Properties

Label 138.4.e.d.13.3
Level $138$
Weight $4$
Character 138.13
Analytic conductor $8.142$
Analytic rank $0$
Dimension $30$
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] = [138,4,Mod(13,138)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(138, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 14]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("138.13");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 138 = 2 \cdot 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 138.e (of order \(11\), degree \(10\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(8.14226358079\)
Analytic rank: \(0\)
Dimension: \(30\)
Relative dimension: \(3\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 13.3
Character \(\chi\) \(=\) 138.13
Dual form 138.4.e.d.85.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.30972 + 1.51150i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(3.30855 - 7.24472i) q^{5} +(-0.853889 - 5.93893i) q^{6} +(-0.555799 - 0.163197i) q^{7} +(-6.73003 + 4.32513i) q^{8} +(3.73874 + 8.18669i) q^{9} +O(q^{10})\) \(q+(1.30972 + 1.51150i) q^{2} +(-2.52376 - 1.62192i) q^{3} +(-0.569259 + 3.95929i) q^{4} +(3.30855 - 7.24472i) q^{5} +(-0.853889 - 5.93893i) q^{6} +(-0.555799 - 0.163197i) q^{7} +(-6.73003 + 4.32513i) q^{8} +(3.73874 + 8.18669i) q^{9} +(15.2837 - 4.48769i) q^{10} +(40.4870 - 46.7244i) q^{11} +(7.85833 - 9.06899i) q^{12} +(43.6631 - 12.8206i) q^{13} +(-0.481269 - 1.05383i) q^{14} +(-20.1004 + 12.9177i) q^{15} +(-15.3519 - 4.50772i) q^{16} +(-2.00930 - 13.9750i) q^{17} +(-7.47747 + 16.3734i) q^{18} +(9.69095 - 67.4021i) q^{19} +(26.8005 + 17.2236i) q^{20} +(1.13801 + 1.31333i) q^{21} +123.651 q^{22} +(108.052 + 22.1748i) q^{23} +24.0000 q^{24} +(40.3181 + 46.5296i) q^{25} +(76.5649 + 49.2052i) q^{26} +(3.84250 - 26.7252i) q^{27} +(0.962538 - 2.10767i) q^{28} +(-2.17278 - 15.1121i) q^{29} +(-45.8510 - 13.4631i) q^{30} +(-50.9769 + 32.7609i) q^{31} +(-13.2933 - 29.1082i) q^{32} +(-177.963 + 52.2546i) q^{33} +(18.4916 - 21.3404i) q^{34} +(-3.02121 + 3.48666i) q^{35} +(-34.5417 + 10.1424i) q^{36} +(-131.736 - 288.461i) q^{37} +(114.571 - 73.6301i) q^{38} +(-130.989 - 38.4619i) q^{39} +(9.06768 + 63.0671i) q^{40} +(-202.824 + 444.123i) q^{41} +(-0.494626 + 3.44020i) q^{42} +(-91.0711 - 58.5279i) q^{43} +(161.948 + 186.898i) q^{44} +71.6801 q^{45} +(108.001 + 192.364i) q^{46} +170.974 q^{47} +(31.4333 + 36.2760i) q^{48} +(-288.268 - 185.258i) q^{49} +(-17.5239 + 121.882i) q^{50} +(-17.5954 + 38.5285i) q^{51} +(25.9049 + 180.173i) q^{52} +(-57.9351 - 17.0113i) q^{53} +(45.4277 - 29.1946i) q^{54} +(-204.552 - 447.907i) q^{55} +(4.44639 - 1.30558i) q^{56} +(-133.779 + 154.389i) q^{57} +(19.9961 - 23.0767i) q^{58} +(301.202 - 88.4410i) q^{59} +(-39.7027 - 86.9367i) q^{60} +(-302.826 + 194.615i) q^{61} +(-116.284 - 34.1439i) q^{62} +(-0.741940 - 5.16030i) q^{63} +(26.5866 - 58.2164i) q^{64} +(51.5797 - 358.745i) q^{65} +(-312.065 - 200.552i) q^{66} +(-375.569 - 433.430i) q^{67} +56.4748 q^{68} +(-236.732 - 231.216i) q^{69} -9.22703 q^{70} +(338.759 + 390.949i) q^{71} +(-60.5703 - 38.9261i) q^{72} +(-161.039 + 1120.05i) q^{73} +(263.472 - 576.922i) q^{74} +(-26.2859 - 182.822i) q^{75} +(261.347 + 76.7385i) q^{76} +(-30.1279 + 19.3620i) q^{77} +(-113.424 - 248.365i) q^{78} +(8.88213 - 2.60803i) q^{79} +(-83.4498 + 96.3061i) q^{80} +(-53.0437 + 61.2157i) q^{81} +(-936.935 + 275.109i) q^{82} +(-166.219 - 363.969i) q^{83} +(-5.84769 + 3.75808i) q^{84} +(-107.893 - 31.6802i) q^{85} +(-30.8130 - 214.309i) q^{86} +(-19.0270 + 41.6633i) q^{87} +(-70.3893 + 489.568i) q^{88} +(846.212 + 543.828i) q^{89} +(93.8810 + 108.344i) q^{90} -26.3602 q^{91} +(-149.306 + 415.186i) q^{92} +181.789 q^{93} +(223.928 + 258.426i) q^{94} +(-456.246 - 293.212i) q^{95} +(-13.6622 + 95.0229i) q^{96} +(127.654 - 279.524i) q^{97} +(-97.5325 - 678.353i) q^{98} +(533.888 + 156.764i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} + 24 q^{8} - 27 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} + 24 q^{8} - 27 q^{9} + 48 q^{10} + 51 q^{11} + 36 q^{12} - 61 q^{13} + 44 q^{14} - 126 q^{15} - 48 q^{16} + 45 q^{17} + 54 q^{18} + 305 q^{19} + 168 q^{20} - 33 q^{21} + 8 q^{22} + 282 q^{23} + 720 q^{24} + 709 q^{25} + 210 q^{26} + 81 q^{27} - 88 q^{28} - 471 q^{29} - 144 q^{30} - 463 q^{31} + 96 q^{32} + 771 q^{33} + 724 q^{34} - 1424 q^{35} - 108 q^{36} - 483 q^{37} + 270 q^{38} + 183 q^{39} + 104 q^{40} + 886 q^{41} - 974 q^{43} + 204 q^{44} - 18 q^{45} + 382 q^{46} - 122 q^{47} + 144 q^{48} + 791 q^{49} - 450 q^{50} - 729 q^{51} - 200 q^{52} - 1117 q^{53} - 162 q^{54} - 2104 q^{55} - 354 q^{57} + 788 q^{58} - 4103 q^{59} + 24 q^{60} - 870 q^{61} - 592 q^{62} - 192 q^{64} - 2058 q^{65} - 24 q^{66} + 1365 q^{67} - 304 q^{68} + 2091 q^{69} - 584 q^{70} - 119 q^{71} + 216 q^{72} - 3314 q^{73} + 966 q^{74} - 675 q^{75} + 208 q^{76} + 606 q^{77} + 1218 q^{78} + 4040 q^{79} - 32 q^{80} - 243 q^{81} - 2300 q^{82} - 2365 q^{83} - 132 q^{84} + 4242 q^{85} - 1946 q^{86} - 402 q^{87} - 1992 q^{88} - 4963 q^{89} + 36 q^{90} + 8054 q^{91} + 3768 q^{92} - 2406 q^{93} - 1450 q^{94} + 1623 q^{95} - 288 q^{96} + 2287 q^{97} - 2748 q^{98} - 2313 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/138\mathbb{Z}\right)^\times\).

\(n\) \(47\) \(97\)
\(\chi(n)\) \(1\) \(e\left(\frac{7}{11}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30972 + 1.51150i 0.463056 + 0.534396i
\(3\) −2.52376 1.62192i −0.485698 0.312139i
\(4\) −0.569259 + 3.95929i −0.0711574 + 0.494911i
\(5\) 3.30855 7.24472i 0.295926 0.647988i −0.702012 0.712165i \(-0.747715\pi\)
0.997939 + 0.0641769i \(0.0204422\pi\)
\(6\) −0.853889 5.93893i −0.0580998 0.404093i
\(7\) −0.555799 0.163197i −0.0300103 0.00881183i 0.266693 0.963782i \(-0.414069\pi\)
−0.296703 + 0.954970i \(0.595887\pi\)
\(8\) −6.73003 + 4.32513i −0.297428 + 0.191145i
\(9\) 3.73874 + 8.18669i 0.138472 + 0.303211i
\(10\) 15.2837 4.48769i 0.483312 0.141913i
\(11\) 40.4870 46.7244i 1.10975 1.28072i 0.153510 0.988147i \(-0.450942\pi\)
0.956242 0.292576i \(-0.0945123\pi\)
\(12\) 7.85833 9.06899i 0.189042 0.218166i
\(13\) 43.6631 12.8206i 0.931535 0.273523i 0.219456 0.975622i \(-0.429572\pi\)
0.712079 + 0.702099i \(0.247754\pi\)
\(14\) −0.481269 1.05383i −0.00918747 0.0201178i
\(15\) −20.1004 + 12.9177i −0.345993 + 0.222356i
\(16\) −15.3519 4.50772i −0.239873 0.0704331i
\(17\) −2.00930 13.9750i −0.0286663 0.199378i 0.970455 0.241280i \(-0.0775674\pi\)
−0.999122 + 0.0419020i \(0.986658\pi\)
\(18\) −7.47747 + 16.3734i −0.0979143 + 0.214402i
\(19\) 9.69095 67.4021i 0.117014 0.813847i −0.843801 0.536656i \(-0.819687\pi\)
0.960815 0.277191i \(-0.0894036\pi\)
\(20\) 26.8005 + 17.2236i 0.299639 + 0.192566i
\(21\) 1.13801 + 1.31333i 0.0118254 + 0.0136473i
\(22\) 123.651 1.19829
\(23\) 108.052 + 22.1748i 0.979584 + 0.201033i
\(24\) 24.0000 0.204124
\(25\) 40.3181 + 46.5296i 0.322545 + 0.372237i
\(26\) 76.5649 + 49.2052i 0.577523 + 0.371152i
\(27\) 3.84250 26.7252i 0.0273885 0.190491i
\(28\) 0.962538 2.10767i 0.00649652 0.0142254i
\(29\) −2.17278 15.1121i −0.0139130 0.0967668i 0.981682 0.190528i \(-0.0610200\pi\)
−0.995595 + 0.0937613i \(0.970111\pi\)
\(30\) −45.8510 13.4631i −0.279041 0.0819337i
\(31\) −50.9769 + 32.7609i −0.295346 + 0.189807i −0.679919 0.733287i \(-0.737985\pi\)
0.384573 + 0.923095i \(0.374349\pi\)
\(32\) −13.2933 29.1082i −0.0734357 0.160802i
\(33\) −177.963 + 52.2546i −0.938768 + 0.275647i
\(34\) 18.4916 21.3404i 0.0932729 0.107643i
\(35\) −3.02121 + 3.48666i −0.0145908 + 0.0168387i
\(36\) −34.5417 + 10.1424i −0.159915 + 0.0469554i
\(37\) −131.736 288.461i −0.585331 1.28170i −0.938223 0.346031i \(-0.887529\pi\)
0.352892 0.935664i \(-0.385198\pi\)
\(38\) 114.571 73.6301i 0.489100 0.314326i
\(39\) −130.989 38.4619i −0.537822 0.157919i
\(40\) 9.06768 + 63.0671i 0.0358432 + 0.249295i
\(41\) −202.824 + 444.123i −0.772581 + 1.69172i −0.0516949 + 0.998663i \(0.516462\pi\)
−0.720886 + 0.693054i \(0.756265\pi\)
\(42\) −0.494626 + 3.44020i −0.00181720 + 0.0126389i
\(43\) −91.0711 58.5279i −0.322982 0.207568i 0.369095 0.929392i \(-0.379668\pi\)
−0.692077 + 0.721824i \(0.743304\pi\)
\(44\) 161.948 + 186.898i 0.554876 + 0.640361i
\(45\) 71.6801 0.237454
\(46\) 108.001 + 192.364i 0.346171 + 0.616575i
\(47\) 170.974 0.530618 0.265309 0.964163i \(-0.414526\pi\)
0.265309 + 0.964163i \(0.414526\pi\)
\(48\) 31.4333 + 36.2760i 0.0945210 + 0.109083i
\(49\) −288.268 185.258i −0.840431 0.540112i
\(50\) −17.5239 + 121.882i −0.0495651 + 0.344733i
\(51\) −17.5954 + 38.5285i −0.0483107 + 0.105786i
\(52\) 25.9049 + 180.173i 0.0690840 + 0.480490i
\(53\) −57.9351 17.0113i −0.150151 0.0440883i 0.205793 0.978595i \(-0.434023\pi\)
−0.355944 + 0.934507i \(0.615841\pi\)
\(54\) 45.4277 29.1946i 0.114480 0.0735719i
\(55\) −204.552 447.907i −0.501488 1.09811i
\(56\) 4.44639 1.30558i 0.0106103 0.00311545i
\(57\) −133.779 + 154.389i −0.310867 + 0.358759i
\(58\) 19.9961 23.0767i 0.0452693 0.0522435i
\(59\) 301.202 88.4410i 0.664631 0.195153i 0.0680201 0.997684i \(-0.478332\pi\)
0.596611 + 0.802531i \(0.296514\pi\)
\(60\) −39.7027 86.9367i −0.0854265 0.187058i
\(61\) −302.826 + 194.615i −0.635622 + 0.408490i −0.818387 0.574667i \(-0.805132\pi\)
0.182765 + 0.983157i \(0.441495\pi\)
\(62\) −116.284 34.1439i −0.238194 0.0699400i
\(63\) −0.741940 5.16030i −0.00148374 0.0103196i
\(64\) 26.5866 58.2164i 0.0519269 0.113704i
\(65\) 51.5797 358.745i 0.0984258 0.684566i
\(66\) −312.065 200.552i −0.582007 0.374033i
\(67\) −375.569 433.430i −0.684822 0.790327i 0.301796 0.953372i \(-0.402414\pi\)
−0.986619 + 0.163045i \(0.947868\pi\)
\(68\) 56.4748 0.100714
\(69\) −236.732 231.216i −0.413032 0.403408i
\(70\) −9.22703 −0.0157549
\(71\) 338.759 + 390.949i 0.566244 + 0.653481i 0.964590 0.263755i \(-0.0849610\pi\)
−0.398346 + 0.917235i \(0.630416\pi\)
\(72\) −60.5703 38.9261i −0.0991427 0.0637151i
\(73\) −161.039 + 1120.05i −0.258195 + 1.79578i 0.287482 + 0.957786i \(0.407182\pi\)
−0.545676 + 0.837996i \(0.683727\pi\)
\(74\) 263.472 576.922i 0.413891 0.906296i
\(75\) −26.2859 182.822i −0.0404698 0.281473i
\(76\) 261.347 + 76.7385i 0.394455 + 0.115823i
\(77\) −30.1279 + 19.3620i −0.0445895 + 0.0286560i
\(78\) −113.424 248.365i −0.164651 0.360535i
\(79\) 8.88213 2.60803i 0.0126496 0.00371426i −0.275402 0.961329i \(-0.588811\pi\)
0.288051 + 0.957615i \(0.406993\pi\)
\(80\) −83.4498 + 96.3061i −0.116625 + 0.134592i
\(81\) −53.0437 + 61.2157i −0.0727623 + 0.0839722i
\(82\) −936.935 + 275.109i −1.26179 + 0.370496i
\(83\) −166.219 363.969i −0.219818 0.481335i 0.767308 0.641279i \(-0.221596\pi\)
−0.987126 + 0.159944i \(0.948869\pi\)
\(84\) −5.84769 + 3.75808i −0.00759565 + 0.00488143i
\(85\) −107.893 31.6802i −0.137678 0.0404259i
\(86\) −30.8130 214.309i −0.0386355 0.268716i
\(87\) −19.0270 + 41.6633i −0.0234472 + 0.0513422i
\(88\) −70.3893 + 489.568i −0.0852673 + 0.593047i
\(89\) 846.212 + 543.828i 1.00785 + 0.647703i 0.936835 0.349772i \(-0.113741\pi\)
0.0710114 + 0.997476i \(0.477377\pi\)
\(90\) 93.8810 + 108.344i 0.109955 + 0.126894i
\(91\) −26.3602 −0.0303659
\(92\) −149.306 + 415.186i −0.169198 + 0.470502i
\(93\) 181.789 0.202695
\(94\) 223.928 + 258.426i 0.245706 + 0.283560i
\(95\) −456.246 293.212i −0.492736 0.316662i
\(96\) −13.6622 + 95.0229i −0.0145249 + 0.101023i
\(97\) 127.654 279.524i 0.133622 0.292591i −0.830980 0.556303i \(-0.812220\pi\)
0.964602 + 0.263712i \(0.0849468\pi\)
\(98\) −97.5325 678.353i −0.100533 0.699225i
\(99\) 533.888 + 156.764i 0.541998 + 0.159145i
\(100\) −207.175 + 133.143i −0.207175 + 0.133143i
\(101\) 651.402 + 1426.37i 0.641752 + 1.40524i 0.898591 + 0.438787i \(0.144592\pi\)
−0.256839 + 0.966454i \(0.582681\pi\)
\(102\) −81.2808 + 23.8662i −0.0789019 + 0.0231677i
\(103\) −440.518 + 508.385i −0.421413 + 0.486336i −0.926267 0.376868i \(-0.877001\pi\)
0.504854 + 0.863205i \(0.331546\pi\)
\(104\) −238.403 + 275.132i −0.224782 + 0.259412i
\(105\) 13.2799 3.89933i 0.0123427 0.00362415i
\(106\) −50.1663 109.849i −0.0459677 0.100655i
\(107\) 804.235 516.851i 0.726620 0.466970i −0.124314 0.992243i \(-0.539673\pi\)
0.850934 + 0.525273i \(0.176037\pi\)
\(108\) 103.625 + 30.4271i 0.0923273 + 0.0271097i
\(109\) 7.68100 + 53.4225i 0.00674960 + 0.0469445i 0.992918 0.118803i \(-0.0379056\pi\)
−0.986168 + 0.165747i \(0.946996\pi\)
\(110\) 409.105 895.814i 0.354606 0.776478i
\(111\) −135.392 + 941.672i −0.115773 + 0.805221i
\(112\) 7.79692 + 5.01077i 0.00657803 + 0.00422744i
\(113\) 1118.99 + 1291.38i 0.931555 + 1.07507i 0.997014 + 0.0772166i \(0.0246033\pi\)
−0.0654593 + 0.997855i \(0.520851\pi\)
\(114\) −408.571 −0.335668
\(115\) 518.147 709.442i 0.420152 0.575268i
\(116\) 61.0698 0.0488809
\(117\) 268.203 + 309.523i 0.211926 + 0.244576i
\(118\) 528.170 + 339.434i 0.412051 + 0.264809i
\(119\) −1.16391 + 8.09520i −0.000896604 + 0.00623601i
\(120\) 79.4053 173.873i 0.0604057 0.132270i
\(121\) −354.559 2466.01i −0.266385 1.85275i
\(122\) −690.778 202.831i −0.512624 0.150520i
\(123\) 1232.21 791.895i 0.903292 0.580510i
\(124\) −100.691 220.481i −0.0729216 0.159676i
\(125\) 1425.72 418.629i 1.02016 0.299546i
\(126\) 6.82806 7.88000i 0.00482771 0.00557148i
\(127\) 342.915 395.745i 0.239596 0.276509i −0.623198 0.782064i \(-0.714167\pi\)
0.862794 + 0.505555i \(0.168712\pi\)
\(128\) 122.815 36.0618i 0.0848080 0.0249019i
\(129\) 134.914 + 295.421i 0.0920816 + 0.201631i
\(130\) 609.797 391.893i 0.411406 0.264395i
\(131\) −221.617 65.0725i −0.147807 0.0434001i 0.206992 0.978343i \(-0.433633\pi\)
−0.354799 + 0.934943i \(0.615451\pi\)
\(132\) −105.584 734.352i −0.0696204 0.484221i
\(133\) −16.3861 + 35.8805i −0.0106831 + 0.0233927i
\(134\) 163.238 1135.35i 0.105236 0.731932i
\(135\) −180.903 116.260i −0.115331 0.0741187i
\(136\) 73.9663 + 85.3616i 0.0466364 + 0.0538213i
\(137\) −2824.53 −1.76143 −0.880716 0.473644i \(-0.842938\pi\)
−0.880716 + 0.473644i \(0.842938\pi\)
\(138\) 39.4301 660.649i 0.0243225 0.407523i
\(139\) 2116.97 1.29179 0.645896 0.763426i \(-0.276484\pi\)
0.645896 + 0.763426i \(0.276484\pi\)
\(140\) −12.0848 13.9467i −0.00729540 0.00841934i
\(141\) −431.496 277.306i −0.257720 0.165627i
\(142\) −147.239 + 1024.07i −0.0870142 + 0.605197i
\(143\) 1168.75 2559.20i 0.683466 1.49658i
\(144\) −20.4933 142.534i −0.0118596 0.0824851i
\(145\) −116.671 34.2578i −0.0668209 0.0196204i
\(146\) −1903.87 + 1223.55i −1.07922 + 0.693571i
\(147\) 427.044 + 935.096i 0.239605 + 0.524663i
\(148\) 1217.09 357.371i 0.675975 0.198484i
\(149\) −45.0426 + 51.9819i −0.0247653 + 0.0285807i −0.767997 0.640453i \(-0.778747\pi\)
0.743232 + 0.669034i \(0.233292\pi\)
\(150\) 241.909 279.177i 0.131678 0.151965i
\(151\) 1415.25 415.554i 0.762723 0.223956i 0.122838 0.992427i \(-0.460800\pi\)
0.639885 + 0.768471i \(0.278982\pi\)
\(152\) 226.302 + 495.532i 0.120760 + 0.264428i
\(153\) 106.897 68.6983i 0.0564842 0.0363002i
\(154\) −68.7249 20.1794i −0.0359611 0.0105591i
\(155\) 68.6835 + 477.705i 0.0355922 + 0.247549i
\(156\) 226.849 496.729i 0.116426 0.254937i
\(157\) −264.137 + 1837.12i −0.134270 + 0.933871i 0.805629 + 0.592420i \(0.201827\pi\)
−0.939900 + 0.341451i \(0.889082\pi\)
\(158\) 15.5752 + 10.0095i 0.00784236 + 0.00503998i
\(159\) 118.623 + 136.899i 0.0591663 + 0.0682815i
\(160\) −254.863 −0.125929
\(161\) −56.4364 29.9586i −0.0276262 0.0146650i
\(162\) −162.000 −0.0785674
\(163\) 573.510 + 661.866i 0.275588 + 0.318045i 0.876623 0.481177i \(-0.159791\pi\)
−0.601036 + 0.799222i \(0.705245\pi\)
\(164\) −1642.95 1055.86i −0.782274 0.502737i
\(165\) −210.230 + 1462.18i −0.0991900 + 0.689882i
\(166\) 332.438 727.938i 0.155435 0.340355i
\(167\) −146.796 1020.99i −0.0680204 0.473093i −0.995151 0.0983551i \(-0.968642\pi\)
0.927131 0.374738i \(-0.122267\pi\)
\(168\) −13.3392 3.91674i −0.00612583 0.00179871i
\(169\) −106.138 + 68.2110i −0.0483106 + 0.0310473i
\(170\) −93.4250 204.572i −0.0421492 0.0922939i
\(171\) 588.032 172.662i 0.262970 0.0772150i
\(172\) 283.572 327.259i 0.125710 0.145077i
\(173\) −1717.70 + 1982.33i −0.754880 + 0.871178i −0.995032 0.0995572i \(-0.968257\pi\)
0.240152 + 0.970735i \(0.422803\pi\)
\(174\) −87.8941 + 25.8080i −0.0382944 + 0.0112443i
\(175\) −14.8153 32.4409i −0.00639959 0.0140131i
\(176\) −832.172 + 534.804i −0.356405 + 0.229048i
\(177\) −903.607 265.323i −0.383725 0.112672i
\(178\) 286.307 + 1991.31i 0.120560 + 0.838512i
\(179\) −1395.85 + 3056.49i −0.582854 + 1.27627i 0.356811 + 0.934177i \(0.383864\pi\)
−0.939665 + 0.342096i \(0.888863\pi\)
\(180\) −40.8046 + 283.802i −0.0168966 + 0.117519i
\(181\) −443.919 285.289i −0.182300 0.117157i 0.446308 0.894879i \(-0.352739\pi\)
−0.628608 + 0.777723i \(0.716375\pi\)
\(182\) −34.5245 39.8434i −0.0140611 0.0162274i
\(183\) 1079.91 0.436226
\(184\) −823.103 + 318.102i −0.329782 + 0.127450i
\(185\) −2525.68 −1.00374
\(186\) 238.093 + 274.774i 0.0938593 + 0.108319i
\(187\) −734.324 471.922i −0.287161 0.184547i
\(188\) −97.3283 + 676.933i −0.0377574 + 0.262609i
\(189\) −6.49713 + 14.2267i −0.00250051 + 0.00547536i
\(190\) −154.366 1073.64i −0.0589416 0.409948i
\(191\) −612.392 179.814i −0.231995 0.0681200i 0.163668 0.986515i \(-0.447667\pi\)
−0.395664 + 0.918395i \(0.629485\pi\)
\(192\) −161.521 + 103.803i −0.0607122 + 0.0390174i
\(193\) −1191.11 2608.17i −0.444238 0.972745i −0.990801 0.135327i \(-0.956791\pi\)
0.546563 0.837418i \(-0.315936\pi\)
\(194\) 589.691 173.149i 0.218234 0.0640792i
\(195\) −712.031 + 821.728i −0.261485 + 0.301770i
\(196\) 897.590 1035.87i 0.327110 0.377505i
\(197\) −2315.22 + 679.811i −0.837324 + 0.245860i −0.672160 0.740406i \(-0.734633\pi\)
−0.165164 + 0.986266i \(0.552815\pi\)
\(198\) 462.297 + 1012.29i 0.165929 + 0.363335i
\(199\) −1960.69 + 1260.06i −0.698441 + 0.448861i −0.841078 0.540914i \(-0.818078\pi\)
0.142637 + 0.989775i \(0.454442\pi\)
\(200\) −472.588 138.764i −0.167085 0.0490606i
\(201\) 244.857 + 1703.02i 0.0859248 + 0.597620i
\(202\) −1302.80 + 2852.74i −0.453787 + 0.993655i
\(203\) −1.25861 + 8.75385i −0.000435160 + 0.00302660i
\(204\) −142.529 91.5978i −0.0489168 0.0314369i
\(205\) 2546.49 + 2938.81i 0.867585 + 1.00125i
\(206\) −1345.38 −0.455034
\(207\) 222.440 + 967.495i 0.0746892 + 0.324858i
\(208\) −728.103 −0.242716
\(209\) −2756.97 3181.71i −0.912456 1.05303i
\(210\) 23.2868 + 14.9655i 0.00765211 + 0.00491771i
\(211\) 285.347 1984.64i 0.0931001 0.647526i −0.888824 0.458249i \(-0.848477\pi\)
0.981924 0.189276i \(-0.0606142\pi\)
\(212\) 100.333 219.698i 0.0325041 0.0711741i
\(213\) −220.858 1536.10i −0.0710468 0.494141i
\(214\) 1834.54 + 538.671i 0.586013 + 0.172069i
\(215\) −725.332 + 466.143i −0.230080 + 0.147864i
\(216\) 89.7296 + 196.481i 0.0282654 + 0.0618926i
\(217\) 33.6794 9.88916i 0.0105360 0.00309364i
\(218\) −70.6881 + 81.5784i −0.0219615 + 0.0253449i
\(219\) 2223.06 2565.55i 0.685938 0.791615i
\(220\) 1889.84 554.906i 0.579149 0.170053i
\(221\) −266.901 584.431i −0.0812384 0.177887i
\(222\) −1600.66 + 1028.68i −0.483916 + 0.310994i
\(223\) −3876.14 1138.14i −1.16397 0.341773i −0.357997 0.933723i \(-0.616540\pi\)
−0.805975 + 0.591950i \(0.798358\pi\)
\(224\) 2.63801 + 18.3477i 0.000786872 + 0.00547281i
\(225\) −230.184 + 504.033i −0.0682028 + 0.149343i
\(226\) −486.360 + 3382.70i −0.143151 + 0.995638i
\(227\) −4316.11 2773.80i −1.26198 0.811028i −0.273430 0.961892i \(-0.588158\pi\)
−0.988555 + 0.150863i \(0.951795\pi\)
\(228\) −535.114 617.555i −0.155433 0.179380i
\(229\) 4423.04 1.27634 0.638172 0.769894i \(-0.279691\pi\)
0.638172 + 0.769894i \(0.279691\pi\)
\(230\) 1750.95 145.992i 0.501975 0.0418541i
\(231\) 107.439 0.0306017
\(232\) 79.9844 + 92.3070i 0.0226346 + 0.0261218i
\(233\) 912.303 + 586.302i 0.256511 + 0.164849i 0.662576 0.748995i \(-0.269463\pi\)
−0.406065 + 0.913844i \(0.633100\pi\)
\(234\) −116.572 + 810.778i −0.0325665 + 0.226505i
\(235\) 565.675 1238.66i 0.157024 0.343834i
\(236\) 178.701 + 1242.89i 0.0492900 + 0.342820i
\(237\) −26.6464 7.82409i −0.00730325 0.00214443i
\(238\) −13.7603 + 8.84320i −0.00374768 + 0.00240849i
\(239\) −1206.66 2642.21i −0.326578 0.715106i 0.673124 0.739530i \(-0.264952\pi\)
−0.999702 + 0.0244241i \(0.992225\pi\)
\(240\) 366.808 107.705i 0.0986557 0.0289679i
\(241\) −2702.81 + 3119.21i −0.722420 + 0.833717i −0.991596 0.129374i \(-0.958703\pi\)
0.269176 + 0.963091i \(0.413249\pi\)
\(242\) 3263.00 3765.70i 0.866750 1.00028i
\(243\) 233.157 68.4610i 0.0615515 0.0180732i
\(244\) −598.149 1309.76i −0.156937 0.343643i
\(245\) −2295.90 + 1475.48i −0.598691 + 0.384756i
\(246\) 2810.80 + 825.327i 0.728497 + 0.213906i
\(247\) −441.001 3067.23i −0.113604 0.790133i
\(248\) 201.381 440.963i 0.0515633 0.112908i
\(249\) −170.832 + 1188.17i −0.0434782 + 0.302397i
\(250\) 2500.05 + 1606.69i 0.632468 + 0.406463i
\(251\) 4735.63 + 5465.21i 1.19088 + 1.37435i 0.910003 + 0.414601i \(0.136079\pi\)
0.280874 + 0.959745i \(0.409376\pi\)
\(252\) 20.8535 0.00521288
\(253\) 5410.81 4150.89i 1.34456 1.03148i
\(254\) 1047.29 0.258712
\(255\) 220.913 + 254.947i 0.0542514 + 0.0626094i
\(256\) 215.361 + 138.404i 0.0525783 + 0.0337901i
\(257\) −341.117 + 2372.52i −0.0827949 + 0.575851i 0.905622 + 0.424086i \(0.139405\pi\)
−0.988417 + 0.151765i \(0.951504\pi\)
\(258\) −269.828 + 590.841i −0.0651115 + 0.142574i
\(259\) 26.1425 + 181.825i 0.00627189 + 0.0436219i
\(260\) 1391.01 + 408.438i 0.331795 + 0.0974239i
\(261\) 115.594 74.2879i 0.0274142 0.0176180i
\(262\) −191.899 420.200i −0.0452502 0.0990841i
\(263\) 6568.73 1928.75i 1.54010 0.452213i 0.601973 0.798516i \(-0.294381\pi\)
0.938123 + 0.346303i \(0.112563\pi\)
\(264\) 971.687 1121.39i 0.226527 0.261426i
\(265\) −314.923 + 363.441i −0.0730022 + 0.0842491i
\(266\) −75.6945 + 22.2259i −0.0174478 + 0.00512315i
\(267\) −1253.59 2744.98i −0.287335 0.629176i
\(268\) 1929.87 1240.25i 0.439872 0.282688i
\(269\) −7083.87 2080.01i −1.60562 0.471452i −0.648516 0.761201i \(-0.724610\pi\)
−0.957103 + 0.289749i \(0.906428\pi\)
\(270\) −61.2069 425.703i −0.0137960 0.0959536i
\(271\) −2495.54 + 5464.48i −0.559386 + 1.22488i 0.392873 + 0.919593i \(0.371481\pi\)
−0.952259 + 0.305291i \(0.901246\pi\)
\(272\) −32.1488 + 223.600i −0.00716657 + 0.0498446i
\(273\) 66.5268 + 42.7542i 0.0147487 + 0.00947839i
\(274\) −3699.35 4269.28i −0.815643 0.941302i
\(275\) 3806.43 0.834677
\(276\) 1050.21 805.668i 0.229041 0.175708i
\(277\) −5329.75 −1.15608 −0.578039 0.816009i \(-0.696182\pi\)
−0.578039 + 0.816009i \(0.696182\pi\)
\(278\) 2772.64 + 3199.80i 0.598172 + 0.690328i
\(279\) −458.792 294.848i −0.0984486 0.0632691i
\(280\) 5.25257 36.5325i 0.00112108 0.00779726i
\(281\) 2277.46 4986.95i 0.483495 1.05871i −0.497993 0.867181i \(-0.665929\pi\)
0.981488 0.191525i \(-0.0613434\pi\)
\(282\) −145.992 1015.40i −0.0308288 0.214419i
\(283\) −4123.51 1210.77i −0.866138 0.254321i −0.181666 0.983360i \(-0.558149\pi\)
−0.684472 + 0.729039i \(0.739967\pi\)
\(284\) −1740.72 + 1118.69i −0.363707 + 0.233740i
\(285\) 675.890 + 1479.99i 0.140478 + 0.307604i
\(286\) 5398.97 1585.28i 1.11625 0.327761i
\(287\) 185.209 213.743i 0.0380925 0.0439611i
\(288\) 188.600 217.656i 0.0385880 0.0445330i
\(289\) 4522.73 1327.99i 0.920563 0.270302i
\(290\) −101.026 221.217i −0.0204568 0.0447942i
\(291\) −775.534 + 498.405i −0.156229 + 0.100402i
\(292\) −4342.93 1275.20i −0.870379 0.255566i
\(293\) 70.0738 + 487.374i 0.0139719 + 0.0971764i 0.995614 0.0935551i \(-0.0298231\pi\)
−0.981642 + 0.190731i \(0.938914\pi\)
\(294\) −854.088 + 1870.19i −0.169427 + 0.370992i
\(295\) 355.814 2474.74i 0.0702247 0.488424i
\(296\) 2134.22 + 1371.58i 0.419084 + 0.269329i
\(297\) −1093.15 1261.56i −0.213572 0.246475i
\(298\) −137.564 −0.0267411
\(299\) 5002.19 417.077i 0.967505 0.0806696i
\(300\) 738.809 0.142184
\(301\) 41.0657 + 47.3923i 0.00786374 + 0.00907524i
\(302\) 2481.69 + 1594.88i 0.472865 + 0.303892i
\(303\) 669.481 4656.35i 0.126933 0.882839i
\(304\) −452.604 + 991.065i −0.0853902 + 0.186979i
\(305\) 408.012 + 2837.79i 0.0765991 + 0.532758i
\(306\) 243.842 + 71.5986i 0.0455540 + 0.0133759i
\(307\) −2742.02 + 1762.19i −0.509756 + 0.327600i −0.770108 0.637913i \(-0.779798\pi\)
0.260352 + 0.965514i \(0.416161\pi\)
\(308\) −59.5092 130.307i −0.0110093 0.0241069i
\(309\) 1936.32 568.556i 0.356484 0.104673i
\(310\) −632.094 + 729.475i −0.115808 + 0.133650i
\(311\) 6520.09 7524.59i 1.18881 1.37196i 0.277251 0.960797i \(-0.410577\pi\)
0.911561 0.411165i \(-0.134878\pi\)
\(312\) 1047.91 307.695i 0.190149 0.0558327i
\(313\) 4269.26 + 9348.37i 0.770967 + 1.68818i 0.724512 + 0.689262i \(0.242065\pi\)
0.0464552 + 0.998920i \(0.485208\pi\)
\(314\) −3122.75 + 2006.87i −0.561232 + 0.360682i
\(315\) −39.8397 11.6980i −0.00712608 0.00209241i
\(316\) 5.26970 + 36.6515i 0.000938113 + 0.00652472i
\(317\) 2496.02 5465.52i 0.442241 0.968373i −0.548941 0.835861i \(-0.684969\pi\)
0.991182 0.132511i \(-0.0423041\pi\)
\(318\) −51.5586 + 358.598i −0.00909202 + 0.0632364i
\(319\) −794.072 510.319i −0.139371 0.0895686i
\(320\) −333.799 385.225i −0.0583123 0.0672960i
\(321\) −2867.99 −0.498678
\(322\) −28.6337 124.541i −0.00495556 0.0215540i
\(323\) −961.416 −0.165618
\(324\) −212.175 244.863i −0.0363812 0.0419861i
\(325\) 2356.95 + 1514.72i 0.402277 + 0.258528i
\(326\) −249.271 + 1733.72i −0.0423493 + 0.294546i
\(327\) 67.2622 147.284i 0.0113749 0.0249077i
\(328\) −555.876 3866.20i −0.0935766 0.650839i
\(329\) −95.0269 27.9024i −0.0159240 0.00467571i
\(330\) −2485.42 + 1597.29i −0.414600 + 0.266447i
\(331\) 3025.33 + 6624.55i 0.502378 + 1.10006i 0.975689 + 0.219160i \(0.0703316\pi\)
−0.473311 + 0.880896i \(0.656941\pi\)
\(332\) 1535.68 450.916i 0.253859 0.0745399i
\(333\) 1869.02 2156.96i 0.307572 0.354957i
\(334\) 1350.96 1559.09i 0.221321 0.255418i
\(335\) −4382.67 + 1286.87i −0.714779 + 0.209878i
\(336\) −11.5505 25.2920i −0.00187538 0.00410652i
\(337\) −1885.13 + 1211.50i −0.304716 + 0.195829i −0.684058 0.729427i \(-0.739787\pi\)
0.379342 + 0.925256i \(0.376150\pi\)
\(338\) −242.112 71.0906i −0.0389621 0.0114403i
\(339\) −729.539 5074.06i −0.116882 0.812935i
\(340\) 186.850 409.144i 0.0298040 0.0652617i
\(341\) −533.166 + 3708.25i −0.0846703 + 0.588895i
\(342\) 1031.14 + 662.671i 0.163033 + 0.104775i
\(343\) 260.098 + 300.169i 0.0409445 + 0.0472524i
\(344\) 866.052 0.135739
\(345\) −2458.34 + 950.067i −0.383630 + 0.148261i
\(346\) −5246.00 −0.815106
\(347\) 1980.03 + 2285.08i 0.306321 + 0.353514i 0.887949 0.459941i \(-0.152129\pi\)
−0.581628 + 0.813455i \(0.697584\pi\)
\(348\) −154.126 99.0505i −0.0237414 0.0152577i
\(349\) −705.581 + 4907.43i −0.108220 + 0.752689i 0.861374 + 0.507971i \(0.169604\pi\)
−0.969594 + 0.244718i \(0.921305\pi\)
\(350\) 29.6305 64.8818i 0.00452519 0.00990879i
\(351\) −174.858 1216.17i −0.0265905 0.184941i
\(352\) −1898.27 557.382i −0.287438 0.0843994i
\(353\) 4704.55 3023.43i 0.709343 0.455867i −0.135572 0.990767i \(-0.543287\pi\)
0.844915 + 0.534900i \(0.179651\pi\)
\(354\) −782.438 1713.30i −0.117475 0.257234i
\(355\) 3953.12 1160.74i 0.591014 0.173537i
\(356\) −2634.88 + 3040.82i −0.392271 + 0.452705i
\(357\) 16.0672 18.5426i 0.00238198 0.00274895i
\(358\) −6448.06 + 1893.32i −0.951929 + 0.279511i
\(359\) 3604.06 + 7891.80i 0.529847 + 1.16020i 0.965575 + 0.260125i \(0.0837639\pi\)
−0.435727 + 0.900079i \(0.643509\pi\)
\(360\) −482.409 + 310.026i −0.0706255 + 0.0453883i
\(361\) 2132.04 + 626.023i 0.310838 + 0.0912703i
\(362\) −150.195 1044.63i −0.0218069 0.151670i
\(363\) −3104.85 + 6798.68i −0.448933 + 0.983026i
\(364\) 15.0058 104.368i 0.00216076 0.0150284i
\(365\) 7581.66 + 4872.44i 1.08724 + 0.698726i
\(366\) 1414.38 + 1632.29i 0.201997 + 0.233117i
\(367\) −9062.51 −1.28899 −0.644494 0.764609i \(-0.722932\pi\)
−0.644494 + 0.764609i \(0.722932\pi\)
\(368\) −1558.85 827.494i −0.220817 0.117218i
\(369\) −4394.20 −0.619927
\(370\) −3307.93 3817.56i −0.464787 0.536393i
\(371\) 29.4241 + 18.9097i 0.00411758 + 0.00264621i
\(372\) −103.485 + 719.755i −0.0144233 + 0.100316i
\(373\) 4759.84 10422.6i 0.660738 1.44682i −0.221094 0.975252i \(-0.570963\pi\)
0.881833 0.471563i \(-0.156310\pi\)
\(374\) −248.451 1728.02i −0.0343506 0.238913i
\(375\) −4277.16 1255.89i −0.588990 0.172943i
\(376\) −1150.66 + 739.482i −0.157821 + 0.101425i
\(377\) −288.617 631.982i −0.0394284 0.0863362i
\(378\) −30.0131 + 8.81265i −0.00408389 + 0.00119914i
\(379\) −6744.39 + 7783.44i −0.914079 + 1.05490i 0.0842107 + 0.996448i \(0.473163\pi\)
−0.998290 + 0.0584558i \(0.981382\pi\)
\(380\) 1420.63 1639.50i 0.191781 0.221327i
\(381\) −1507.30 + 442.584i −0.202681 + 0.0595125i
\(382\) −530.273 1161.14i −0.0710239 0.155521i
\(383\) 472.048 303.367i 0.0629779 0.0404734i −0.508773 0.860901i \(-0.669901\pi\)
0.571751 + 0.820427i \(0.306264\pi\)
\(384\) −368.445 108.185i −0.0489639 0.0143771i
\(385\) 40.5927 + 282.329i 0.00537350 + 0.0373735i
\(386\) 2382.22 5216.33i 0.314124 0.687835i
\(387\) 138.659 964.391i 0.0182129 0.126674i
\(388\) 1034.05 + 664.541i 0.135298 + 0.0869509i
\(389\) 6082.44 + 7019.51i 0.792781 + 0.914918i 0.997962 0.0638056i \(-0.0203238\pi\)
−0.205181 + 0.978724i \(0.565778\pi\)
\(390\) −2174.60 −0.282347
\(391\) 92.7835 1554.58i 0.0120007 0.201071i
\(392\) 2741.32 0.353208
\(393\) 453.765 + 523.672i 0.0582427 + 0.0672157i
\(394\) −4059.83 2609.09i −0.519115 0.333615i
\(395\) 10.4926 72.9774i 0.00133655 0.00929593i
\(396\) −924.594 + 2024.58i −0.117330 + 0.256916i
\(397\) −1515.96 10543.7i −0.191646 1.33293i −0.827650 0.561244i \(-0.810323\pi\)
0.636004 0.771686i \(-0.280586\pi\)
\(398\) −4472.54 1313.26i −0.563287 0.165396i
\(399\) 99.5498 63.9768i 0.0124905 0.00802718i
\(400\) −409.217 896.059i −0.0511521 0.112007i
\(401\) 548.904 161.173i 0.0683565 0.0200713i −0.247376 0.968920i \(-0.579568\pi\)
0.315732 + 0.948848i \(0.397750\pi\)
\(402\) −2253.42 + 2600.58i −0.279578 + 0.322650i
\(403\) −1805.79 + 2084.00i −0.223208 + 0.257596i
\(404\) −6018.23 + 1767.11i −0.741134 + 0.217617i
\(405\) 267.993 + 586.823i 0.0328807 + 0.0719986i
\(406\) −14.8799 + 9.56272i −0.00181891 + 0.00116894i
\(407\) −18811.8 5523.63i −2.29107 0.672718i
\(408\) −48.2232 335.400i −0.00585148 0.0406980i
\(409\) −765.198 + 1675.55i −0.0925101 + 0.202569i −0.950231 0.311547i \(-0.899153\pi\)
0.857721 + 0.514116i \(0.171880\pi\)
\(410\) −1106.81 + 7698.05i −0.133321 + 0.927267i
\(411\) 7128.45 + 4581.18i 0.855524 + 0.549812i
\(412\) −1762.07 2033.54i −0.210706 0.243168i
\(413\) −181.841 −0.0216654
\(414\) −1171.03 + 1603.37i −0.139017 + 0.190341i
\(415\) −3186.80 −0.376949
\(416\) −953.612 1100.53i −0.112391 0.129706i
\(417\) −5342.72 3433.56i −0.627420 0.403219i
\(418\) 1198.29 8334.31i 0.140216 0.975225i
\(419\) −1404.20 + 3074.76i −0.163722 + 0.358501i −0.973657 0.228019i \(-0.926775\pi\)
0.809935 + 0.586520i \(0.199502\pi\)
\(420\) 7.87886 + 54.7987i 0.000915355 + 0.00636643i
\(421\) 1520.12 + 446.348i 0.175977 + 0.0516714i 0.368534 0.929614i \(-0.379860\pi\)
−0.192557 + 0.981286i \(0.561678\pi\)
\(422\) 3373.50 2168.02i 0.389146 0.250089i
\(423\) 639.225 + 1399.71i 0.0734756 + 0.160889i
\(424\) 463.481 136.090i 0.0530863 0.0155876i
\(425\) 569.239 656.937i 0.0649698 0.0749791i
\(426\) 2032.56 2345.69i 0.231168 0.266782i
\(427\) 200.071 58.7462i 0.0226748 0.00665791i
\(428\) 1588.54 + 3478.42i 0.179404 + 0.392840i
\(429\) −7100.47 + 4563.19i −0.799100 + 0.513550i
\(430\) −1654.56 485.822i −0.185558 0.0544847i
\(431\) −545.238 3792.21i −0.0609355 0.423815i −0.997340 0.0728925i \(-0.976777\pi\)
0.936404 0.350923i \(-0.114132\pi\)
\(432\) −179.459 + 392.961i −0.0199867 + 0.0437647i
\(433\) 449.847 3128.75i 0.0499267 0.347248i −0.949511 0.313732i \(-0.898421\pi\)
0.999438 0.0335156i \(-0.0106704\pi\)
\(434\) 59.0581 + 37.9543i 0.00653198 + 0.00419785i
\(435\) 238.887 + 275.691i 0.0263305 + 0.0303870i
\(436\) −215.887 −0.0237136
\(437\) 2541.76 7068.05i 0.278235 0.773708i
\(438\) 6789.42 0.740664
\(439\) 4343.46 + 5012.62i 0.472214 + 0.544964i 0.941026 0.338334i \(-0.109863\pi\)
−0.468812 + 0.883298i \(0.655318\pi\)
\(440\) 3313.90 + 2129.71i 0.359054 + 0.230750i
\(441\) 438.896 3052.59i 0.0473919 0.329618i
\(442\) 533.801 1168.86i 0.0574442 0.125785i
\(443\) 560.557 + 3898.76i 0.0601194 + 0.418139i 0.997549 + 0.0699656i \(0.0222890\pi\)
−0.937430 + 0.348174i \(0.886802\pi\)
\(444\) −3651.28 1072.11i −0.390275 0.114595i
\(445\) 6739.62 4331.29i 0.717952 0.461400i
\(446\) −3356.37 7349.43i −0.356343 0.780282i
\(447\) 197.987 58.1343i 0.0209496 0.00615136i
\(448\) −24.2775 + 28.0178i −0.00256028 + 0.00295472i
\(449\) 3580.84 4132.51i 0.376370 0.434354i −0.535688 0.844416i \(-0.679948\pi\)
0.912058 + 0.410062i \(0.134493\pi\)
\(450\) −1063.32 + 312.220i −0.111390 + 0.0327071i
\(451\) 12539.7 + 27458.0i 1.30925 + 2.86685i
\(452\) −5749.95 + 3695.27i −0.598352 + 0.384537i
\(453\) −4245.74 1246.66i −0.440358 0.129301i
\(454\) −1460.31 10156.7i −0.150960 1.04995i
\(455\) −87.2141 + 190.972i −0.00898607 + 0.0196767i
\(456\) 232.583 1617.65i 0.0238853 0.166126i
\(457\) 12376.5 + 7953.92i 1.26685 + 0.814155i 0.989206 0.146530i \(-0.0468104\pi\)
0.277643 + 0.960684i \(0.410447\pi\)
\(458\) 5792.95 + 6685.42i 0.591019 + 0.682072i
\(459\) −381.205 −0.0387650
\(460\) 2513.92 + 2455.35i 0.254809 + 0.248872i
\(461\) −9104.80 −0.919854 −0.459927 0.887957i \(-0.652124\pi\)
−0.459927 + 0.887957i \(0.652124\pi\)
\(462\) 140.716 + 162.394i 0.0141703 + 0.0163534i
\(463\) −12256.4 7876.70i −1.23024 0.790629i −0.246314 0.969190i \(-0.579220\pi\)
−0.983929 + 0.178561i \(0.942856\pi\)
\(464\) −34.7646 + 241.793i −0.00347824 + 0.0241917i
\(465\) 601.459 1317.01i 0.0599828 0.131344i
\(466\) 308.669 + 2146.84i 0.0306841 + 0.213413i
\(467\) 10608.2 + 3114.86i 1.05116 + 0.308648i 0.761285 0.648418i \(-0.224569\pi\)
0.289872 + 0.957065i \(0.406387\pi\)
\(468\) −1378.17 + 885.694i −0.136124 + 0.0874813i
\(469\) 138.006 + 302.192i 0.0135875 + 0.0297525i
\(470\) 2613.10 767.277i 0.256454 0.0753018i
\(471\) 3646.28 4208.03i 0.356713 0.411668i
\(472\) −1644.58 + 1897.95i −0.160377 + 0.185085i
\(473\) −6421.88 + 1885.63i −0.624267 + 0.183301i
\(474\) −23.0733 50.5234i −0.00223584 0.00489581i
\(475\) 3526.91 2266.61i 0.340686 0.218945i
\(476\) −31.3886 9.21654i −0.00302247 0.000887477i
\(477\) −77.3379 537.897i −0.00742361 0.0516323i
\(478\) 2413.31 5284.42i 0.230925 0.505656i
\(479\) −905.423 + 6297.35i −0.0863671 + 0.600696i 0.899969 + 0.435953i \(0.143589\pi\)
−0.986336 + 0.164743i \(0.947320\pi\)
\(480\) 643.212 + 413.367i 0.0611635 + 0.0393074i
\(481\) −9450.25 10906.2i −0.895830 1.03384i
\(482\) −8254.60 −0.780056
\(483\) 93.8416 + 167.144i 0.00884045 + 0.0157460i
\(484\) 9965.47 0.935901
\(485\) −1602.72 1849.64i −0.150053 0.173171i
\(486\) 408.849 + 262.751i 0.0381600 + 0.0245240i
\(487\) 95.6374 665.173i 0.00889886 0.0618930i −0.984888 0.173192i \(-0.944592\pi\)
0.993787 + 0.111299i \(0.0355011\pi\)
\(488\) 1196.30 2619.53i 0.110971 0.242993i
\(489\) −373.907 2600.58i −0.0345780 0.240496i
\(490\) −5237.17 1537.77i −0.482840 0.141774i
\(491\) 12150.1 7808.38i 1.11675 0.717693i 0.153998 0.988071i \(-0.450785\pi\)
0.962754 + 0.270378i \(0.0871488\pi\)
\(492\) 2433.89 + 5329.48i 0.223025 + 0.488356i
\(493\) −206.825 + 60.7293i −0.0188944 + 0.00554789i
\(494\) 4058.52 4683.78i 0.369639 0.426586i
\(495\) 2902.11 3349.21i 0.263515 0.304113i
\(496\) 930.268 273.151i 0.0842143 0.0247275i
\(497\) −124.480 272.574i −0.0112348 0.0246008i
\(498\) −2019.65 + 1297.95i −0.181733 + 0.116792i
\(499\) −11185.9 3284.46i −1.00350 0.294655i −0.261610 0.965174i \(-0.584253\pi\)
−0.741893 + 0.670519i \(0.766072\pi\)
\(500\) 845.867 + 5883.14i 0.0756567 + 0.526204i
\(501\) −1285.49 + 2814.82i −0.114633 + 0.251012i
\(502\) −2058.30 + 14315.8i −0.183001 + 1.27280i
\(503\) −4719.83 3033.25i −0.418383 0.268879i 0.314467 0.949268i \(-0.398174\pi\)
−0.732851 + 0.680390i \(0.761811\pi\)
\(504\) 27.3122 + 31.5200i 0.00241386 + 0.00278574i
\(505\) 12488.9 1.10049
\(506\) 13360.7 + 2741.93i 1.17383 + 0.240896i
\(507\) 378.501 0.0331554
\(508\) 1371.66 + 1582.98i 0.119798 + 0.138255i
\(509\) −10112.9 6499.19i −0.880644 0.565956i 0.0203469 0.999793i \(-0.493523\pi\)
−0.900991 + 0.433837i \(0.857159\pi\)
\(510\) −96.0179 + 667.819i −0.00833676 + 0.0579834i
\(511\) 272.295 596.242i 0.0235726 0.0516168i
\(512\) 72.8652 + 506.789i 0.00628949 + 0.0437443i
\(513\) −1764.09 517.985i −0.151826 0.0445801i
\(514\) −4032.83 + 2591.74i −0.346071 + 0.222406i
\(515\) 2225.63 + 4873.45i 0.190433 + 0.416990i
\(516\) −1246.46 + 365.992i −0.106341 + 0.0312247i
\(517\) 6922.20 7988.64i 0.588855 0.679575i
\(518\) −240.589 + 277.655i −0.0204071 + 0.0235511i
\(519\) 7550.25 2216.95i 0.638573 0.187502i
\(520\) 1204.48 + 2637.45i 0.101577 + 0.222423i
\(521\) 3744.31 2406.32i 0.314858 0.202347i −0.373661 0.927566i \(-0.621898\pi\)
0.688519 + 0.725218i \(0.258261\pi\)
\(522\) 263.682 + 77.4241i 0.0221093 + 0.00649188i
\(523\) −256.153 1781.58i −0.0214164 0.148954i 0.976307 0.216389i \(-0.0694278\pi\)
−0.997724 + 0.0674342i \(0.978519\pi\)
\(524\) 383.798 840.400i 0.0319967 0.0700631i
\(525\) −15.2264 + 105.902i −0.00126578 + 0.00880372i
\(526\) 11518.5 + 7402.50i 0.954812 + 0.613620i
\(527\) 560.261 + 646.575i 0.0463099 + 0.0534445i
\(528\) 2967.61 0.244600
\(529\) 11183.6 + 4792.08i 0.919171 + 0.393858i
\(530\) −961.803 −0.0788265
\(531\) 1850.16 + 2135.19i 0.151205 + 0.174500i
\(532\) −132.733 85.3024i −0.0108171 0.00695174i
\(533\) −3161.99 + 21992.1i −0.256962 + 1.78721i
\(534\) 2507.18 5489.96i 0.203177 0.444895i
\(535\) −1083.58 7536.49i −0.0875653 0.609030i
\(536\) 4402.23 + 1292.61i 0.354753 + 0.104165i
\(537\) 8480.18 5449.88i 0.681465 0.437951i
\(538\) −6133.96 13431.5i −0.491550 1.07634i
\(539\) −20327.2 + 5968.60i −1.62440 + 0.476968i
\(540\) 563.286 650.066i 0.0448888 0.0518045i
\(541\) 7782.04 8980.95i 0.618440 0.713718i −0.356970 0.934116i \(-0.616190\pi\)
0.975410 + 0.220398i \(0.0707356\pi\)
\(542\) −11528.0 + 3384.93i −0.913600 + 0.268257i
\(543\) 657.628 + 1440.00i 0.0519733 + 0.113806i
\(544\) −380.077 + 244.261i −0.0299553 + 0.0192511i
\(545\) 412.444 + 121.105i 0.0324168 + 0.00951844i
\(546\) 22.5087 + 156.551i 0.00176425 + 0.0122707i
\(547\) −5868.10 + 12849.3i −0.458687 + 1.00438i 0.529098 + 0.848561i \(0.322530\pi\)
−0.987785 + 0.155824i \(0.950197\pi\)
\(548\) 1607.89 11183.1i 0.125339 0.871752i
\(549\) −2725.44 1751.53i −0.211874 0.136163i
\(550\) 4985.36 + 5753.41i 0.386502 + 0.446048i
\(551\) −1039.64 −0.0803814
\(552\) 2593.25 + 532.196i 0.199957 + 0.0410358i
\(553\) −5.36230 −0.000412348
\(554\) −6980.48 8055.91i −0.535329 0.617803i
\(555\) 6374.20 + 4096.45i 0.487513 + 0.313306i
\(556\) −1205.10 + 8381.69i −0.0919205 + 0.639321i
\(557\) 3546.12 7764.93i 0.269756 0.590683i −0.725473 0.688251i \(-0.758379\pi\)
0.995229 + 0.0975676i \(0.0311062\pi\)
\(558\) −155.228 1079.63i −0.0117765 0.0819076i
\(559\) −4726.81 1387.92i −0.357644 0.105014i
\(560\) 62.0982 39.9081i 0.00468594 0.00301147i
\(561\) 1087.84 + 2382.03i 0.0818691 + 0.179268i
\(562\) 10520.6 3089.13i 0.789654 0.231863i
\(563\) −532.103 + 614.079i −0.0398321 + 0.0459687i −0.775316 0.631573i \(-0.782409\pi\)
0.735484 + 0.677542i \(0.236955\pi\)
\(564\) 1343.57 1550.56i 0.100309 0.115763i
\(565\) 13058.0 3834.16i 0.972305 0.285494i
\(566\) −3570.57 7818.45i −0.265163 0.580626i
\(567\) 39.4719 25.3670i 0.00292357 0.00187886i
\(568\) −3970.76 1165.92i −0.293327 0.0861285i
\(569\) −3041.51 21154.2i −0.224089 1.55858i −0.722338 0.691541i \(-0.756932\pi\)
0.498248 0.867034i \(-0.333977\pi\)
\(570\) −1351.78 + 2959.98i −0.0993330 + 0.217509i
\(571\) −3595.90 + 25010.1i −0.263544 + 1.83299i 0.242101 + 0.970251i \(0.422163\pi\)
−0.505646 + 0.862741i \(0.668746\pi\)
\(572\) 9467.29 + 6084.26i 0.692041 + 0.444748i
\(573\) 1253.89 + 1447.06i 0.0914168 + 0.105501i
\(574\) 565.644 0.0411316
\(575\) 3324.67 + 5921.67i 0.241128 + 0.429479i
\(576\) 576.000 0.0416667
\(577\) −11791.1 13607.7i −0.850731 0.981796i 0.149244 0.988800i \(-0.452316\pi\)
−0.999975 + 0.00700411i \(0.997771\pi\)
\(578\) 7930.77 + 5096.80i 0.570721 + 0.366780i
\(579\) −1224.17 + 8514.27i −0.0878664 + 0.611124i
\(580\) 202.053 442.434i 0.0144651 0.0316743i
\(581\) 32.9856 + 229.420i 0.00235538 + 0.0163820i
\(582\) −1769.07 519.447i −0.125997 0.0369961i
\(583\) −3140.46 + 2018.25i −0.223095 + 0.143375i
\(584\) −3760.57 8234.49i −0.266461 0.583469i
\(585\) 3129.77 918.985i 0.221197 0.0649493i
\(586\) −644.888 + 744.240i −0.0454609 + 0.0524647i
\(587\) 10888.0 12565.4i 0.765578 0.883525i −0.230402 0.973096i \(-0.574004\pi\)
0.995980 + 0.0895710i \(0.0285496\pi\)
\(588\) −3945.41 + 1158.48i −0.276711 + 0.0812496i
\(589\) 1714.13 + 3753.43i 0.119915 + 0.262576i
\(590\) 4206.59 2703.41i 0.293529 0.188640i
\(591\) 6945.67 + 2039.43i 0.483429 + 0.141948i
\(592\) 722.091 + 5022.25i 0.0501313 + 0.348671i
\(593\) −1817.76 + 3980.34i −0.125879 + 0.275637i −0.962071 0.272801i \(-0.912050\pi\)
0.836191 + 0.548438i \(0.184777\pi\)
\(594\) 475.127 3304.58i 0.0328194 0.228264i
\(595\) 54.7966 + 35.2156i 0.00377553 + 0.00242639i
\(596\) −180.170 207.928i −0.0123827 0.0142903i
\(597\) 6992.04 0.479338
\(598\) 7181.88 + 7014.55i 0.491119 + 0.479676i
\(599\) −23046.7 −1.57206 −0.786028 0.618191i \(-0.787866\pi\)
−0.786028 + 0.618191i \(0.787866\pi\)
\(600\) 967.634 + 1116.71i 0.0658392 + 0.0759825i
\(601\) 8750.53 + 5623.63i 0.593913 + 0.381685i 0.802794 0.596256i \(-0.203346\pi\)
−0.208881 + 0.977941i \(0.566982\pi\)
\(602\) −17.8488 + 124.141i −0.00120841 + 0.00840469i
\(603\) 2144.20 4695.15i 0.144807 0.317083i
\(604\) 839.655 + 5839.93i 0.0565647 + 0.393416i
\(605\) −19038.6 5590.25i −1.27939 0.375663i
\(606\) 7914.90 5086.60i 0.530562 0.340972i
\(607\) −6973.23 15269.2i −0.466284 1.02102i −0.986010 0.166687i \(-0.946693\pi\)
0.519725 0.854333i \(-0.326034\pi\)
\(608\) −2090.78 + 613.908i −0.139461 + 0.0409494i
\(609\) 17.3745 20.0513i 0.00115608 0.00133418i
\(610\) −3754.93 + 4333.42i −0.249234 + 0.287631i
\(611\) 7465.23 2191.99i 0.494290 0.145137i
\(612\) 211.144 + 462.342i 0.0139461 + 0.0305377i
\(613\) 3847.28 2472.50i 0.253491 0.162909i −0.407724 0.913105i \(-0.633677\pi\)
0.661215 + 0.750196i \(0.270041\pi\)
\(614\) −6254.82 1836.58i −0.411114 0.120714i
\(615\) −1660.22 11547.1i −0.108856 0.757110i
\(616\) 119.018 260.614i 0.00778472 0.0170462i
\(617\) 3280.80 22818.5i 0.214068 1.48888i −0.545314 0.838232i \(-0.683590\pi\)
0.759383 0.650644i \(-0.225501\pi\)
\(618\) 3395.41 + 2182.10i 0.221009 + 0.142034i
\(619\) −5907.45 6817.56i −0.383587 0.442683i 0.530816 0.847487i \(-0.321885\pi\)
−0.914404 + 0.404804i \(0.867340\pi\)
\(620\) −1930.47 −0.125047
\(621\) 1007.82 2802.51i 0.0651245 0.181096i
\(622\) 19912.9 1.28366
\(623\) −381.573 440.358i −0.0245383 0.0283188i
\(624\) 1837.56 + 1180.93i 0.117886 + 0.0757610i
\(625\) 588.973 4096.40i 0.0376943 0.262169i
\(626\) −8538.52 + 18696.7i −0.545156 + 1.19373i
\(627\) 1797.44 + 12501.5i 0.114486 + 0.796268i
\(628\) −7123.30 2091.59i −0.452629 0.132904i
\(629\) −3766.55 + 2420.61i −0.238763 + 0.153444i
\(630\) −34.4974 75.5388i −0.00218160 0.00477705i
\(631\) −19335.0 + 5677.26i −1.21983 + 0.358175i −0.827403 0.561608i \(-0.810183\pi\)
−0.392427 + 0.919783i \(0.628365\pi\)
\(632\) −48.4969 + 55.9685i −0.00305238 + 0.00352264i
\(633\) −3939.07 + 4545.93i −0.247337 + 0.285442i
\(634\) 11530.2 3385.58i 0.722277 0.212080i
\(635\) −1732.51 3793.66i −0.108272 0.237082i
\(636\) −609.548 + 391.733i −0.0380034 + 0.0244233i
\(637\) −14961.8 4393.18i −0.930624 0.273256i
\(638\) −268.666 1868.61i −0.0166718 0.115955i
\(639\) −1934.05 + 4234.97i −0.119734 + 0.262180i
\(640\) 145.083 1009.07i 0.00896079 0.0623237i
\(641\) 19981.3 + 12841.2i 1.23122 + 0.791259i 0.984081 0.177720i \(-0.0568721\pi\)
0.247142 + 0.968979i \(0.420508\pi\)
\(642\) −3756.27 4334.96i −0.230916 0.266491i
\(643\) −25010.2 −1.53391 −0.766955 0.641701i \(-0.778229\pi\)
−0.766955 + 0.641701i \(0.778229\pi\)
\(644\) 150.741 206.394i 0.00922368 0.0126290i
\(645\) 2586.61 0.157903
\(646\) −1259.19 1453.18i −0.0766905 0.0885055i
\(647\) −19947.3 12819.4i −1.21207 0.778951i −0.231067 0.972938i \(-0.574222\pi\)
−0.981004 + 0.193987i \(0.937858\pi\)
\(648\) 92.2200 641.404i 0.00559065 0.0388839i
\(649\) 8062.42 17654.2i 0.487639 1.06778i
\(650\) 797.451 + 5546.39i 0.0481209 + 0.334688i
\(651\) −101.038 29.6675i −0.00608294 0.00178611i
\(652\) −2946.99 + 1893.92i −0.177014 + 0.113760i
\(653\) −787.562 1724.52i −0.0471971 0.103347i 0.884565 0.466418i \(-0.154456\pi\)
−0.931762 + 0.363071i \(0.881728\pi\)
\(654\) 310.714 91.2338i 0.0185778 0.00545493i
\(655\) −1204.66 + 1390.25i −0.0718627 + 0.0829340i
\(656\) 5115.72 5903.85i 0.304474 0.351382i
\(657\) −9771.59 + 2869.20i −0.580253 + 0.170378i
\(658\) −82.2843 180.178i −0.00487504 0.0106748i
\(659\) 1635.13 1050.83i 0.0966548 0.0621163i −0.491421 0.870922i \(-0.663522\pi\)
0.588075 + 0.808806i \(0.299886\pi\)
\(660\) −5669.51 1664.72i −0.334372 0.0981804i
\(661\) −2300.80 16002.4i −0.135387 0.941635i −0.938370 0.345633i \(-0.887664\pi\)
0.802983 0.596002i \(-0.203245\pi\)
\(662\) −6050.66 + 13249.1i −0.355235 + 0.777857i
\(663\) −274.308 + 1907.86i −0.0160682 + 0.111757i
\(664\) 2692.87 + 1730.60i 0.157385 + 0.101145i
\(665\) 205.730 + 237.425i 0.0119968 + 0.0138450i
\(666\) 5708.13 0.332111
\(667\) 100.333 1681.07i 0.00582444 0.0975882i
\(668\) 4125.95 0.238979
\(669\) 7936.48 + 9159.19i 0.458658 + 0.529320i
\(670\) −7685.18 4938.97i −0.443141 0.284789i
\(671\) −3167.26 + 22028.8i −0.182221 + 1.26738i
\(672\) 23.1009 50.5840i 0.00132610 0.00290375i
\(673\) 3504.57 + 24374.8i 0.200730 + 1.39611i 0.802126 + 0.597155i \(0.203702\pi\)
−0.601396 + 0.798951i \(0.705389\pi\)
\(674\) −4300.17 1262.64i −0.245751 0.0721591i
\(675\) 1398.43 898.719i 0.0797418 0.0512470i
\(676\) −209.646 459.062i −0.0119280 0.0261187i
\(677\) −3584.08 + 1052.38i −0.203468 + 0.0597435i −0.381878 0.924213i \(-0.624723\pi\)
0.178411 + 0.983956i \(0.442904\pi\)
\(678\) 6713.94 7748.30i 0.380306 0.438896i
\(679\) −116.568 + 134.526i −0.00658829 + 0.00760329i
\(680\) 863.143 253.442i 0.0486765 0.0142927i
\(681\) 6393.95 + 14000.8i 0.359790 + 0.787830i
\(682\) −6303.32 + 4050.90i −0.353910 + 0.227444i
\(683\) 7210.09 + 2117.07i 0.403933 + 0.118605i 0.477387 0.878693i \(-0.341584\pi\)
−0.0734538 + 0.997299i \(0.523402\pi\)
\(684\) 348.874 + 2426.47i 0.0195023 + 0.135641i
\(685\) −9345.13 + 20463.0i −0.521254 + 1.14139i
\(686\) −113.049 + 786.275i −0.00629190 + 0.0437611i
\(687\) −11162.7 7173.83i −0.619917 0.398397i
\(688\) 1134.29 + 1309.04i 0.0628550 + 0.0725386i
\(689\) −2747.72 −0.151930
\(690\) −4655.76 2471.45i −0.256872 0.136357i
\(691\) 19606.9 1.07942 0.539712 0.841850i \(-0.318533\pi\)
0.539712 + 0.841850i \(0.318533\pi\)
\(692\) −6870.80 7929.32i −0.377440 0.435589i
\(693\) −271.151 174.258i −0.0148632 0.00955199i
\(694\) −860.603 + 5985.62i −0.0470721 + 0.327394i
\(695\) 7004.11 15336.9i 0.382275 0.837065i
\(696\) −52.1468 362.689i −0.00283997 0.0197524i
\(697\) 6614.15 + 1942.09i 0.359439 + 0.105541i
\(698\) −8341.68 + 5360.88i −0.452346 + 0.290705i
\(699\) −1351.50 2959.37i −0.0731307 0.160134i
\(700\) 136.876 40.1906i 0.00739064 0.00217009i
\(701\) −18868.5 + 21775.5i −1.01663 + 1.17325i −0.0318373 + 0.999493i \(0.510136\pi\)
−0.984789 + 0.173756i \(0.944410\pi\)
\(702\) 1609.22 1857.14i 0.0865186 0.0998478i
\(703\) −20719.5 + 6083.80i −1.11160 + 0.326394i
\(704\) −1643.72 3599.25i −0.0879973 0.192687i
\(705\) −3436.63 + 2208.59i −0.183590 + 0.117986i
\(706\) 10731.6 + 3151.07i 0.572079 + 0.167978i
\(707\) −129.269 899.083i −0.00687645 0.0478267i
\(708\) 1564.88 3426.60i 0.0830673 0.181892i
\(709\) −1784.56 + 12411.9i −0.0945282 + 0.657458i 0.886376 + 0.462966i \(0.153215\pi\)
−0.980904 + 0.194492i \(0.937694\pi\)
\(710\) 6931.95 + 4454.89i 0.366410 + 0.235478i
\(711\) 54.5591 + 62.9645i 0.00287781 + 0.00332117i
\(712\) −8047.15 −0.423567
\(713\) −6234.63 + 2409.48i −0.327474 + 0.126558i
\(714\) 49.0707 0.00257202
\(715\) −14673.8 16934.5i −0.767511 0.885755i
\(716\) −11306.9 7266.51i −0.590166 0.379277i
\(717\) −1240.15 + 8625.40i −0.0645943 + 0.449263i
\(718\) −7208.13 + 15783.6i −0.374659 + 0.820388i
\(719\) 2335.41 + 16243.2i 0.121135 + 0.842514i 0.956274 + 0.292474i \(0.0944785\pi\)
−0.835138 + 0.550040i \(0.814612\pi\)
\(720\) −1100.42 323.114i −0.0569589 0.0167246i
\(721\) 327.806 210.668i 0.0169322 0.0108817i
\(722\) 1846.14 + 4042.49i 0.0951611 + 0.208374i
\(723\) 11880.3 3488.38i 0.611113 0.179439i
\(724\) 1382.25 1595.20i 0.0709541 0.0818854i
\(725\) 615.555 710.388i 0.0315326 0.0363905i
\(726\) −14342.7 + 4211.40i −0.733206 + 0.215289i
\(727\) 8970.11 + 19641.8i 0.457611 + 1.00203i 0.988026 + 0.154290i \(0.0493090\pi\)
−0.530415 + 0.847738i \(0.677964\pi\)
\(728\) 177.405 114.011i 0.00903167 0.00580431i
\(729\) −699.470 205.383i −0.0355368 0.0104345i
\(730\) 2565.18 + 17841.2i 0.130057 + 0.904565i
\(731\) −634.937 + 1390.32i −0.0321259 + 0.0703458i
\(732\) −614.750 + 4275.68i −0.0310407 + 0.215893i
\(733\) −20572.2 13221.0i −1.03663 0.666205i −0.0924825 0.995714i \(-0.529480\pi\)
−0.944152 + 0.329510i \(0.893117\pi\)
\(734\) −11869.4 13698.0i −0.596875 0.688830i
\(735\) 8187.41 0.410880
\(736\) −790.899 3439.98i −0.0396099 0.172282i
\(737\) −35457.4 −1.77217
\(738\) −5755.18 6641.83i −0.287061 0.331286i
\(739\) 25630.8 + 16471.9i 1.27584 + 0.819931i 0.990368 0.138457i \(-0.0442142\pi\)
0.285469 + 0.958388i \(0.407851\pi\)
\(740\) 1437.77 9999.88i 0.0714234 0.496761i
\(741\) −3861.82 + 8456.21i −0.191454 + 0.419226i
\(742\) 9.95534 + 69.2409i 0.000492550 + 0.00342576i
\(743\) −16254.7 4772.81i −0.802593 0.235663i −0.145389 0.989375i \(-0.546443\pi\)
−0.657205 + 0.753712i \(0.728261\pi\)
\(744\) −1223.45 + 786.261i −0.0602872 + 0.0387442i
\(745\) 227.569 + 498.306i 0.0111912 + 0.0245054i
\(746\) 21987.8 6456.21i 1.07913 0.316861i
\(747\) 2358.25 2721.57i 0.115507 0.133302i
\(748\) 2286.49 2638.75i 0.111768 0.128987i
\(749\) −531.342 + 156.016i −0.0259210 + 0.00761108i
\(750\) −3703.61 8109.78i −0.180316 0.394836i
\(751\) 34497.5 22170.2i 1.67621 1.07723i 0.791371 0.611337i \(-0.209368\pi\)
0.884839 0.465898i \(-0.154268\pi\)
\(752\) −2624.77 770.701i −0.127281 0.0373731i
\(753\) −3087.45 21473.7i −0.149420 1.03924i
\(754\) 577.233 1263.96i 0.0278801 0.0610489i
\(755\) 1671.85 11628.0i 0.0805891 0.560510i
\(756\) −52.6292 33.8227i −0.00253188 0.00162714i
\(757\) −18312.9 21134.2i −0.879250 1.01471i −0.999758 0.0219960i \(-0.992998\pi\)
0.120508 0.992712i \(-0.461548\pi\)
\(758\) −20597.9 −0.987006
\(759\) −20388.0 + 1699.93i −0.975017 + 0.0812959i
\(760\) 4338.73 0.207082
\(761\) 17643.7 + 20361.9i 0.840452 + 0.969933i 0.999851 0.0172811i \(-0.00550101\pi\)
−0.159399 + 0.987214i \(0.550956\pi\)
\(762\) −2643.11 1698.62i −0.125656 0.0807541i
\(763\) 4.44932 30.9457i 0.000211109 0.00146830i
\(764\) 1060.55 2322.27i 0.0502215 0.109970i
\(765\) −144.027 1001.73i −0.00680693 0.0473433i
\(766\) 1076.79 + 316.174i 0.0507911 + 0.0149136i
\(767\) 12017.6 7723.22i 0.565748 0.363584i
\(768\) −319.039 698.597i −0.0149900 0.0328235i
\(769\) 6952.57 2041.46i 0.326029 0.0957307i −0.114622 0.993409i \(-0.536566\pi\)
0.440651 + 0.897678i \(0.354748\pi\)
\(770\) −373.574 + 431.128i −0.0174840 + 0.0201776i
\(771\) 4708.94 5434.41i 0.219959 0.253846i
\(772\) 11004.5 3231.22i 0.513033 0.150640i
\(773\) 13567.7 + 29709.1i 0.631300 + 1.38235i 0.907008 + 0.421113i \(0.138361\pi\)
−0.275708 + 0.961242i \(0.588912\pi\)
\(774\) 1639.28 1053.50i 0.0761275 0.0489242i
\(775\) −3579.64 1051.08i −0.165915 0.0487172i
\(776\) 349.859 + 2433.32i 0.0161845 + 0.112566i
\(777\) 228.929 501.285i 0.0105699 0.0231448i
\(778\) −2643.68 + 18387.2i −0.121826 + 0.847318i
\(779\) 27969.3 + 17974.7i 1.28640 + 0.826717i
\(780\) −2848.12 3286.91i −0.130743 0.150885i
\(781\) 31982.2 1.46532
\(782\) 2471.27 1895.83i 0.113008 0.0866941i
\(783\) −412.221 −0.0188143
\(784\) 3590.36 + 4143.50i 0.163555 + 0.188753i
\(785\) 12435.5 + 7991.80i 0.565403 + 0.363363i
\(786\) −197.225 + 1371.73i −0.00895010 + 0.0622493i
\(787\) 7878.80 17252.2i 0.356860 0.781415i −0.643019 0.765851i \(-0.722318\pi\)
0.999879 0.0155644i \(-0.00495450\pi\)
\(788\) −1373.60 9553.62i −0.0620972 0.431895i
\(789\) −19706.2 5786.26i −0.889175 0.261085i
\(790\) 124.048 79.7206i 0.00558660 0.00359029i
\(791\) −411.183 900.366i −0.0184829 0.0404720i
\(792\) −4271.11 + 1254.11i −0.191625 + 0.0562663i
\(793\) −10727.2 + 12379.9i −0.480373 + 0.554380i
\(794\) 13951.3 16100.7i 0.623569 0.719637i
\(795\) 1384.26 406.457i 0.0617545 0.0181327i
\(796\) −3872.80 8480.24i −0.172447 0.377606i
\(797\) 32724.7 21030.9i 1.45441 0.934695i 0.455401 0.890287i \(-0.349496\pi\)
0.999013 0.0444087i \(-0.0141404\pi\)
\(798\) 227.083 + 66.6777i 0.0100735 + 0.00295785i
\(799\) −343.537 2389.35i −0.0152109 0.105794i
\(800\) 818.433 1792.12i 0.0361700 0.0792012i
\(801\) −1288.38 + 8960.90i −0.0568324 + 0.395278i
\(802\) 962.524 + 618.577i 0.0423789 + 0.0272353i
\(803\) 45813.8 + 52871.9i 2.01337 + 2.32355i
\(804\) −6882.12 −0.301883
\(805\) −403.765 + 309.747i −0.0176781 + 0.0135617i
\(806\) −5515.04 −0.241016
\(807\) 14504.4 + 16738.9i 0.632687 + 0.730160i
\(808\) −10553.2 6782.13i −0.459480 0.295290i
\(809\) −1045.80 + 7273.68i −0.0454490 + 0.316105i 0.954397 + 0.298541i \(0.0965001\pi\)
−0.999846 + 0.0175637i \(0.994409\pi\)
\(810\) −535.986 + 1173.65i −0.0232502 + 0.0509107i
\(811\) −5033.01 35005.4i −0.217920 1.51567i −0.745698 0.666284i \(-0.767884\pi\)
0.527779 0.849382i \(-0.323025\pi\)
\(812\) −33.9425 9.96643i −0.00146693 0.000430730i
\(813\) 15161.1 9743.46i 0.654027 0.420317i
\(814\) −16289.2 35668.4i −0.701396 1.53584i
\(815\) 6692.53 1965.10i 0.287643 0.0844596i
\(816\) 443.798 512.170i 0.0190392 0.0219725i
\(817\) −4827.47 + 5571.19i −0.206722 + 0.238570i
\(818\) −3534.79 + 1037.91i −0.151089 + 0.0443638i
\(819\) −98.5538 215.803i −0.00420482 0.00920727i
\(820\) −13085.2 + 8409.35i −0.557263 + 0.358131i
\(821\) 32948.0 + 9674.42i 1.40060 + 0.411254i 0.892891 0.450273i \(-0.148673\pi\)
0.507712 + 0.861527i \(0.330492\pi\)
\(822\) 2411.84 + 16774.7i 0.102339 + 0.711782i
\(823\) 19115.7 41857.5i 0.809636 1.77285i 0.200669 0.979659i \(-0.435689\pi\)
0.608967 0.793196i \(-0.291584\pi\)
\(824\) 765.870 5326.74i 0.0323790 0.225201i
\(825\) −9606.51 6173.73i −0.405401 0.260535i
\(826\) −238.162 274.853i −0.0100323 0.0115779i
\(827\) −19003.5 −0.799052 −0.399526 0.916722i \(-0.630825\pi\)
−0.399526 + 0.916722i \(0.630825\pi\)
\(828\) −3957.22 + 329.949i −0.166090 + 0.0138484i
\(829\) 13720.7 0.574838 0.287419 0.957805i \(-0.407203\pi\)
0.287419 + 0.957805i \(0.407203\pi\)
\(830\) −4173.82 4816.85i −0.174549 0.201440i
\(831\) 13451.0 + 8644.44i 0.561504 + 0.360857i
\(832\) 414.479 2882.77i 0.0172710 0.120123i
\(833\) −2009.77 + 4400.78i −0.0835947 + 0.183047i
\(834\) −1807.66 12572.5i −0.0750528 0.522004i
\(835\) −7882.46 2314.50i −0.326687 0.0959240i
\(836\) 14166.7 9104.40i 0.586084 0.376653i
\(837\) 679.661 + 1488.25i 0.0280675 + 0.0614593i
\(838\) −6486.60 + 1904.64i −0.267394 + 0.0785139i
\(839\) 22210.0 25631.7i 0.913914 1.05471i −0.0843863 0.996433i \(-0.526893\pi\)
0.998300 0.0582798i \(-0.0185616\pi\)
\(840\) −72.5091 + 83.6799i −0.00297833 + 0.00343718i
\(841\) 23177.4 6805.50i 0.950323 0.279040i
\(842\) 1316.28 + 2882.25i 0.0538742 + 0.117968i
\(843\) −13836.2 + 8892.00i −0.565296 + 0.363294i
\(844\) 7695.30 + 2259.54i 0.313843 + 0.0921525i
\(845\) 143.005 + 994.623i 0.00582192 + 0.0404924i
\(846\) −1278.45 + 2799.41i −0.0519551 + 0.113766i
\(847\) −205.383 + 1428.47i −0.00833180 + 0.0579489i
\(848\) 812.731 + 522.310i 0.0329119 + 0.0211512i
\(849\) 8442.97 + 9743.71i 0.341298 + 0.393879i
\(850\) 1738.50 0.0701532
\(851\) −7837.77 34090.1i −0.315717 1.37320i
\(852\) 6207.60 0.249611
\(853\) −26327.4 30383.4i −1.05678 1.21959i −0.974829 0.222952i \(-0.928431\pi\)
−0.0819500 0.996636i \(-0.526115\pi\)
\(854\) 350.832 + 225.466i 0.0140577 + 0.00903431i
\(855\) 694.649 4831.39i 0.0277854 0.193251i
\(856\) −3177.08 + 6956.84i −0.126858 + 0.277780i
\(857\) 752.904 + 5236.56i 0.0300101 + 0.208725i 0.999309 0.0371590i \(-0.0118308\pi\)
−0.969299 + 0.245884i \(0.920922\pi\)
\(858\) −16196.9 4755.84i −0.644467 0.189233i
\(859\) 27155.7 17451.9i 1.07863 0.693191i 0.124386 0.992234i \(-0.460304\pi\)
0.954240 + 0.299043i \(0.0966674\pi\)
\(860\) −1432.69 3137.15i −0.0568073 0.124391i
\(861\) −814.098 + 239.041i −0.0322234 + 0.00946166i
\(862\) 5017.82 5790.87i 0.198269 0.228814i
\(863\) 5597.24 6459.56i 0.220779 0.254793i −0.634545 0.772886i \(-0.718813\pi\)
0.855324 + 0.518093i \(0.173358\pi\)
\(864\) −829.002 + 243.417i −0.0326426 + 0.00958474i
\(865\) 8678.34 + 19002.9i 0.341124 + 0.746958i
\(866\) 5318.28 3417.85i 0.208687 0.134115i
\(867\) −13568.2 3983.98i −0.531487 0.156059i
\(868\) 19.9817 + 138.976i 0.000781363 + 0.00543450i
\(869\) 237.752 520.604i 0.00928099 0.0203225i
\(870\) −103.830 + 722.156i −0.00404618 + 0.0281418i
\(871\) −21955.4 14109.9i −0.854109 0.548903i
\(872\) −282.752 326.314i −0.0109807 0.0126725i
\(873\) 2765.64 0.107220
\(874\) 14012.3 5415.31i 0.542305 0.209583i
\(875\) −860.732 −0.0332549
\(876\) 8892.24 + 10262.2i 0.342969 + 0.395808i
\(877\) −11244.0 7226.05i −0.432932 0.278229i 0.305970 0.952041i \(-0.401019\pi\)
−0.738902 + 0.673813i \(0.764656\pi\)
\(878\) −1887.85 + 13130.3i −0.0725646 + 0.504698i
\(879\) 613.633 1343.67i 0.0235465 0.0515595i
\(880\) 1121.22 + 7798.29i 0.0429505 + 0.298727i
\(881\) −5956.58 1749.01i −0.227789 0.0668849i 0.165846 0.986152i \(-0.446964\pi\)
−0.393635 + 0.919267i \(0.628783\pi\)
\(882\) 5188.82 3334.65i 0.198091 0.127306i
\(883\) 16848.7 + 36893.5i 0.642133 + 1.40608i 0.898274 + 0.439436i \(0.144822\pi\)
−0.256141 + 0.966640i \(0.582451\pi\)
\(884\) 2465.86 724.043i 0.0938190 0.0275477i
\(885\) −4911.83 + 5668.55i −0.186564 + 0.215306i
\(886\) −5158.80 + 5953.57i −0.195613 + 0.225750i
\(887\) 30330.9 8905.95i 1.14815 0.337128i 0.348334 0.937370i \(-0.386747\pi\)
0.799818 + 0.600242i \(0.204929\pi\)
\(888\) −3161.66 6923.07i −0.119480 0.261625i
\(889\) −255.176 + 163.992i −0.00962692 + 0.00618684i
\(890\) 15373.8 + 4514.15i 0.579022 + 0.170016i
\(891\) 712.691 + 4956.88i 0.0267969 + 0.186377i
\(892\) 6712.74 14698.9i 0.251972 0.551742i
\(893\) 1656.90 11524.0i 0.0620895 0.431842i
\(894\) 347.178 + 223.118i 0.0129881 + 0.00834695i
\(895\) 17525.2 + 20225.1i 0.654527 + 0.755365i
\(896\) −74.1457 −0.00276455
\(897\) −13300.8 7060.56i −0.495095 0.262815i
\(898\) 10936.2 0.406398
\(899\) 605.845 + 699.183i 0.0224762 + 0.0259389i
\(900\) −1864.58 1198.29i −0.0690584 0.0443812i
\(901\) −121.323 + 843.823i −0.00448598 + 0.0312007i
\(902\) −25079.3 + 54916.1i −0.925777 + 2.02717i
\(903\) −26.7733 186.212i −0.000986665 0.00686240i
\(904\) −13116.2 3851.27i −0.482566 0.141694i
\(905\) −3535.57 + 2272.17i −0.129863 + 0.0834581i
\(906\) −3676.41 8050.21i −0.134813 0.295199i
\(907\) −3913.53 + 1149.12i −0.143271 + 0.0420681i −0.352582 0.935781i \(-0.614696\pi\)
0.209311 + 0.977849i \(0.432878\pi\)
\(908\) 13439.2 15509.7i 0.491186 0.566859i
\(909\) −9241.84 + 10665.7i −0.337220 + 0.389172i
\(910\) −402.881 + 118.296i −0.0146762 + 0.00430933i
\(911\) −14070.2 30809.4i −0.511707 1.12048i −0.972485 0.232967i \(-0.925157\pi\)
0.460777 0.887516i \(-0.347571\pi\)
\(912\) 2749.69 1767.12i 0.0998372 0.0641615i
\(913\) −23736.0 6969.51i −0.860400 0.252636i
\(914\) 4187.48 + 29124.5i 0.151542 + 1.05400i
\(915\) 3572.95 7823.66i 0.129091 0.282669i
\(916\) −2517.86 + 17512.1i −0.0908213 + 0.631676i
\(917\) 112.555 + 72.3344i 0.00405330 + 0.00260490i
\(918\) −499.272 576.191i −0.0179504 0.0207158i
\(919\) −33069.6 −1.18701 −0.593507 0.804829i \(-0.702257\pi\)
−0.593507 + 0.804829i \(0.702257\pi\)
\(920\) −418.719 + 7015.61i −0.0150052 + 0.251411i
\(921\) 9778.32 0.349844
\(922\) −11924.7 13761.9i −0.425944 0.491566i
\(923\) 19803.5 + 12726.9i 0.706219 + 0.453859i
\(924\) −61.1609 + 425.383i −0.00217754 + 0.0151451i
\(925\) 8110.64 17759.8i 0.288298 0.631286i
\(926\) −4146.83 28841.8i −0.147163 1.02354i
\(927\) −5808.97 1705.67i −0.205816 0.0604331i
\(928\) −411.002 + 264.135i −0.0145386 + 0.00934337i
\(929\) 13396.6 + 29334.5i 0.473121 + 1.03599i 0.984298 + 0.176515i \(0.0564824\pi\)
−0.511177 + 0.859475i \(0.670790\pi\)
\(930\) 2778.41 815.813i 0.0979650 0.0287651i
\(931\) −15280.4 + 17634.5i −0.537910 + 0.620782i
\(932\) −2840.67 + 3278.31i −0.0998384 + 0.115220i
\(933\) −28659.5 + 8415.18i −1.00565 + 0.295285i
\(934\) 9185.72 + 20113.9i 0.321805 + 0.704655i
\(935\) −5848.49 + 3758.60i −0.204563 + 0.131465i
\(936\) −3143.74 923.086i −0.109782 0.0322350i
\(937\) 4750.12 + 33037.8i 0.165613 + 1.15186i 0.887821 + 0.460189i \(0.152218\pi\)
−0.722208 + 0.691676i \(0.756873\pi\)
\(938\) −276.013 + 604.384i −0.00960782 + 0.0210382i
\(939\) 4387.75 30517.5i 0.152491 1.06060i
\(940\) 4582.18 + 2944.79i 0.158994 + 0.102179i
\(941\) −21866.6 25235.4i −0.757525 0.874231i 0.237750 0.971326i \(-0.423590\pi\)
−0.995275 + 0.0970957i \(0.969045\pi\)
\(942\) 11136.0 0.385172
\(943\) −31764.0 + 43490.9i −1.09690 + 1.50186i
\(944\) −5022.69 −0.173172
\(945\) 81.5727 + 94.1399i 0.00280800 + 0.00324060i
\(946\) −11261.0 7237.01i −0.387026 0.248727i
\(947\) −516.601 + 3593.04i −0.0177268 + 0.123292i −0.996763 0.0803923i \(-0.974383\pi\)
0.979037 + 0.203685i \(0.0652918\pi\)
\(948\) 46.1465 101.047i 0.00158098 0.00346186i
\(949\) 7328.31 + 50969.5i 0.250671 + 1.74346i
\(950\) 8045.24 + 2362.30i 0.274760 + 0.0806769i
\(951\) −15164.0 + 9745.31i −0.517062 + 0.332296i
\(952\) −27.1796 59.5150i −0.000925310 0.00202615i
\(953\) 13837.0 4062.91i 0.470330 0.138101i −0.0379744 0.999279i \(-0.512091\pi\)
0.508305 + 0.861177i \(0.330272\pi\)
\(954\) 711.740 821.392i 0.0241545 0.0278758i
\(955\) −3328.84 + 3841.68i −0.112794 + 0.130172i
\(956\) 11148.2 3273.39i 0.377152 0.110742i
\(957\) 1176.35 + 2575.85i 0.0397346 + 0.0870065i
\(958\) −10704.3 + 6879.23i −0.361002 + 0.232002i
\(959\) 1569.87 + 460.956i 0.0528612 + 0.0155214i
\(960\) 217.624 + 1513.61i 0.00731645 + 0.0508871i
\(961\) −10850.3 + 23758.8i −0.364213 + 0.797514i
\(962\) 4107.47 28568.1i 0.137661 0.957455i
\(963\) 7238.12 + 4651.66i 0.242207 + 0.155657i
\(964\) −10811.2 12476.8i −0.361210 0.416858i
\(965\) −22836.3 −0.761789
\(966\) −129.731 + 360.753i −0.00432095 + 0.0120156i
\(967\) −55472.9 −1.84476 −0.922382 0.386279i \(-0.873760\pi\)
−0.922382 + 0.386279i \(0.873760\pi\)
\(968\) 13052.0 + 15062.8i 0.433375 + 0.500141i
\(969\) 2426.38 + 1559.34i 0.0804403 + 0.0516958i
\(970\) 696.609 4845.02i 0.0230585 0.160375i
\(971\) −4426.99 + 9693.75i −0.146312 + 0.320378i −0.968572 0.248734i \(-0.919986\pi\)
0.822260 + 0.569112i \(0.192713\pi\)
\(972\) 138.330 + 962.106i 0.00456475 + 0.0317485i
\(973\) −1176.61 345.484i −0.0387671 0.0113830i
\(974\) 1130.67 726.635i 0.0371960 0.0239044i
\(975\) −3491.62 7645.58i −0.114689 0.251133i
\(976\) 5526.23 1622.65i 0.181240 0.0532169i
\(977\) −11182.9 + 12905.7i −0.366194 + 0.422610i −0.908705 0.417438i \(-0.862928\pi\)
0.542512 + 0.840048i \(0.317473\pi\)
\(978\) 3441.06 3971.20i 0.112508 0.129841i
\(979\) 59670.6 17520.9i 1.94799 0.571981i
\(980\) −4534.90 9930.04i −0.147818 0.323677i
\(981\) −408.636 + 262.615i −0.0132994 + 0.00854703i
\(982\) 27715.6 + 8138.03i 0.900651 + 0.264455i
\(983\) 2583.94 + 17971.7i 0.0838401 + 0.583120i 0.987827 + 0.155559i \(0.0497180\pi\)
−0.903986 + 0.427561i \(0.859373\pi\)
\(984\) −4867.78 + 10659.0i −0.157702 + 0.345320i
\(985\) −2735.00 + 19022.3i −0.0884714 + 0.615332i
\(986\) −362.675 233.077i −0.0117139 0.00752809i
\(987\) 194.570 + 224.545i 0.00627479 + 0.00724150i
\(988\) 12395.1 0.399129
\(989\) −8542.59 8343.55i −0.274660 0.268260i
\(990\) 8863.29 0.284539
\(991\) −19455.8 22453.2i −0.623646 0.719726i 0.352749 0.935718i \(-0.385247\pi\)
−0.976395 + 0.215992i \(0.930701\pi\)
\(992\) 1631.26 + 1048.35i 0.0522102 + 0.0335535i
\(993\) 3109.30 21625.6i 0.0993661 0.691107i
\(994\) 248.961 545.147i 0.00794421 0.0173954i
\(995\) 2641.73 + 18373.7i 0.0841694 + 0.585411i
\(996\) −4607.04 1352.75i −0.146566 0.0430356i
\(997\) −15998.8 + 10281.8i −0.508212 + 0.326608i −0.769494 0.638654i \(-0.779491\pi\)
0.261281 + 0.965263i \(0.415855\pi\)
\(998\) −9685.89 21209.1i −0.307216 0.672709i
\(999\) −8215.37 + 2412.25i −0.260183 + 0.0763966i
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 138.4.e.d.13.3 30
23.16 even 11 inner 138.4.e.d.85.3 yes 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
138.4.e.d.13.3 30 1.1 even 1 trivial
138.4.e.d.85.3 yes 30 23.16 even 11 inner