 483644. 279232.i 2.11675 1.22211i
\(479\) 36794.2 137318.i 0.160364 0.598488i −0.838222 0.545330i \(-0.816404\pi\)
0.998586 0.0531586i \(-0.0169289\pi\)
\(480\) 364327.i 1.58128i
\(481\) −6499.15 280639.i −0.0280910 1.21299i
\(482\) 342049. 1.47229
\(483\) 176473. + 47285.7i 0.756455 + 0.202692i
\(484\) 118591. + 205406.i 0.506246 + 0.876844i
\(485\) −72072.0 41610.8i −0.306396 0.176898i
\(486\) 272102. 272102.i 1.15202 1.15202i
\(487\) 66412.1 + 247853.i 0.280020 + 1.04505i 0.952402 + 0.304845i \(0.0986045\pi\)
−0.672382 + 0.740204i \(0.734729\pi\)
\(488\) −396472. + 106234.i −1.66484 + 0.446093i
\(489\) 29459.0 + 29459.0i 0.123197 + 0.123197i
\(490\) −180119. + 311976.i −0.750185 + 1.29936i
\(491\) −246510. + 142323.i −1.02252 + 0.590352i −0.914833 0.403833i \(-0.867678\pi\)
−0.107687 + 0.994185i \(0.534344\pi\)
\(492\) −96023.5 + 358365.i −0.396686 + 1.48045i
\(493\) 112622.i 0.463370i
\(494\) −69763.2 238160.i −0.285873 0.975923i
\(495\) −289169. −1.18016
\(496\) −40805.6 10933.8i −0.165866 0.0444436i
\(497\) −81254.1 140736.i −0.328952 0.569762i
\(498\) −162527. 93834.9i −0.655339 0.378360i
\(499\) −119045. + 119045.i −0.478089 + 0.478089i −0.904520 0.426431i \(-0.859771\pi\)
0.426431 + 0.904520i \(0.359771\pi\)
\(500\) −85996.0 320942.i −0.343984 1.28377i
\(501\) 372936. 99927.8i 1.48579 0.398117i
\(502\) 176390. + 176390.i 0.699951 + 0.699951i
\(503\) −7841.79 + 13582.4i −0.0309941 + 0.0536834i −0.881106 0.472918i \(-0.843201\pi\)
0.850112 + 0.526601i \(0.176534\pi\)
\(504\) 183133. 105732.i 0.720949 0.416240i
\(505\) −21298.4 + 79486.9i −0.0835151 + 0.311683i
\(506\) 285990.i 1.11699i
\(507\) 369718. + 191208.i 1.43832 + 0.743857i
\(508\) −124174. −0.481174
\(509\) −339655. 91010.2i −1.31100 0.351281i −0.465400 0.885101i \(-0.654089\pi\)
−0.845598 + 0.533820i \(0.820756\pi\)
\(510\) 190013. + 329113.i 0.730539 + 1.26533i
\(511\) 113395. + 65468.4i 0.434261 + 0.250720i
\(512\) −64604.8 + 64604.8i −0.246448 + 0.246448i
\(513\) −42512.2 158658.i −0.161539 0.602873i
\(514\) −24523.3 + 6571.00i −0.0928225 + 0.0248717i
\(515\) −110839. 110839.i −0.417907 0.417907i
\(516\) 482963. 836517.i 1.81391 3.14178i
\(517\) 85353.3 49278.7i 0.319330 0.184365i
\(518\) −62330.3 + 232620.i −0.232295 + 0.866937i
\(519\) 771175.i 2.86298i
\(520\) 338979. 99295.4i 1.25362 0.367217i
\(521\) 393166. 1.44844 0.724220 0.689569i \(-0.242200\pi\)
0.724220 + 0.689569i \(0.242200\pi\)
\(522\) −677532. 181544.i −2.48650 0.666256i
\(523\) −105537. 182796.i −0.385836 0.668287i 0.606049 0.795427i \(-0.292754\pi\)
−0.991885 + 0.127140i \(0.959420\pi\)
\(524\) −663566. 383110.i −2.41669 1.39528i
\(525\) 44947.9 44947.9i 0.163076 0.163076i
\(526\) 5881.98 + 21951.8i 0.0212595 + 0.0793414i
\(527\) −126044. + 33773.3i −0.453837 + 0.121605i
\(528\) 35457.8 + 35457.8i 0.127187 + 0.127187i
\(529\) 21195.3 36711.4i 0.0757406 0.131187i
\(530\) 342656. 197833.i 1.21985 0.704282i
\(531\) 120300. 448965.i 0.426654 1.59229i
\(532\) 133869.i 0.472996i
\(533\) 158710. 3675.48i 0.558664 0.0129378i
\(534\) −885612. −3.10571
\(535\) 16244.7 + 4352.75i 0.0567550 + 0.0152075i
\(536\) 123706. + 214265.i 0.430588 + 0.745800i
\(537\) −481509. 277999.i −1.66977 0.964041i
\(538\) 328206. 328206.i 1.13392 1.13392i
\(539\) 38001.5 + 141823.i 0.130805 + 0.488169i
\(540\) 551307. 147722.i 1.89063 0.506592i
\(541\) −153707. 153707.i −0.525169 0.525169i 0.393959 0.919128i \(-0.371105\pi\)
−0.919128 + 0.393959i \(0.871105\pi\)
\(542\) 40902.2 70844.6i 0.139235 0.241162i
\(543\) −300044. + 173230.i −1.01762 + 0.587522i
\(544\) −31245.7 + 116610.i −0.105582 + 0.394039i
\(545\) 213265.i 0.718002i
\(546\) −258280. 246588.i −0.866373 0.827153i
\(547\) 555728. 1.85732 0.928662 0.370926i \(-0.120960\pi\)
0.928662 + 0.370926i \(0.120960\pi\)
\(548\) −191485. 51308.2i −0.637637 0.170854i
\(549\) 370002. + 640863.i 1.22761 + 2.12628i
\(550\) 86173.2 + 49752.1i 0.284870 + 0.164470i
\(551\) 128614. 128614.i 0.423627 0.423627i
\(552\) −156041. 582353.i −0.512107 1.91121i
\(553\) −84409.9 + 22617.6i −0.276022 + 0.0739598i
\(554\) 263734. + 263734.i 0.859305 + 0.859305i
\(555\) −347122. + 601232.i −1.12693 + 1.95190i
\(556\) 488169. 281845.i 1.57914 0.911717i
\(557\) 5258.75 19625.9i 0.0169501 0.0632586i −0.956933 0.290310i \(-0.906242\pi\)
0.973883 + 0.227051i \(0.0729084\pi\)
\(558\) 812721.i 2.61019i
\(559\) −401604. 97702.8i −1.28521 0.312668i
\(560\) −28398.0 −0.0905550
\(561\) 149614. + 40088.9i 0.475385 + 0.127379i
\(562\) −133476. 231187.i −0.422600 0.731964i
\(563\) 172856. + 99798.3i 0.545340 + 0.314852i 0.747240 0.664554i \(-0.231378\pi\)
−0.201901 + 0.979406i \(0.564712\pi\)
\(564\) −358671. + 358671.i −1.12756 + 1.12756i
\(565\) −151236. 564421.i −0.473760 1.76810i
\(566\) −260315. + 69751.3i −0.812582 + 0.217731i
\(567\) −929.715 929.715i −0.00289190 0.00289190i
\(568\) −268136. + 464424.i −0.831108 + 1.43952i
\(569\) 281029. 162252.i 0.868015 0.501149i 0.00132689 0.999999i \(-0.499578\pi\)
0.866688 + 0.498850i \(0.166244\pi\)
\(570\) −158851. + 592840.i −0.488923 + 1.82468i
\(571\) 478957.i 1.46901i 0.678605 + 0.734504i \(0.262585\pi\)
−0.678605 + 0.734504i \(0.737415\pi\)
\(572\) 168642. 308372.i 0.515436 0.942502i
\(573\) 220245. 0.670806
\(574\) −131554. 35249.8i −0.399283 0.106988i
\(575\) −56056.8 97093.3i −0.169548 0.293666i
\(576\) 732789. + 423076.i 2.20869 + 1.27519i
\(577\) −178299. + 178299.i −0.535547 + 0.535547i −0.922218 0.386671i \(-0.873625\pi\)
0.386671 + 0.922218i \(0.373625\pi\)
\(578\) 109325. + 408006.i 0.327237 + 1.22127i
\(579\) 820113. 219749.i 2.44634 0.655495i
\(580\) 446909. + 446909.i 1.32851 + 1.32851i
\(581\) 21659.1 37514.6i 0.0641635 0.111134i
\(582\) 240440. 138818.i 0.709839 0.409826i
\(583\) 41738.6 155771.i 0.122801 0.458299i
\(584\) 432086.i 1.26691i
\(585\) −331091. 543979.i −0.967466 1.58954i
\(586\) 112004. 0.326167
\(587\) −208395. 55839.4i −0.604800 0.162056i −0.0565918 0.998397i \(-0.518023\pi\)
−0.548209 + 0.836342i \(0.684690\pi\)
\(588\) −377829. 654420.i −1.09280 1.89279i
\(589\) −182511. 105372.i −0.526087 0.303736i
\(590\) −470984. + 470984.i −1.35301 + 1.35301i
\(591\) −96883.4 361574.i −0.277379 1.03519i
\(592\) 71937.7 19275.7i 0.205264 0.0550004i
\(593\) −151916. 151916.i −0.432011 0.432011i 0.457301 0.889312i \(-0.348816\pi\)
−0.889312 + 0.457301i \(0.848816\pi\)
\(594\) 184985. 320404.i 0.524282 0.908082i
\(595\) −75966.2 + 43859.1i −0.214579 + 0.123887i
\(596\) −1519.42 + 5670.55i −0.00427745 + 0.0159637i
\(597\) 972016.i 2.72725i
\(598\) −537999. + 327451.i −1.50445 + 0.915681i
\(599\) −544593. −1.51781 −0.758907 0.651199i \(-0.774266\pi\)
−0.758907 + 0.651199i \(0.774266\pi\)
\(600\) −202617. 54291.2i −0.562826 0.150809i
\(601\) 317137. + 549298.i 0.878008 + 1.52075i 0.853524 + 0.521054i \(0.174461\pi\)
0.0244843 + 0.999700i \(0.492206\pi\)
\(602\) 307082. + 177294.i 0.847347 + 0.489216i
\(603\) 315407. 315407.i 0.867436 0.867436i
\(604\) 211048. + 787640.i 0.578504 + 2.15901i
\(605\) −242446. + 64963.1i −0.662375 + 0.177483i
\(606\) −194123. 194123.i −0.528604 0.528604i
\(607\) 95785.7 165906.i 0.259970 0.450281i −0.706264 0.707949i \(-0.749621\pi\)
0.966234 + 0.257668i \(0.0829540\pi\)
\(608\) −168851. + 97486.2i −0.456769 + 0.263716i
\(609\) 67737.8 252801.i 0.182640 0.681623i
\(610\) 1.06044e6i 2.84989i
\(611\) 190429. + 104142.i 0.510096 + 0.278961i
\(612\) −493147. −1.31666
\(613\) −184028. 49310.1i −0.489736 0.131224i 0.00549620 0.999985i \(-0.498250\pi\)
−0.495233 + 0.868760i \(0.664917\pi\)
\(614\) 157594. + 272960.i 0.418025 + 0.724041i
\(615\) −340017. 196309.i −0.898980 0.519026i
\(616\) −87334.6 + 87334.6i −0.230157 + 0.230157i
\(617\) 179296. + 669141.i 0.470977 + 1.75771i 0.636271 + 0.771465i \(0.280476\pi\)
−0.165294 + 0.986244i \(0.552857\pi\)
\(618\) 505118. 135346.i 1.32256 0.354379i
\(619\) −103746. 103746.i −0.270763 0.270763i 0.558644 0.829407i \(-0.311322\pi\)
−0.829407 + 0.558644i \(0.811322\pi\)
\(620\) 366151. 634192.i 0.952526 1.64982i
\(621\) −361007. + 208427.i −0.936121 + 0.540470i
\(622\) 51879.6 193617.i 0.134096 0.500453i
\(623\) 204418.i 0.526676i
\(624\) −26104.2 + 107301.i −0.0670412 + 0.275571i
\(625\) 475057. 1.21615
\(626\) 67139.8 + 17990.1i 0.171329 + 0.0459075i
\(627\) 125077. + 216640.i 0.318158 + 0.551065i
\(628\) −369625. 213403.i −0.937220 0.541104i
\(629\) 162667. 162667.i 0.411148 0.411148i
\(630\) 141400. + 527712.i 0.356261 + 1.32958i
\(631\) −484445. + 129807.i −1.21671 + 0.326015i −0.809389 0.587272i \(-0.800202\pi\)
−0.407316 + 0.913287i \(0.633535\pi\)
\(632\) 203912. + 203912.i 0.510516 + 0.510516i
\(633\) −212003. + 367200.i −0.529097 + 0.916422i
\(634\) −116522. + 67274.1i −0.289888 + 0.167367i
\(635\) 34010.6 126929.i 0.0843464 0.314785i
\(636\) 829973.i 2.05187i
\(637\) −223285. + 233872.i −0.550275 + 0.576366i
\(638\) 409687. 1.00649
\(639\) 933886. + 250234.i 2.28714 + 0.612837i
\(640\) −406284. 703704.i −0.991903 1.71803i
\(641\) 411467. + 237561.i 1.00143 + 0.578174i 0.908670 0.417515i \(-0.137099\pi\)
0.0927567 + 0.995689i \(0.470432\pi\)
\(642\) −39672.7 + 39672.7i −0.0962547 + 0.0962547i
\(643\) −73868.4 275681.i −0.178664 0.666783i −0.995898 0.0904777i \(-0.971161\pi\)
0.817235 0.576305i \(-0.195506\pi\)
\(644\) 328165. 87931.5i 0.791262 0.212018i
\(645\) 722799. + 722799.i 1.73739 + 1.73739i
\(646\) 101687. 176127.i 0.243669 0.422048i
\(647\) −90764.9 + 52403.1i −0.216825 + 0.125184i −0.604479 0.796621i \(-0.706619\pi\)
0.387654 + 0.921805i \(0.373285\pi\)
\(648\) −1122.97 + 4191.00i −0.00267436 + 0.00998085i
\(649\) 271478.i 0.644533i
\(650\) 5073.37 + 219072.i 0.0120080 + 0.518514i
\(651\) −303243. −0.715531
\(652\) 74832.6 + 20051.3i 0.176034 + 0.0471681i
\(653\) 95438.9 + 165305.i 0.223820 + 0.387668i 0.955965 0.293481i \(-0.0948139\pi\)
−0.732145 + 0.681149i \(0.761481\pi\)
\(654\) −616153. 355736.i −1.44057 0.831711i
\(655\) 573359. 573359.i 1.33642 1.33642i
\(656\) 10901.0 + 40683.1i 0.0253314 + 0.0945381i
\(657\) −752454. + 201620.i −1.74321 + 0.467091i
\(658\) −131667. 131667.i −0.304105 0.304105i
\(659\) 184755. 320004.i 0.425426 0.736860i −0.571034 0.820927i \(-0.693457\pi\)
0.996460 + 0.0840664i \(0.0267908\pi\)
\(660\) −752785. + 434620.i −1.72816 + 0.997751i
\(661\) −167346. + 624543.i −0.383011 + 1.42942i 0.458266 + 0.888815i \(0.348471\pi\)
−0.841278 + 0.540603i \(0.818196\pi\)
\(662\) 230316.i 0.525544i
\(663\) 95889.4 + 327351.i 0.218144 + 0.744709i
\(664\) −142948. −0.324222
\(665\) −136840. 36666.2i −0.309435 0.0829129i
\(666\) −716387. 1.24082e6i −1.61510 2.79744i
\(667\) −399760. 230802.i −0.898562 0.518785i
\(668\) 507680. 507680.i 1.13772 1.13772i
\(669\) −81609.1 304569.i −0.182342 0.680509i
\(670\) −617424. + 165438.i −1.37541 + 0.368541i
\(671\) −305623. 305623.i −0.678798 0.678798i
\(672\) −140274. + 242961.i −0.310626 + 0.538020i
\(673\) −438672. + 253268.i −0.968523 + 0.559177i −0.898786 0.438388i \(-0.855549\pi\)
−0.0697375 + 0.997565i \(0.522216\pi\)
\(674\) 117239. 437542.i 0.258079 0.963163i
\(675\) 145036.i 0.318323i
\(676\) 773193. 35831.1i 1.69198 0.0784092i
\(677\) 125231. 0.273234 0.136617 0.990624i \(-0.456377\pi\)
0.136617 + 0.990624i \(0.456377\pi\)
\(678\) 1.88297e6 + 504539.i 4.09622 + 1.09758i
\(679\) 32042.1 + 55498.6i 0.0694995 + 0.120377i
\(680\) 250686. + 144733.i 0.542140 + 0.313005i
\(681\) −752031. + 752031.i −1.62159 + 1.62159i
\(682\) −122858. 458513.i −0.264141 0.985786i
\(683\) 236156. 63277.9i 0.506242 0.135647i 0.00334667 0.999994i \(-0.498935\pi\)
0.502896 + 0.864347i \(0.332268\pi\)
\(684\) −563172. 563172.i −1.20373 1.20373i
\(685\) 104894. 181681.i 0.223547 0.387194i
\(686\) 541708. 312755.i 1.15111 0.664594i
\(687\) −70326.4 + 262462.i −0.149006 + 0.556100i
\(688\) 109656.i 0.231663i
\(689\) 340822. 99835.5i 0.717942 0.210303i
\(690\) 1.55762e6 3.27162
\(691\) −483617. 129585.i −1.01285 0.271393i −0.286031 0.958220i \(-0.592336\pi\)
−0.726820 + 0.686827i \(0.759003\pi\)
\(692\) 717030. + 1.24193e6i 1.49736 + 2.59350i
\(693\) 192840. + 111336.i 0.401542 + 0.231831i
\(694\) −629364. + 629364.i −1.30672 + 1.30672i
\(695\) 154392. + 576198.i 0.319635 + 1.19289i
\(696\) −834233. + 223532.i −1.72214 + 0.461447i
\(697\) 91993.4 + 91993.4i 0.189361 + 0.189361i
\(698\) −454289. + 786852.i −0.932441 + 1.61504i
\(699\) 34019.7 19641.3i 0.0696267 0.0401990i
\(700\) 30593.9 114178.i 0.0624366 0.233016i
\(701\) 790148.i 1.60795i −0.594663 0.803975i \(-0.702715\pi\)
0.594663 0.803975i \(-0.297285\pi\)
\(702\) 814541. 18863.5i 1.65287 0.0382779i
\(703\) 371530. 0.751767
\(704\) −477374. 127912.i −0.963192 0.258087i
\(705\) −268392. 464869.i −0.539997 0.935302i
\(706\) −224565. 129653.i −0.450540 0.260119i
\(707\) 44807.6 44807.6i 0.0896423 0.0896423i
\(708\) −361620. 1.34958e6i −0.721416 2.69236i
\(709\) 863561. 231390.i 1.71791 0.460313i 0.740569 0.671981i \(-0.234556\pi\)
0.977342 + 0.211668i \(0.0678895\pi\)
\(710\) −979688. 979688.i −1.94344 1.94344i
\(711\) 259953. 450251.i 0.514227 0.890668i
\(712\) −584197. + 337286.i −1.15239 + 0.665332i
\(713\) −138427. + 516617.i −0.272296 + 1.01622i
\(714\) 292637.i 0.574027i
\(715\) 269024. + 256846.i 0.526235 + 0.502413i
\(716\) −1.03392e6 −2.01680
\(717\) −1.19747e6 320860.i −2.32930 0.624133i
\(718\) 83278.6 + 144243.i 0.161542 + 0.279798i
\(719\) 689802. + 398258.i 1.33434 + 0.770382i 0.985962 0.166971i \(-0.0533987\pi\)
0.348380 + 0.937354i \(0.386732\pi\)
\(720\) 119467. 119467.i 0.230453 0.230453i
\(721\) 31240.7 + 116592.i 0.0600966 + 0.224284i
\(722\) −509156. + 136428.i −0.976735 + 0.261715i
\(723\) −536905. 536905.i −1.02712 1.02712i
\(724\) −322136. + 557955.i −0.614556 + 1.06444i
\(725\) −139088. + 80302.6i −0.264615 + 0.152775i
\(726\) 216724. 808823.i 0.411181 1.53455i
\(727\) 60581.5i 0.114623i 0.998356 + 0.0573114i \(0.0182528\pi\)
−0.998356 + 0.0573114i \(0.981747\pi\)
\(728\) −264288. 64296.2i −0.498671 0.121317i
\(729\) −859042. −1.61644
\(730\) 1.07828e6 + 288925.i 2.02342 + 0.542175i
\(731\) −169358. 293336.i −0.316935 0.548947i
\(732\) 1.92643e6 + 1.11222e6i 3.59526 + 2.07573i
\(733\) 572778. 572778.i 1.06605 1.06605i 0.0683928 0.997658i \(-0.478213\pi\)
0.997658 0.0683928i \(-0.0217871\pi\)
\(734\) −371322. 1.38579e6i −0.689222 2.57221i
\(735\) 772428. 206971.i 1.42983 0.383121i
\(736\) 349885. + 349885.i 0.645907 + 0.645907i
\(737\) −130264. + 225623.i −0.239822 + 0.415383i
\(738\) 701724. 405140.i 1.28841 0.743863i
\(739\) 40364.3 150642.i 0.0739110 0.275839i −0.919073 0.394087i \(-0.871061\pi\)
0.992984 + 0.118247i \(0.0377276\pi\)
\(740\) 1.29100e6i 2.35756i
\(741\) −264328. + 483339.i −0.481401 + 0.880269i
\(742\) −304680. −0.553395
\(743\) 96406.5 + 25832.0i 0.174634 + 0.0467930i 0.345076 0.938575i \(-0.387853\pi\)
−0.170442 + 0.985368i \(0.554520\pi\)
\(744\) 500345. + 866622.i 0.903906 + 1.56561i
\(745\) −5380.23 3106.27i −0.00969366 0.00559664i
\(746\) −902098. + 902098.i −1.62097 + 1.62097i
\(747\) 66702.3 + 248937.i 0.119536 + 0.446116i
\(748\) 278219. 74548.5i 0.497259 0.133240i
\(749\) −9157.31 9157.31i −0.0163232 0.0163232i
\(750\) −586516. + 1.01587e6i −1.04269 + 1.80600i
\(751\) 521537. 301110.i 0.924710 0.533882i 0.0395753 0.999217i \(-0.487399\pi\)
0.885135 + 0.465335i \(0.154066\pi\)
\(752\) −14903.8 + 55621.7i −0.0263549 + 0.0983578i
\(753\) 553750.i 0.976616i
\(754\) 469081. + 770695.i 0.825097 + 1.35563i
\(755\) −862924. −1.51383
\(756\) −424530. 113753.i −0.742788 0.199030i
\(757\) −96392.8 166957.i −0.168210 0.291349i 0.769580 0.638550i \(-0.220465\pi\)
−0.937791 + 0.347201i \(0.887132\pi\)
\(758\) −1.11094e6 641404.i −1.93354 1.11633i
\(759\) 448910. 448910.i 0.779249 0.779249i
\(760\) 120997. + 451567.i 0.209482 + 0.781799i
\(761\) 86176.8 23091.0i 0.148806 0.0398725i −0.183647 0.982992i \(-0.558790\pi\)
0.332453 + 0.943120i \(0.392124\pi\)
\(762\) 309986. + 309986.i 0.533866 + 0.533866i
\(763\) 82111.4 142221.i 0.141044 0.244295i
\(764\) 354692. 204782.i 0.607666 0.350836i
\(765\) 135071. 504090.i 0.230801 0.861361i
\(766\) 795331.i 1.35547i
\(767\) −510699. + 310835.i −0.868109 + 0.528371i
\(768\) 1.20913e6 2.04999
\(769\) 1.06047e6 + 284153.i 1.79327 + 0.480507i 0.992896 0.118988i \(-0.0379650\pi\)
0.800379 + 0.599494i \(0.204632\pi\)
\(770\) −159547. 276344.i −0.269097 0.466089i
\(771\) 48807.9 + 28179.2i 0.0821072 + 0.0474046i
\(772\) 1.11643e6 1.11643e6i 1.87325 1.87325i
\(773\) −25594.4 95519.7i −0.0428338 0.159858i 0.941196 0.337860i \(-0.109703\pi\)
−0.984030 + 0.178003i \(0.943036\pi\)
\(774\) −2.03771e6 + 546003.i −3.40142 + 0.911408i
\(775\) 131583. + 131583.i 0.219077 + 0.219077i
\(776\) 105738. 183143.i 0.175593 0.304136i
\(777\) 462975. 267299.i 0.766859 0.442746i
\(778\) 6796.11 25363.4i 0.0112280 0.0419034i
\(779\) 210112.i 0.346239i
\(780\) −1.67952e6 918494.i −2.76055 1.50969i
\(781\) −564698. −0.925794
\(782\) −498548. 133586.i −0.815255 0.218447i
\(783\) 298576. + 517150.i 0.487003 + 0.843515i
\(784\) −74292.6 42892.9i −0.120869 0.0697835i
\(785\) 319377. 319377.i 0.518280 0.518280i
\(786\) 700128. + 2.61291e6i 1.13327 + 4.22941i
\(787\) −562536. + 150731.i −0.908241 + 0.243362i −0.682552 0.730837i \(-0.739130\pi\)
−0.225689 + 0.974199i \(0.572463\pi\)
\(788\) −492213. 492213.i −0.792684 0.792684i
\(789\) 25224.4 43690.0i 0.0405198 0.0701823i
\(790\) −645219. + 372518.i −1.03384 + 0.596888i
\(791\) −116458. + 434629.i −0.186131 + 0.694649i
\(792\) 734812.i 1.17146i
\(793\) 225001. 924861.i 0.357799 1.47072i
\(794\) 1.20756e6 1.91544
\(795\) −848390. 227326.i −1.34234 0.359678i
\(796\) −903770. 1.56538e6i −1.42637 2.47054i
\(797\) 432314. + 249597.i 0.680586 + 0.392936i 0.800076 0.599899i \(-0.204793\pi\)
−0.119490 + 0.992835i \(0.538126\pi\)
\(798\) 334190. 334190.i 0.524793 0.524793i
\(799\) 46036.1 + 171809.i 0.0721115 + 0.269124i
\(800\) 166293. 44558.2i 0.259833 0.0696221i
\(801\) 859962. + 859962.i 1.34034 + 1.34034i
\(802\) 1.02502e6 1.77538e6i 1.59361 2.76022i
\(803\) 394034. 227495.i 0.611086 0.352810i
\(804\) 347033. 1.29515e6i 0.536857 2.00358i
\(805\) 359531.i 0.554811i
\(806\) 721875. 756103.i 1.11120 1.16389i
\(807\) −1.03035e6 −1.58211
\(808\) −201985. 54121.7i −0.309383 0.0828990i
\(809\) −434066. 751824.i −0.663222 1.14873i −0.979764 0.200155i \(-0.935855\pi\)
0.316542 0.948578i \(-0.397478\pi\)
\(810\) −9707.84 5604.82i −0.0147963 0.00854264i
\(811\) −607624. + 607624.i −0.923833 + 0.923833i −0.997298 0.0734651i \(-0.976594\pi\)
0.0734651 + 0.997298i \(0.476594\pi\)
\(812\) −125964. 470103.i −0.191044 0.712986i
\(813\) −175406. + 46999.8i −0.265377 + 0.0711075i
\(814\) 591737. + 591737.i 0.893059 + 0.893059i
\(815\) −40992.6 + 71001.3i −0.0617149 + 0.106893i
\(816\) −78373.5 + 45249.0i −0.117703 + 0.0679561i
\(817\) 141583. 528394.i 0.212113 0.791615i
\(818\) 1.07955e6i 1.61338i
\(819\) 11353.3 + 490244.i 0.0169260 + 0.730878i
\(820\) −730103. −1.08582
\(821\) −255430. 68442.2i −0.378953 0.101540i 0.0643141 0.997930i \(-0.479514\pi\)
−0.443267 + 0.896390i \(0.646181\pi\)
\(822\) 349936. + 606106.i 0.517898 + 0.897026i
\(823\) −558509. 322455.i −0.824575 0.476069i 0.0274163 0.999624i \(-0.491272\pi\)
−0.851992 + 0.523555i \(0.824605\pi\)
\(824\) 281656. 281656.i 0.414824 0.414824i
\(825\) −57169.1 213358.i −0.0839950 0.313474i
\(826\) 495427. 132749.i 0.726138 0.194568i
\(827\) 820167. + 820167.i 1.19920 + 1.19920i 0.974407 + 0.224792i \(0.0721702\pi\)
0.224792 + 0.974407i \(0.427830\pi\)
\(828\) −1.01063e6 + 1.75047e6i −1.47412 + 2.55325i
\(829\) −1.17667e6 + 679351.i −1.71217 + 0.988519i −0.780535 + 0.625113i \(0.785053\pi\)
−0.931631 + 0.363406i \(0.881614\pi\)
\(830\) 95585.8 356731.i 0.138751 0.517827i
\(831\) 827953.i 1.19896i
\(832\) −305955. 1.04448e6i −0.441988 1.50888i
\(833\) −264982. −0.381879
\(834\) −1.92225e6 515067.i −2.76362 0.740511i
\(835\) 379895. + 657997.i 0.544867 + 0.943737i
\(836\) 402859. + 232591.i 0.576421 + 0.332797i
\(837\) 489245. 489245.i 0.698353 0.698353i
\(838\) 455110. + 1.69849e6i 0.648080 + 2.41867i
\(839\) 490865. 131527.i 0.697330 0.186849i 0.107295 0.994227i \(-0.465781\pi\)
0.590034 + 0.807378i \(0.299114\pi\)
\(840\) 475660. + 475660.i 0.674121 + 0.674121i
\(841\) 23012.0 39858.0i 0.0325359 0.0563538i
\(842\) 86325.7 49840.2i 0.121763 0.0703000i
\(843\) −153374. + 572400.i −0.215823 + 0.805461i
\(844\) 788474.i 1.10688i
\(845\) −175148. + 800165.i −0.245296 + 1.12064i
\(846\) 1.10781e6 1.54784
\(847\) 186694. + 50024.4i 0.260233 + 0.0697293i
\(848\) 47111.1 + 81598.8i 0.0655136 + 0.113473i
\(849\) 518096. + 299123.i 0.718778 + 0.414987i
\(850\) −126981. + 126981.i −0.175752 + 0.175752i
\(851\) −244038. 910762.i −0.336975 1.25761i
\(852\) 2.80725e6 752202.i 3.86725 1.03623i
\(853\) 572753. + 572753.i 0.787171 + 0.787171i 0.981029 0.193859i \(-0.0621003\pi\)
−0.193859 + 0.981029i \(0.562100\pi\)
\(854\) −408293. + 707184.i −0.559830 + 0.969654i
\(855\) 729919. 421419.i 0.998487 0.576477i
\(856\) −11060.8 + 41279.6i −0.0150953 + 0.0563362i
\(857\) 68607.9i 0.0934141i −0.998909 0.0467071i \(-0.985127\pi\)
0.998909 0.0467071i \(-0.0148727\pi\)
\(858\) −1.19081e6 + 348819.i −1.61759 + 0.473834i
\(859\) 507339. 0.687563 0.343781 0.939050i \(-0.388292\pi\)
0.343781 + 0.939050i \(0.388292\pi\)
\(860\) 1.83608e6 + 491975.i 2.48253 + 0.665191i
\(861\) 151166. + 261827.i 0.203915 + 0.353190i
\(862\) −432389. 249640.i −0.581916 0.335970i
\(863\) −722013. + 722013.i −0.969445 + 0.969445i −0.999547 0.0301019i \(-0.990417\pi\)
0.0301019 + 0.999547i \(0.490417\pi\)
\(864\) −165674. 618302.i −0.221935 0.828272i
\(865\) −1.46588e6 + 392782.i −1.95915 + 0.524952i
\(866\) −1.53931e6 1.53931e6i −2.05253 2.05253i
\(867\) 468831. 812039.i 0.623703 1.08029i
\(868\) −488355. + 281952.i −0.648181 + 0.374227i
\(869\) −78593.5 + 293315.i −0.104075 + 0.388414i
\(870\) 2.23132e6i 2.94797i
\(871\) −573586. + 13283.4i −0.756071 + 0.0175094i
\(872\) −541929. −0.712705
\(873\) −368273. 98678.4i −0.483216 0.129477i
\(874\) −416786. 721894.i −0.545620 0.945041i
\(875\) −234485. 135380.i −0.306267 0.176823i
\(876\) −1.65581e6 + 1.65581e6i −2.15775 + 2.15775i
\(877\) −238238. 889116.i −0.309750 1.15600i −0.928779 0.370635i \(-0.879140\pi\)
0.619028 0.785369i \(-0.287527\pi\)
\(878\) 1.68593e6 451745.i 2.18701 0.586009i
\(879\) −175810. 175810.i −0.227544 0.227544i
\(880\) −49340.0 + 85459.4i −0.0637139 + 0.110356i
\(881\) 789311. 455709.i 1.01694 0.587132i 0.103725 0.994606i \(-0.466924\pi\)
0.913217 + 0.407474i \(0.133590\pi\)
\(882\) −427146. + 1.59413e6i −0.549084 + 2.04921i
\(883\) 761482.i 0.976648i 0.872662 + 0.488324i \(0.162392\pi\)
−0.872662 + 0.488324i \(0.837608\pi\)
\(884\) 458792. + 438023.i 0.587099 + 0.560522i
\(885\) 1.47858e6 1.88781
\(886\) −2678.72 717.761i −0.00341240 0.000914351i
\(887\) 221118. + 382987.i 0.281045 + 0.486785i 0.971642 0.236455i \(-0.0759856\pi\)
−0.690597 + 0.723240i \(0.742652\pi\)
\(888\) −1.52780e6 882075.i −1.93749 1.11861i
\(889\) −71551.3 + 71551.3i −0.0905345 + 0.0905345i
\(890\) −451069. 1.68341e6i −0.569460 2.12525i
\(891\) −4413.16 + 1182.50i −0.00555897 + 0.00148952i
\(892\) −414612. 414612.i −0.521090 0.521090i
\(893\) −143632. + 248778.i −0.180114 + 0.311967i
\(894\) 17949.0 10362.8i 0.0224577 0.0129659i
\(895\) 283187. 1.05687e6i 0.353531 1.31939i
\(896\) 625712.i 0.779396i
\(897\) 1.35847e6 + 330491.i 1.68836 + 0.410747i
\(898\) −930154. −1.15346
\(899\) 740064. + 198300.i 0.915693 + 0.245359i
\(900\) 351628. + 609038.i 0.434109 + 0.751899i
\(901\) 252049. + 145521.i 0.310481 + 0.179256i
\(902\) −334647. + 334647.i −0.411314 + 0.411314i
\(903\) −203725. 760311.i −0.249844 0.932429i
\(904\) 1.43426e6 384308.i 1.75505 0.470265i
\(905\) −482105. 482105.i −0.588633 0.588633i
\(906\) 1.43940e6 2.49311e6i 1.75358 3.03729i
\(907\) −1.15076e6 + 664392.i −1.39885 + 0.807625i −0.994272 0.106880i \(-0.965914\pi\)
−0.404575 + 0.914505i \(0.632581\pi\)
\(908\) −511873. + 1.91033e6i −0.620855 + 2.31706i
\(909\) 377000.i 0.456261i
\(910\) 337175. 616544.i 0.407167 0.744528i
\(911\) −77944.7 −0.0939183 −0.0469591 0.998897i \(-0.514953\pi\)
−0.0469591 + 0.998897i \(0.514953\pi\)
\(912\) −141176. 37828.1i −0.169735 0.0454805i
\(913\) −75262.9 130359.i −0.0902900 0.156387i
\(914\) 790554. + 456427.i 0.946323 + 0.546360i
\(915\) −1.66455e6 + 1.66455e6i −1.98817 + 1.98817i
\(916\) 130778. + 488069.i 0.155863 + 0.581688i
\(917\) −603116. + 161604.i −0.717236 + 0.192183i
\(918\) 472133. + 472133.i 0.560247 + 0.560247i
\(919\) 221789. 384149.i 0.262608 0.454851i −0.704326 0.709877i \(-0.748751\pi\)
0.966934 + 0.255026i \(0.0820840\pi\)
\(920\) 1.02749e6 593220.i 1.21395 0.700874i
\(921\) 181088. 675829.i 0.213486 0.796741i
\(922\) 104384.i 0.122793i
\(923\) −646564. 1.06230e6i −0.758942 1.24693i
\(924\) 669353. 0.783991
\(925\) −316880. 84907.9i −0.370350 0.0992349i
\(926\) 680739. + 1.17907e6i 0.793887 + 1.37505i
\(927\) −621913. 359062.i −0.723720 0.417840i
\(928\) 501218. 501218.i 0.582010 0.582010i
\(929\) 53117.1 + 198236.i 0.0615464 + 0.229694i 0.989847 0.142136i \(-0.0453970\pi\)
−0.928301 + 0.371830i \(0.878730\pi\)
\(930\) −2.49725e6 + 669135.i −2.88732 + 0.773656i
\(931\) −302608. 302608.i −0.349126 0.349126i
\(932\) 36524.5 63262.3i 0.0420487 0.0728305i
\(933\) −385349. + 222481.i −0.442681 + 0.255582i
\(934\) −390691. + 1.45808e6i −0.447857 + 1.67142i
\(935\) 304811.i 0.348664i
\(936\) 1.38231e6 841340.i 1.57781 0.960329i
\(937\) 774009. 0.881590 0.440795 0.897608i \(-0.354697\pi\)
0.440795 + 0.897608i \(0.354697\pi\)
\(938\) 475443. + 127394.i 0.540372 + 0.144792i
\(939\) −77149.0 133626.i −0.0874982 0.151551i
\(940\) −864460. 499096.i −0.978338 0.564844i
\(941\) 828766. 828766.i 0.935950 0.935950i −0.0621190 0.998069i \(-0.519786\pi\)
0.998069 + 0.0621190i \(0.0197858\pi\)
\(942\) 389990. + 1.45546e6i 0.439493 + 1.64021i
\(943\) 515066. 138011.i 0.579214 0.155200i
\(944\) −112158. 112158.i −0.125860 0.125860i
\(945\) 232554. 402795.i 0.260411 0.451045i
\(946\) 1.06708e6 616077.i 1.19238 0.688418i
\(947\) −17653.9 + 65885.2i −0.0196852 + 0.0734663i −0.975070 0.221899i \(-0.928775\pi\)
0.955384 + 0.295365i \(0.0954412\pi\)
\(948\) 1.56283e6i 1.73898i
\(949\) 879118. + 480772.i 0.976145 + 0.533834i
\(950\) −290024. −0.321356
\(951\) 288500. + 77303.2i 0.318995 + 0.0854745i
\(952\) −111451. 193039.i −0.122973 0.212995i
\(953\) −1.43168e6 826582.i −1.57638 0.910123i −0.995359 0.0962331i \(-0.969321\pi\)
−0.581020 0.813889i \(-0.697346\pi\)
\(954\) 1.28175e6 1.28175e6i 1.40834 1.40834i
\(955\) 112177. + 418652.i 0.122998 + 0.459035i
\(956\) −2.22678e6 + 596664.i −2.43647 + 0.652851i
\(957\) −643074. 643074.i −0.702161 0.702161i
\(958\) −466654. + 808269.i −0.508469 + 0.880693i
\(959\) −139902. + 80772.6i −0.152120 + 0.0878267i
\(960\) −696660. + 2.59997e6i −0.755924 + 2.82115i
\(961\) 35790.5i 0.0387544i
\(962\) −435641. + 1.79069e6i −0.470737 + 1.93495i
\(963\) 77047.3 0.0830816
\(964\) −1.36386e6 365446.i −1.46763 0.393250i
\(965\) 835416. + 1.44698e6i 0.897115 + 1.55385i
\(966\) −1.03874e6 599716.i −1.11315 0.642675i
\(967\) 264009. 264009.i 0.282335 0.282335i −0.551704 0.834040i \(-0.686022\pi\)
0.834040 + 0.551704i \(0.186022\pi\)
\(968\) −165079. 616082.i −0.176173 0.657488i
\(969\) −436077. + 116847.i −0.464425 + 0.124442i
\(970\) 386334. + 386334.i 0.410601 + 0.410601i
\(971\) −82653.0 + 143159.i −0.0876637 + 0.151838i −0.906523 0.422156i \(-0.861273\pi\)
0.818859 + 0.573994i \(0.194607\pi\)
\(972\) −1.37567e6 + 794245.i −1.45607 + 0.840663i
\(973\) 118888. 443697.i 0.125578 0.468663i
\(974\) 1.68458e6i 1.77572i
\(975\) 335908. 351835.i 0.353354 0.370109i
\(976\) 252529. 0.265101
\(977\) 1.60136e6 + 429084.i 1.67765 + 0.449525i 0.967157 0.254181i \(-0.0818058\pi\)
0.710492 + 0.703705i \(0.248473\pi\)
\(978\) −136755. 236867.i −0.142977 0.247644i
\(979\) −615164. 355165.i −0.641838 0.370566i
\(980\) 1.05151e6 1.05151e6i 1.09487 1.09487i
\(981\) 252874. + 943740.i 0.262764 + 0.980650i
\(982\) 1.80505e6 483662.i 1.87183 0.501556i
\(983\) 1.27109e6 + 1.27109e6i 1.31544 + 1.31544i 0.917347 + 0.398089i \(0.130326\pi\)
0.398089 + 0.917347i \(0.369674\pi\)
\(984\) 498843. 864021.i 0.515197 0.892347i
\(985\) 637950. 368321.i 0.657528 0.379624i
\(986\) −191364. + 714181.i −0.196837 + 0.734606i
\(987\) 413347.i 0.424307i
\(988\) 23717.9 + 1.02416e6i 0.0242976 + 1.04919i
\(989\) −1.38830e6 −1.41935
\(990\) 1.83374e6 + 491350.i 1.87097 + 0.501326i
\(991\) −21120.3 36581.5i −0.0215057 0.0372490i 0.855072 0.518509i \(-0.173513\pi\)
−0.876578 + 0.481260i \(0.840179\pi\)
\(992\) −711259. 410645.i −0.722777 0.417295i
\(993\) −361521. + 361521.i −0.366636 + 0.366636i
\(994\) 276130. + 1.03053e6i 0.279474 + 1.04301i
\(995\) 1.84765e6 495077.i 1.86627 0.500065i
\(996\) 547795. + 547795.i 0.552203 + 0.552203i
\(997\) 92901.4 160910.i 0.0934613 0.161880i −0.815504 0.578751i \(-0.803540\pi\)
0.908965 + 0.416872i \(0.136874\pi\)
\(998\) 957189. 552633.i 0.961029 0.554850i
\(999\) −315699. + 1.17821e6i −0.316332 + 1.18057i
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 13.5.f.a.2.1 16
3.2 odd 2 117.5.bd.c.28.4 16
13.2 odd 12 169.5.d.c.99.1 16
13.3 even 3 169.5.d.d.70.8 16
13.7 odd 12 inner 13.5.f.a.7.1 yes 16
13.10 even 6 169.5.d.c.70.1 16
13.11 odd 12 169.5.d.d.99.8 16
39.20 even 12 117.5.bd.c.46.4 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.5.f.a.2.1 16 1.1 even 1 trivial
13.5.f.a.7.1 yes 16 13.7 odd 12 inner
117.5.bd.c.28.4 16 3.2 odd 2
117.5.bd.c.46.4 16 39.20 even 12
169.5.d.c.70.1 16 13.10 even 6
169.5.d.c.99.1 16 13.2 odd 12
169.5.d.d.70.8 16 13.3 even 3
169.5.d.d.99.8 16 13.11 odd 12