Properties

Label 74.4.c.a.63.1
Level $74$
Weight $4$
Character 74.63
Analytic conductor $4.366$
Analytic rank $0$
Dimension $8$
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] = [74,4,Mod(47,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.47");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 74.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.36614134042\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 48x^{6} + 157x^{5} + 1944x^{4} + 3005x^{3} + 12895x^{2} - 11550x + 44100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 63.1
Root \(3.81550 - 6.60864i\) of defining polynomial
Character \(\chi\) \(=\) 74.63
Dual form 74.4.c.a.47.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-4.31550 + 7.47467i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.90148 + 5.02551i) q^{5} -17.2620 q^{6} +(8.58362 - 14.8673i) q^{7} -8.00000 q^{8} +(-23.7471 - 41.1312i) q^{9} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-4.31550 + 7.47467i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.90148 + 5.02551i) q^{5} -17.2620 q^{6} +(8.58362 - 14.8673i) q^{7} -8.00000 q^{8} +(-23.7471 - 41.1312i) q^{9} -11.6059 q^{10} +9.76027 q^{11} +(-17.2620 - 29.8987i) q^{12} +(-32.6872 + 56.6158i) q^{13} +34.3345 q^{14} +(-25.0427 - 43.3752i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(12.0789 + 20.9213i) q^{17} +(47.4942 - 82.2624i) q^{18} +(-34.7123 + 60.1234i) q^{19} +(-11.6059 - 20.1020i) q^{20} +(74.0852 + 128.319i) q^{21} +(9.76027 + 16.9053i) q^{22} -68.4060 q^{23} +(34.5240 - 59.7973i) q^{24} +(45.6628 + 79.0904i) q^{25} -130.749 q^{26} +176.885 q^{27} +(34.3345 + 59.4690i) q^{28} +229.161 q^{29} +(50.0853 - 86.7503i) q^{30} -271.380 q^{31} +(16.0000 - 27.7128i) q^{32} +(-42.1205 + 72.9548i) q^{33} +(-24.1578 + 41.8426i) q^{34} +(49.8103 + 86.2740i) q^{35} +189.977 q^{36} +(207.031 - 88.2672i) q^{37} -138.849 q^{38} +(-282.123 - 488.651i) q^{39} +(23.2118 - 40.2041i) q^{40} +(-121.151 + 209.839i) q^{41} +(-148.170 + 256.639i) q^{42} +189.254 q^{43} +(-19.5205 + 33.8106i) q^{44} +275.607 q^{45} +(-68.4060 - 118.483i) q^{46} +506.929 q^{47} +138.096 q^{48} +(24.1431 + 41.8171i) q^{49} +(-91.3257 + 158.181i) q^{50} -208.506 q^{51} +(-130.749 - 226.463i) q^{52} +(183.223 + 317.352i) q^{53} +(176.885 + 306.375i) q^{54} +(-28.3192 + 49.0503i) q^{55} +(-68.6689 + 118.938i) q^{56} +(-299.602 - 518.925i) q^{57} +(229.161 + 396.918i) q^{58} +(-444.496 - 769.890i) q^{59} +200.341 q^{60} +(-303.061 + 524.918i) q^{61} +(-271.380 - 470.044i) q^{62} -815.344 q^{63} +64.0000 q^{64} +(-189.682 - 328.539i) q^{65} -168.482 q^{66} +(-125.813 + 217.914i) q^{67} -96.6313 q^{68} +(295.206 - 511.312i) q^{69} +(-99.6207 + 172.548i) q^{70} +(356.160 - 616.887i) q^{71} +(189.977 + 329.049i) q^{72} -87.8669 q^{73} +(359.914 + 270.321i) q^{74} -788.232 q^{75} +(-138.849 - 240.494i) q^{76} +(83.7784 - 145.109i) q^{77} +(564.246 - 977.303i) q^{78} +(-216.786 + 375.485i) q^{79} +92.8473 q^{80} +(-122.178 + 211.618i) q^{81} -484.602 q^{82} +(455.726 + 789.341i) q^{83} -592.682 q^{84} -140.187 q^{85} +(189.254 + 327.798i) q^{86} +(-988.943 + 1712.90i) q^{87} -78.0822 q^{88} +(-370.719 - 642.105i) q^{89} +(275.607 + 477.365i) q^{90} +(561.148 + 971.937i) q^{91} +(136.812 - 236.965i) q^{92} +(1171.14 - 2028.47i) q^{93} +(506.929 + 878.027i) q^{94} +(-201.434 - 348.893i) q^{95} +(138.096 + 239.189i) q^{96} +1383.10 q^{97} +(-48.2862 + 83.6341i) q^{98} +(-231.778 - 401.452i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9} - 40 q^{10} + 64 q^{11} - 20 q^{12} - 61 q^{13} + 12 q^{14} - 43 q^{15} - 64 q^{16} + 12 q^{17} - 14 q^{18} - 71 q^{19} - 40 q^{20} + 67 q^{21} + 64 q^{22} - 52 q^{23} + 40 q^{24} + 48 q^{25} - 244 q^{26} + 658 q^{27} + 12 q^{28} + 322 q^{29} + 86 q^{30} - 112 q^{31} + 128 q^{32} + 280 q^{33} - 24 q^{34} - 359 q^{35} - 56 q^{36} + 557 q^{37} - 284 q^{38} - 389 q^{39} + 80 q^{40} + 92 q^{41} - 134 q^{42} + 532 q^{43} - 128 q^{44} + 330 q^{45} - 52 q^{46} + 280 q^{47} + 160 q^{48} + 87 q^{49} - 96 q^{50} - 1306 q^{51} - 244 q^{52} + 159 q^{53} + 658 q^{54} - 872 q^{55} - 24 q^{56} - 469 q^{57} + 322 q^{58} + 263 q^{59} + 344 q^{60} - 206 q^{61} - 112 q^{62} - 2328 q^{63} + 512 q^{64} - 731 q^{65} + 1120 q^{66} + 245 q^{67} - 96 q^{68} - 360 q^{69} + 718 q^{70} - 957 q^{71} - 56 q^{72} - 272 q^{73} - 178 q^{74} - 3232 q^{75} - 284 q^{76} + 744 q^{77} + 778 q^{78} + 173 q^{79} + 320 q^{80} - 528 q^{81} + 368 q^{82} + 1217 q^{83} - 536 q^{84} + 2988 q^{85} + 532 q^{86} - 2336 q^{87} - 512 q^{88} - 2136 q^{89} + 330 q^{90} + 1575 q^{91} + 104 q^{92} + 2608 q^{93} + 280 q^{94} + 891 q^{95} + 160 q^{96} + 5262 q^{97} - 174 q^{98} - 176 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) −4.31550 + 7.47467i −0.830519 + 1.43850i 0.0671091 + 0.997746i \(0.478622\pi\)
−0.897628 + 0.440755i \(0.854711\pi\)
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −2.90148 + 5.02551i −0.259516 + 0.449495i −0.966112 0.258122i \(-0.916896\pi\)
0.706596 + 0.707617i \(0.250230\pi\)
\(6\) −17.2620 −1.17453
\(7\) 8.58362 14.8673i 0.463472 0.802756i −0.535659 0.844434i \(-0.679937\pi\)
0.999131 + 0.0416776i \(0.0132702\pi\)
\(8\) −8.00000 −0.353553
\(9\) −23.7471 41.1312i −0.879522 1.52338i
\(10\) −11.6059 −0.367011
\(11\) 9.76027 0.267530 0.133765 0.991013i \(-0.457293\pi\)
0.133765 + 0.991013i \(0.457293\pi\)
\(12\) −17.2620 29.8987i −0.415259 0.719250i
\(13\) −32.6872 + 56.6158i −0.697368 + 1.20788i 0.272007 + 0.962295i \(0.412312\pi\)
−0.969376 + 0.245582i \(0.921021\pi\)
\(14\) 34.3345 0.655448
\(15\) −25.0427 43.3752i −0.431066 0.746628i
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 12.0789 + 20.9213i 0.172327 + 0.298480i 0.939233 0.343280i \(-0.111538\pi\)
−0.766906 + 0.641760i \(0.778205\pi\)
\(18\) 47.4942 82.2624i 0.621916 1.07719i
\(19\) −34.7123 + 60.1234i −0.419134 + 0.725961i −0.995853 0.0909820i \(-0.970999\pi\)
0.576719 + 0.816943i \(0.304333\pi\)
\(20\) −11.6059 20.1020i −0.129758 0.224748i
\(21\) 74.0852 + 128.319i 0.769844 + 1.33341i
\(22\) 9.76027 + 16.9053i 0.0945862 + 0.163828i
\(23\) −68.4060 −0.620158 −0.310079 0.950711i \(-0.600356\pi\)
−0.310079 + 0.950711i \(0.600356\pi\)
\(24\) 34.5240 59.7973i 0.293633 0.508587i
\(25\) 45.6628 + 79.0904i 0.365303 + 0.632723i
\(26\) −130.749 −0.986228
\(27\) 176.885 1.26080
\(28\) 34.3345 + 59.4690i 0.231736 + 0.401378i
\(29\) 229.161 1.46738 0.733691 0.679483i \(-0.237796\pi\)
0.733691 + 0.679483i \(0.237796\pi\)
\(30\) 50.0853 86.7503i 0.304810 0.527946i
\(31\) −271.380 −1.57230 −0.786149 0.618036i \(-0.787928\pi\)
−0.786149 + 0.618036i \(0.787928\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) −42.1205 + 72.9548i −0.222189 + 0.384842i
\(34\) −24.1578 + 41.8426i −0.121854 + 0.211057i
\(35\) 49.8103 + 86.2740i 0.240557 + 0.416656i
\(36\) 189.977 0.879522
\(37\) 207.031 88.2672i 0.919884 0.392190i
\(38\) −138.849 −0.592744
\(39\) −282.123 488.651i −1.15835 2.00633i
\(40\) 23.2118 40.2041i 0.0917528 0.158920i
\(41\) −121.151 + 209.839i −0.461477 + 0.799301i −0.999035 0.0439258i \(-0.986013\pi\)
0.537558 + 0.843227i \(0.319347\pi\)
\(42\) −148.170 + 256.639i −0.544362 + 0.942862i
\(43\) 189.254 0.671185 0.335593 0.942007i \(-0.391063\pi\)
0.335593 + 0.942007i \(0.391063\pi\)
\(44\) −19.5205 + 33.8106i −0.0668826 + 0.115844i
\(45\) 275.607 0.913001
\(46\) −68.4060 118.483i −0.219259 0.379768i
\(47\) 506.929 1.57326 0.786630 0.617424i \(-0.211824\pi\)
0.786630 + 0.617424i \(0.211824\pi\)
\(48\) 138.096 0.415259
\(49\) 24.1431 + 41.8171i 0.0703880 + 0.121916i
\(50\) −91.3257 + 158.181i −0.258308 + 0.447403i
\(51\) −208.506 −0.572484
\(52\) −130.749 226.463i −0.348684 0.603939i
\(53\) 183.223 + 317.352i 0.474862 + 0.822485i 0.999586 0.0287878i \(-0.00916471\pi\)
−0.524724 + 0.851273i \(0.675831\pi\)
\(54\) 176.885 + 306.375i 0.445760 + 0.772080i
\(55\) −28.3192 + 49.0503i −0.0694284 + 0.120254i
\(56\) −68.6689 + 118.938i −0.163862 + 0.283817i
\(57\) −299.602 518.925i −0.696196 1.20585i
\(58\) 229.161 + 396.918i 0.518798 + 0.898584i
\(59\) −444.496 769.890i −0.980822 1.69883i −0.659206 0.751963i \(-0.729107\pi\)
−0.321616 0.946870i \(-0.604226\pi\)
\(60\) 200.341 0.431066
\(61\) −303.061 + 524.918i −0.636115 + 1.10178i 0.350163 + 0.936689i \(0.386126\pi\)
−0.986278 + 0.165095i \(0.947207\pi\)
\(62\) −271.380 470.044i −0.555892 0.962832i
\(63\) −815.344 −1.63053
\(64\) 64.0000 0.125000
\(65\) −189.682 328.539i −0.361957 0.626927i
\(66\) −168.482 −0.314223
\(67\) −125.813 + 217.914i −0.229410 + 0.397349i −0.957633 0.287990i \(-0.907013\pi\)
0.728224 + 0.685340i \(0.240346\pi\)
\(68\) −96.6313 −0.172327
\(69\) 295.206 511.312i 0.515053 0.892098i
\(70\) −99.6207 + 172.548i −0.170099 + 0.294621i
\(71\) 356.160 616.887i 0.595329 1.03114i −0.398171 0.917311i \(-0.630355\pi\)
0.993500 0.113829i \(-0.0363116\pi\)
\(72\) 189.977 + 329.049i 0.310958 + 0.538595i
\(73\) −87.8669 −0.140877 −0.0704387 0.997516i \(-0.522440\pi\)
−0.0704387 + 0.997516i \(0.522440\pi\)
\(74\) 359.914 + 270.321i 0.565395 + 0.424652i
\(75\) −788.232 −1.21356
\(76\) −138.849 240.494i −0.209567 0.362980i
\(77\) 83.7784 145.109i 0.123993 0.214762i
\(78\) 564.246 977.303i 0.819080 1.41869i
\(79\) −216.786 + 375.485i −0.308739 + 0.534751i −0.978087 0.208198i \(-0.933240\pi\)
0.669348 + 0.742949i \(0.266574\pi\)
\(80\) 92.8473 0.129758
\(81\) −122.178 + 211.618i −0.167596 + 0.290285i
\(82\) −484.602 −0.652626
\(83\) 455.726 + 789.341i 0.602680 + 1.04387i 0.992413 + 0.122945i \(0.0392339\pi\)
−0.389733 + 0.920928i \(0.627433\pi\)
\(84\) −592.682 −0.769844
\(85\) −140.187 −0.178887
\(86\) 189.254 + 327.798i 0.237300 + 0.411015i
\(87\) −988.943 + 1712.90i −1.21869 + 2.11083i
\(88\) −78.0822 −0.0945862
\(89\) −370.719 642.105i −0.441530 0.764752i 0.556273 0.830999i \(-0.312231\pi\)
−0.997803 + 0.0662470i \(0.978897\pi\)
\(90\) 275.607 + 477.365i 0.322794 + 0.559096i
\(91\) 561.148 + 971.937i 0.646421 + 1.11963i
\(92\) 136.812 236.965i 0.155040 0.268536i
\(93\) 1171.14 2028.47i 1.30582 2.26175i
\(94\) 506.929 + 878.027i 0.556232 + 0.963421i
\(95\) −201.434 348.893i −0.217544 0.376797i
\(96\) 138.096 + 239.189i 0.146816 + 0.254293i
\(97\) 1383.10 1.44775 0.723877 0.689929i \(-0.242358\pi\)
0.723877 + 0.689929i \(0.242358\pi\)
\(98\) −48.2862 + 83.6341i −0.0497719 + 0.0862074i
\(99\) −231.778 401.452i −0.235299 0.407550i
\(100\) −365.303 −0.365303
\(101\) 1171.73 1.15437 0.577186 0.816613i \(-0.304151\pi\)
0.577186 + 0.816613i \(0.304151\pi\)
\(102\) −208.506 361.143i −0.202404 0.350574i
\(103\) 1351.30 1.29270 0.646349 0.763042i \(-0.276295\pi\)
0.646349 + 0.763042i \(0.276295\pi\)
\(104\) 261.497 452.927i 0.246557 0.427049i
\(105\) −859.826 −0.799147
\(106\) −366.447 + 634.705i −0.335778 + 0.581585i
\(107\) 711.235 1231.89i 0.642595 1.11301i −0.342257 0.939607i \(-0.611191\pi\)
0.984851 0.173400i \(-0.0554754\pi\)
\(108\) −353.771 + 612.749i −0.315200 + 0.545943i
\(109\) 929.141 + 1609.32i 0.816473 + 1.41417i 0.908266 + 0.418394i \(0.137407\pi\)
−0.0917929 + 0.995778i \(0.529260\pi\)
\(110\) −113.277 −0.0981866
\(111\) −233.676 + 1928.41i −0.199815 + 1.64897i
\(112\) −274.676 −0.231736
\(113\) −351.085 608.097i −0.292277 0.506238i 0.682071 0.731286i \(-0.261080\pi\)
−0.974348 + 0.225048i \(0.927746\pi\)
\(114\) 599.203 1037.85i 0.492285 0.852663i
\(115\) 198.479 343.775i 0.160941 0.278758i
\(116\) −458.321 + 793.836i −0.366846 + 0.635395i
\(117\) 3104.90 2.45340
\(118\) 888.992 1539.78i 0.693546 1.20126i
\(119\) 414.723 0.319476
\(120\) 200.341 + 347.001i 0.152405 + 0.263973i
\(121\) −1235.74 −0.928428
\(122\) −1212.25 −0.899603
\(123\) −1045.65 1811.12i −0.766530 1.32767i
\(124\) 542.760 940.087i 0.393075 0.680825i
\(125\) −1255.33 −0.898240
\(126\) −815.344 1412.22i −0.576481 0.998494i
\(127\) −859.202 1488.18i −0.600329 1.03980i −0.992771 0.120024i \(-0.961703\pi\)
0.392442 0.919777i \(-0.371631\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) −816.726 + 1414.61i −0.557432 + 0.965500i
\(130\) 379.364 657.078i 0.255942 0.443305i
\(131\) −96.2362 166.686i −0.0641847 0.111171i 0.832147 0.554555i \(-0.187111\pi\)
−0.896332 + 0.443383i \(0.853778\pi\)
\(132\) −168.482 291.819i −0.111094 0.192421i
\(133\) 595.913 + 1032.15i 0.388513 + 0.672924i
\(134\) −503.250 −0.324434
\(135\) −513.229 + 888.939i −0.327198 + 0.566724i
\(136\) −96.6313 167.370i −0.0609269 0.105529i
\(137\) 92.2200 0.0575101 0.0287551 0.999586i \(-0.490846\pi\)
0.0287551 + 0.999586i \(0.490846\pi\)
\(138\) 1180.82 0.728395
\(139\) 311.822 + 540.091i 0.190276 + 0.329568i 0.945342 0.326081i \(-0.105728\pi\)
−0.755066 + 0.655649i \(0.772395\pi\)
\(140\) −398.483 −0.240557
\(141\) −2187.65 + 3789.13i −1.30662 + 2.26314i
\(142\) 1424.64 0.841922
\(143\) −319.036 + 552.586i −0.186567 + 0.323144i
\(144\) −379.954 + 658.099i −0.219881 + 0.380844i
\(145\) −664.905 + 1151.65i −0.380809 + 0.659581i
\(146\) −87.8669 152.190i −0.0498077 0.0862694i
\(147\) −416.758 −0.233834
\(148\) −108.296 + 893.711i −0.0601478 + 0.496369i
\(149\) 58.8320 0.0323470 0.0161735 0.999869i \(-0.494852\pi\)
0.0161735 + 0.999869i \(0.494852\pi\)
\(150\) −788.232 1365.26i −0.429059 0.743153i
\(151\) −757.096 + 1311.33i −0.408024 + 0.706718i −0.994668 0.103127i \(-0.967115\pi\)
0.586644 + 0.809845i \(0.300449\pi\)
\(152\) 277.698 480.987i 0.148186 0.256666i
\(153\) 573.678 993.640i 0.303132 0.525039i
\(154\) 335.114 0.175352
\(155\) 787.403 1363.82i 0.408037 0.706741i
\(156\) 2256.98 1.15835
\(157\) 569.365 + 986.169i 0.289428 + 0.501305i 0.973673 0.227947i \(-0.0732015\pi\)
−0.684245 + 0.729252i \(0.739868\pi\)
\(158\) −867.145 −0.436622
\(159\) −3162.80 −1.57753
\(160\) 92.8473 + 160.816i 0.0458764 + 0.0794602i
\(161\) −587.171 + 1017.01i −0.287426 + 0.497836i
\(162\) −488.711 −0.237017
\(163\) −879.922 1524.07i −0.422827 0.732358i 0.573388 0.819284i \(-0.305629\pi\)
−0.996215 + 0.0869262i \(0.972296\pi\)
\(164\) −484.602 839.356i −0.230738 0.399650i
\(165\) −244.423 423.354i −0.115323 0.199746i
\(166\) −911.453 + 1578.68i −0.426159 + 0.738130i
\(167\) 44.9020 77.7726i 0.0208061 0.0360373i −0.855435 0.517910i \(-0.826710\pi\)
0.876241 + 0.481873i \(0.160043\pi\)
\(168\) −592.682 1026.55i −0.272181 0.471431i
\(169\) −1038.40 1798.56i −0.472645 0.818646i
\(170\) −140.187 242.811i −0.0632461 0.109545i
\(171\) 3297.26 1.47455
\(172\) −378.508 + 655.595i −0.167796 + 0.290632i
\(173\) −1894.94 3282.13i −0.832773 1.44241i −0.895831 0.444395i \(-0.853419\pi\)
0.0630579 0.998010i \(-0.479915\pi\)
\(174\) −3955.77 −1.72349
\(175\) 1567.81 0.677230
\(176\) −78.0822 135.242i −0.0334413 0.0579220i
\(177\) 7672.90 3.25836
\(178\) 741.439 1284.21i 0.312209 0.540762i
\(179\) −3592.46 −1.50007 −0.750036 0.661398i \(-0.769964\pi\)
−0.750036 + 0.661398i \(0.769964\pi\)
\(180\) −551.213 + 954.730i −0.228250 + 0.395341i
\(181\) 148.612 257.403i 0.0610289 0.105705i −0.833897 0.551921i \(-0.813895\pi\)
0.894926 + 0.446215i \(0.147228\pi\)
\(182\) −1122.30 + 1943.87i −0.457089 + 0.791701i
\(183\) −2615.72 4530.56i −1.05661 1.83010i
\(184\) 547.248 0.219259
\(185\) −157.109 + 1296.54i −0.0624373 + 0.515263i
\(186\) 4684.56 1.84671
\(187\) 117.893 + 204.197i 0.0461028 + 0.0798524i
\(188\) −1013.86 + 1756.05i −0.393315 + 0.681242i
\(189\) 1518.32 2629.80i 0.584345 1.01212i
\(190\) 402.867 697.787i 0.153827 0.266436i
\(191\) 2865.50 1.08555 0.542775 0.839878i \(-0.317374\pi\)
0.542775 + 0.839878i \(0.317374\pi\)
\(192\) −276.192 + 478.379i −0.103815 + 0.179813i
\(193\) −4810.44 −1.79411 −0.897054 0.441921i \(-0.854297\pi\)
−0.897054 + 0.441921i \(0.854297\pi\)
\(194\) 1383.10 + 2395.59i 0.511858 + 0.886565i
\(195\) 3274.29 1.20245
\(196\) −193.145 −0.0703880
\(197\) 212.593 + 368.221i 0.0768863 + 0.133171i 0.901905 0.431934i \(-0.142169\pi\)
−0.825019 + 0.565105i \(0.808836\pi\)
\(198\) 463.556 802.903i 0.166381 0.288181i
\(199\) −243.177 −0.0866248 −0.0433124 0.999062i \(-0.513791\pi\)
−0.0433124 + 0.999062i \(0.513791\pi\)
\(200\) −365.303 632.723i −0.129154 0.223701i
\(201\) −1085.89 1880.81i −0.381058 0.660012i
\(202\) 1171.73 + 2029.50i 0.408132 + 0.706905i
\(203\) 1967.03 3406.99i 0.680090 1.17795i
\(204\) 417.012 722.287i 0.143121 0.247893i
\(205\) −703.031 1217.69i −0.239521 0.414863i
\(206\) 1351.30 + 2340.53i 0.457038 + 0.791613i
\(207\) 1624.44 + 2813.62i 0.545443 + 0.944735i
\(208\) 1045.99 0.348684
\(209\) −338.801 + 586.821i −0.112131 + 0.194216i
\(210\) −859.826 1489.26i −0.282541 0.489376i
\(211\) 1994.72 0.650817 0.325409 0.945573i \(-0.394498\pi\)
0.325409 + 0.945573i \(0.394498\pi\)
\(212\) −1465.79 −0.474862
\(213\) 3074.01 + 5324.35i 0.988864 + 1.71276i
\(214\) 2844.94 0.908766
\(215\) −549.117 + 951.098i −0.174183 + 0.301695i
\(216\) −1415.08 −0.445760
\(217\) −2329.42 + 4034.67i −0.728716 + 1.26217i
\(218\) −1858.28 + 3218.64i −0.577333 + 0.999971i
\(219\) 379.190 656.776i 0.117001 0.202652i
\(220\) −113.277 196.201i −0.0347142 0.0601268i
\(221\) −1579.30 −0.480703
\(222\) −3573.77 + 1523.67i −1.08043 + 0.460639i
\(223\) 88.6288 0.0266145 0.0133072 0.999911i \(-0.495764\pi\)
0.0133072 + 0.999911i \(0.495764\pi\)
\(224\) −274.676 475.752i −0.0819310 0.141909i
\(225\) 2168.72 3756.33i 0.642584 1.11299i
\(226\) 702.170 1216.19i 0.206671 0.357965i
\(227\) −2024.37 + 3506.31i −0.591903 + 1.02521i 0.402073 + 0.915608i \(0.368290\pi\)
−0.993976 + 0.109599i \(0.965043\pi\)
\(228\) 2396.81 0.696196
\(229\) −1795.58 + 3110.04i −0.518145 + 0.897454i 0.481632 + 0.876373i \(0.340044\pi\)
−0.999778 + 0.0210808i \(0.993289\pi\)
\(230\) 793.914 0.227605
\(231\) 723.092 + 1252.43i 0.205957 + 0.356727i
\(232\) −1833.29 −0.518798
\(233\) 6048.01 1.70051 0.850253 0.526374i \(-0.176449\pi\)
0.850253 + 0.526374i \(0.176449\pi\)
\(234\) 3104.90 + 5377.85i 0.867409 + 1.50240i
\(235\) −1470.84 + 2547.58i −0.408286 + 0.707173i
\(236\) 3555.97 0.980822
\(237\) −1871.08 3240.81i −0.512826 0.888241i
\(238\) 414.723 + 718.321i 0.112952 + 0.195638i
\(239\) −96.0036 166.283i −0.0259831 0.0450040i 0.852741 0.522333i \(-0.174938\pi\)
−0.878725 + 0.477329i \(0.841605\pi\)
\(240\) −400.683 + 694.003i −0.107766 + 0.186657i
\(241\) 632.495 1095.51i 0.169056 0.292814i −0.769032 0.639210i \(-0.779261\pi\)
0.938088 + 0.346396i \(0.112595\pi\)
\(242\) −1235.74 2140.36i −0.328249 0.568543i
\(243\) 1333.44 + 2309.58i 0.352017 + 0.609711i
\(244\) −1212.25 2099.67i −0.318058 0.550892i
\(245\) −280.203 −0.0730673
\(246\) 2091.30 3622.24i 0.542018 0.938803i
\(247\) −2269.29 3930.53i −0.584581 1.01252i
\(248\) 2171.04 0.555892
\(249\) −7866.75 −2.00215
\(250\) −1255.33 2174.29i −0.317576 0.550057i
\(251\) 3414.91 0.858754 0.429377 0.903125i \(-0.358733\pi\)
0.429377 + 0.903125i \(0.358733\pi\)
\(252\) 1630.69 2824.43i 0.407634 0.706042i
\(253\) −667.662 −0.165911
\(254\) 1718.40 2976.36i 0.424497 0.735250i
\(255\) 604.976 1047.85i 0.148569 0.257329i
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −512.189 887.138i −0.124317 0.215323i 0.797149 0.603783i \(-0.206341\pi\)
−0.921466 + 0.388460i \(0.873007\pi\)
\(258\) −3266.90 −0.788328
\(259\) 464.786 3835.64i 0.111507 0.920212i
\(260\) 1517.46 0.361957
\(261\) −5441.90 9425.65i −1.29060 2.23538i
\(262\) 192.472 333.372i 0.0453854 0.0786099i
\(263\) −693.678 + 1201.49i −0.162639 + 0.281699i −0.935814 0.352493i \(-0.885334\pi\)
0.773175 + 0.634192i \(0.218667\pi\)
\(264\) 336.964 583.638i 0.0785556 0.136062i
\(265\) −2126.48 −0.492937
\(266\) −1191.83 + 2064.30i −0.274720 + 0.475829i
\(267\) 6399.36 1.46680
\(268\) −503.250 871.655i −0.114705 0.198675i
\(269\) −2176.91 −0.493415 −0.246708 0.969090i \(-0.579349\pi\)
−0.246708 + 0.969090i \(0.579349\pi\)
\(270\) −2052.92 −0.462728
\(271\) −2806.93 4861.75i −0.629184 1.08978i −0.987716 0.156261i \(-0.950056\pi\)
0.358532 0.933518i \(-0.383278\pi\)
\(272\) 193.263 334.741i 0.0430819 0.0746200i
\(273\) −9686.54 −2.14746
\(274\) 92.2200 + 159.730i 0.0203329 + 0.0352176i
\(275\) 445.682 + 771.944i 0.0977296 + 0.169273i
\(276\) 1180.82 + 2045.25i 0.257526 + 0.446049i
\(277\) −857.615 + 1485.43i −0.186026 + 0.322206i −0.943922 0.330170i \(-0.892894\pi\)
0.757896 + 0.652375i \(0.226227\pi\)
\(278\) −623.644 + 1080.18i −0.134546 + 0.233040i
\(279\) 6444.48 + 11162.2i 1.38287 + 2.39520i
\(280\) −398.483 690.192i −0.0850496 0.147310i
\(281\) 1966.75 + 3406.51i 0.417531 + 0.723185i 0.995690 0.0927386i \(-0.0295621\pi\)
−0.578159 + 0.815924i \(0.696229\pi\)
\(282\) −8750.62 −1.84784
\(283\) 2183.88 3782.59i 0.458721 0.794528i −0.540173 0.841554i \(-0.681641\pi\)
0.998894 + 0.0470263i \(0.0149744\pi\)
\(284\) 1424.64 + 2467.55i 0.297665 + 0.515570i
\(285\) 3477.15 0.722697
\(286\) −1276.14 −0.263846
\(287\) 2079.82 + 3602.35i 0.427763 + 0.740907i
\(288\) −1519.81 −0.310958
\(289\) 2164.70 3749.37i 0.440607 0.763153i
\(290\) −2659.62 −0.538546
\(291\) −5968.75 + 10338.2i −1.20239 + 2.08259i
\(292\) 175.734 304.380i 0.0352193 0.0610017i
\(293\) 4265.97 7388.89i 0.850583 1.47325i −0.0300994 0.999547i \(-0.509582\pi\)
0.880683 0.473707i \(-0.157084\pi\)
\(294\) −416.758 721.846i −0.0826729 0.143194i
\(295\) 5158.78 1.01816
\(296\) −1656.25 + 706.137i −0.325228 + 0.138660i
\(297\) 1726.45 0.337302
\(298\) 58.8320 + 101.900i 0.0114364 + 0.0198084i
\(299\) 2236.00 3872.86i 0.432479 0.749075i
\(300\) 1576.46 2730.52i 0.303391 0.525488i
\(301\) 1624.48 2813.69i 0.311075 0.538798i
\(302\) −3028.38 −0.577033
\(303\) −5056.60 + 8758.30i −0.958727 + 1.66056i
\(304\) 1110.79 0.209567
\(305\) −1758.65 3046.07i −0.330164 0.571861i
\(306\) 2294.71 0.428693
\(307\) −2528.60 −0.470081 −0.235041 0.971986i \(-0.575522\pi\)
−0.235041 + 0.971986i \(0.575522\pi\)
\(308\) 335.114 + 580.434i 0.0619964 + 0.107381i
\(309\) −5831.55 + 10100.5i −1.07361 + 1.85955i
\(310\) 3149.61 0.577051
\(311\) 3170.22 + 5490.98i 0.578028 + 1.00117i 0.995705 + 0.0925779i \(0.0295107\pi\)
−0.417678 + 0.908595i \(0.637156\pi\)
\(312\) 2256.98 + 3909.21i 0.409540 + 0.709344i
\(313\) −1270.57 2200.70i −0.229448 0.397415i 0.728197 0.685368i \(-0.240359\pi\)
−0.957645 + 0.287953i \(0.907025\pi\)
\(314\) −1138.73 + 1972.34i −0.204657 + 0.354476i
\(315\) 2365.70 4097.52i 0.423150 0.732917i
\(316\) −867.145 1501.94i −0.154369 0.267376i
\(317\) 1346.25 + 2331.77i 0.238526 + 0.413140i 0.960292 0.278998i \(-0.0900024\pi\)
−0.721765 + 0.692138i \(0.756669\pi\)
\(318\) −3162.80 5478.14i −0.557740 0.966034i
\(319\) 2236.67 0.392569
\(320\) −185.695 + 321.632i −0.0324395 + 0.0561869i
\(321\) 6138.67 + 10632.5i 1.06737 + 1.84875i
\(322\) −2348.68 −0.406481
\(323\) −1677.14 −0.288913
\(324\) −488.711 846.471i −0.0837981 0.145143i
\(325\) −5970.36 −1.01900
\(326\) 1759.84 3048.14i 0.298984 0.517855i
\(327\) −16038.8 −2.71238
\(328\) 969.204 1678.71i 0.163157 0.282596i
\(329\) 4351.29 7536.65i 0.729162 1.26295i
\(330\) 488.847 846.707i 0.0815458 0.141241i
\(331\) −2620.44 4538.73i −0.435143 0.753689i 0.562165 0.827025i \(-0.309969\pi\)
−0.997307 + 0.0733361i \(0.976635\pi\)
\(332\) −3645.81 −0.602680
\(333\) −8546.92 6419.35i −1.40651 1.05639i
\(334\) 179.608 0.0294243
\(335\) −730.085 1264.54i −0.119071 0.206237i
\(336\) 1185.36 2053.11i 0.192461 0.333352i
\(337\) 4870.76 8436.41i 0.787322 1.36368i −0.140280 0.990112i \(-0.544800\pi\)
0.927602 0.373570i \(-0.121866\pi\)
\(338\) 2076.80 3597.13i 0.334211 0.578870i
\(339\) 6060.43 0.970965
\(340\) 280.374 485.621i 0.0447217 0.0774603i
\(341\) −2648.74 −0.420638
\(342\) 3297.26 + 5711.02i 0.521332 + 0.902973i
\(343\) 6717.30 1.05743
\(344\) −1514.03 −0.237300
\(345\) 1713.07 + 2967.12i 0.267329 + 0.463028i
\(346\) 3789.88 6564.27i 0.588859 1.01993i
\(347\) 8864.95 1.37146 0.685728 0.727858i \(-0.259484\pi\)
0.685728 + 0.727858i \(0.259484\pi\)
\(348\) −3955.77 6851.60i −0.609344 1.05541i
\(349\) 297.082 + 514.561i 0.0455657 + 0.0789221i 0.887909 0.460020i \(-0.152158\pi\)
−0.842343 + 0.538942i \(0.818824\pi\)
\(350\) 1567.81 + 2715.53i 0.239437 + 0.414717i
\(351\) −5781.88 + 10014.5i −0.879242 + 1.52289i
\(352\) 156.164 270.485i 0.0236466 0.0409570i
\(353\) 1504.59 + 2606.02i 0.226859 + 0.392931i 0.956875 0.290498i \(-0.0938211\pi\)
−0.730017 + 0.683429i \(0.760488\pi\)
\(354\) 7672.90 + 13289.8i 1.15201 + 1.99533i
\(355\) 2066.78 + 3579.77i 0.308995 + 0.535195i
\(356\) 2965.75 0.441530
\(357\) −1789.74 + 3099.92i −0.265330 + 0.459566i
\(358\) −3592.46 6222.32i −0.530355 0.918602i
\(359\) 2508.18 0.368737 0.184368 0.982857i \(-0.440976\pi\)
0.184368 + 0.982857i \(0.440976\pi\)
\(360\) −2204.85 −0.322794
\(361\) 1019.62 + 1766.03i 0.148654 + 0.257476i
\(362\) 594.448 0.0863080
\(363\) 5332.82 9236.72i 0.771076 1.33554i
\(364\) −4489.18 −0.646421
\(365\) 254.944 441.576i 0.0365599 0.0633237i
\(366\) 5231.45 9061.13i 0.747137 1.29408i
\(367\) −4818.85 + 8346.50i −0.685401 + 1.18715i 0.287910 + 0.957657i \(0.407040\pi\)
−0.973311 + 0.229491i \(0.926294\pi\)
\(368\) 547.248 + 947.862i 0.0775198 + 0.134268i
\(369\) 11507.9 1.62352
\(370\) −2402.79 + 1024.42i −0.337608 + 0.143938i
\(371\) 6290.88 0.880340
\(372\) 4684.56 + 8113.90i 0.652912 + 1.13088i
\(373\) −5551.33 + 9615.19i −0.770609 + 1.33473i 0.166621 + 0.986021i \(0.446714\pi\)
−0.937230 + 0.348712i \(0.886619\pi\)
\(374\) −235.787 + 408.395i −0.0325996 + 0.0564642i
\(375\) 5417.37 9383.16i 0.746005 1.29212i
\(376\) −4055.44 −0.556232
\(377\) −7490.62 + 12974.1i −1.02331 + 1.77242i
\(378\) 6073.27 0.826389
\(379\) −3690.26 6391.71i −0.500147 0.866280i −1.00000 0.000169856i \(-0.999946\pi\)
0.499853 0.866110i \(-0.333387\pi\)
\(380\) 1611.47 0.217544
\(381\) 14831.5 1.99434
\(382\) 2865.50 + 4963.19i 0.383800 + 0.664761i
\(383\) −1862.27 + 3225.55i −0.248454 + 0.430334i −0.963097 0.269155i \(-0.913256\pi\)
0.714643 + 0.699489i \(0.246589\pi\)
\(384\) −1104.77 −0.146816
\(385\) 486.163 + 842.058i 0.0643562 + 0.111468i
\(386\) −4810.44 8331.92i −0.634313 1.09866i
\(387\) −4494.23 7784.24i −0.590322 1.02247i
\(388\) −2766.19 + 4791.19i −0.361938 + 0.626896i
\(389\) −1634.82 + 2831.59i −0.213081 + 0.369067i −0.952677 0.303984i \(-0.901683\pi\)
0.739596 + 0.673051i \(0.235017\pi\)
\(390\) 3274.29 + 5671.24i 0.425129 + 0.736345i
\(391\) −826.270 1431.14i −0.106870 0.185105i
\(392\) −193.145 334.537i −0.0248859 0.0431037i
\(393\) 1661.23 0.213226
\(394\) −425.185 + 736.442i −0.0543668 + 0.0941661i
\(395\) −1258.00 2178.92i −0.160245 0.277553i
\(396\) 1854.23 0.235299
\(397\) 12159.0 1.53714 0.768570 0.639765i \(-0.220968\pi\)
0.768570 + 0.639765i \(0.220968\pi\)
\(398\) −243.177 421.194i −0.0306265 0.0530467i
\(399\) −10286.7 −1.29067
\(400\) 730.606 1265.45i 0.0913257 0.158181i
\(401\) −179.867 −0.0223994 −0.0111997 0.999937i \(-0.503565\pi\)
−0.0111997 + 0.999937i \(0.503565\pi\)
\(402\) 2171.78 3761.63i 0.269449 0.466699i
\(403\) 8870.64 15364.4i 1.09647 1.89914i
\(404\) −2343.46 + 4058.99i −0.288593 + 0.499858i
\(405\) −708.991 1228.01i −0.0869878 0.150667i
\(406\) 7868.11 0.961793
\(407\) 2020.68 861.512i 0.246097 0.104923i
\(408\) 1668.05 0.202404
\(409\) 2272.68 + 3936.39i 0.274759 + 0.475897i 0.970074 0.242808i \(-0.0780684\pi\)
−0.695315 + 0.718705i \(0.744735\pi\)
\(410\) 1406.06 2435.37i 0.169367 0.293352i
\(411\) −397.976 + 689.314i −0.0477632 + 0.0827284i
\(412\) −2702.61 + 4681.06i −0.323175 + 0.559755i
\(413\) −15261.5 −1.81833
\(414\) −3248.89 + 5627.24i −0.385686 + 0.668028i
\(415\) −5289.12 −0.625621
\(416\) 1045.99 + 1811.71i 0.123278 + 0.213525i
\(417\) −5382.67 −0.632112
\(418\) −1355.20 −0.158577
\(419\) −417.523 723.170i −0.0486809 0.0843179i 0.840658 0.541566i \(-0.182168\pi\)
−0.889339 + 0.457248i \(0.848835\pi\)
\(420\) 1719.65 2978.53i 0.199787 0.346041i
\(421\) −16250.4 −1.88122 −0.940611 0.339486i \(-0.889747\pi\)
−0.940611 + 0.339486i \(0.889747\pi\)
\(422\) 1994.72 + 3454.96i 0.230099 + 0.398543i
\(423\) −12038.1 20850.6i −1.38372 2.39667i
\(424\) −1465.79 2538.82i −0.167889 0.290792i
\(425\) −1103.11 + 1910.65i −0.125903 + 0.218071i
\(426\) −6148.03 + 10648.7i −0.699232 + 1.21111i
\(427\) 5202.72 + 9011.38i 0.589643 + 1.02129i
\(428\) 2844.94 + 4927.58i 0.321297 + 0.556503i
\(429\) −2753.60 4769.37i −0.309895 0.536754i
\(430\) −2196.47 −0.246333
\(431\) −5307.38 + 9192.65i −0.593150 + 1.02737i 0.400656 + 0.916229i \(0.368782\pi\)
−0.993805 + 0.111137i \(0.964551\pi\)
\(432\) −1415.08 2451.00i −0.157600 0.272971i
\(433\) 12682.2 1.40754 0.703772 0.710426i \(-0.251498\pi\)
0.703772 + 0.710426i \(0.251498\pi\)
\(434\) −9317.68 −1.03056
\(435\) −5738.80 9939.88i −0.632538 1.09559i
\(436\) −7433.12 −0.816473
\(437\) 2374.53 4112.80i 0.259929 0.450211i
\(438\) 1516.76 0.165465
\(439\) 6302.87 10916.9i 0.685238 1.18687i −0.288124 0.957593i \(-0.593031\pi\)
0.973362 0.229274i \(-0.0736352\pi\)
\(440\) 226.554 392.403i 0.0245467 0.0425161i
\(441\) 1146.66 1986.07i 0.123816 0.214455i
\(442\) −1579.30 2735.43i −0.169954 0.294369i
\(443\) 6136.72 0.658159 0.329080 0.944302i \(-0.393262\pi\)
0.329080 + 0.944302i \(0.393262\pi\)
\(444\) −6212.84 4666.29i −0.664073 0.498766i
\(445\) 4302.54 0.458337
\(446\) 88.6288 + 153.510i 0.00940963 + 0.0162980i
\(447\) −253.890 + 439.750i −0.0268648 + 0.0465312i
\(448\) 549.351 951.504i 0.0579340 0.100345i
\(449\) 1808.77 3132.89i 0.190114 0.329288i −0.755174 0.655525i \(-0.772447\pi\)
0.945288 + 0.326237i \(0.105781\pi\)
\(450\) 8674.88 0.908751
\(451\) −1182.46 + 2048.09i −0.123459 + 0.213837i
\(452\) 2808.68 0.292277
\(453\) −6534.50 11318.1i −0.677743 1.17388i
\(454\) −8097.47 −0.837077
\(455\) −6512.64 −0.671027
\(456\) 2396.81 + 4151.40i 0.246143 + 0.426331i
\(457\) 4963.05 8596.25i 0.508012 0.879903i −0.491945 0.870626i \(-0.663714\pi\)
0.999957 0.00927627i \(-0.00295277\pi\)
\(458\) −7182.32 −0.732768
\(459\) 2136.58 + 3700.67i 0.217271 + 0.376324i
\(460\) 793.914 + 1375.10i 0.0804705 + 0.139379i
\(461\) 374.446 + 648.560i 0.0378302 + 0.0655237i 0.884321 0.466880i \(-0.154622\pi\)
−0.846490 + 0.532404i \(0.821289\pi\)
\(462\) −1446.18 + 2504.86i −0.145633 + 0.252244i
\(463\) −6416.71 + 11114.1i −0.644081 + 1.11558i 0.340432 + 0.940269i \(0.389427\pi\)
−0.984513 + 0.175312i \(0.943907\pi\)
\(464\) −1833.29 3175.34i −0.183423 0.317698i
\(465\) 6796.07 + 11771.1i 0.677764 + 1.17392i
\(466\) 6048.01 + 10475.5i 0.601220 + 1.04134i
\(467\) −10067.2 −0.997551 −0.498775 0.866731i \(-0.666217\pi\)
−0.498775 + 0.866731i \(0.666217\pi\)
\(468\) −6209.80 + 10755.7i −0.613351 + 1.06235i
\(469\) 2159.85 + 3740.98i 0.212650 + 0.368320i
\(470\) −5883.38 −0.577404
\(471\) −9828.38 −0.961503
\(472\) 3555.97 + 6159.12i 0.346773 + 0.600628i
\(473\) 1847.17 0.179562
\(474\) 3742.16 6481.62i 0.362623 0.628081i
\(475\) −6340.24 −0.612443
\(476\) −829.446 + 1436.64i −0.0798689 + 0.138337i
\(477\) 8702.05 15072.4i 0.835303 1.44679i
\(478\) 192.007 332.566i 0.0183728 0.0318226i
\(479\) −4530.90 7847.75i −0.432196 0.748586i 0.564866 0.825183i \(-0.308928\pi\)
−0.997062 + 0.0765967i \(0.975595\pi\)
\(480\) −1602.73 −0.152405
\(481\) −1769.94 + 14606.4i −0.167781 + 1.38461i
\(482\) 2529.98 0.239082
\(483\) −5067.87 8777.81i −0.477425 0.826924i
\(484\) 2471.47 4280.72i 0.232107 0.402021i
\(485\) −4013.02 + 6950.76i −0.375715 + 0.650758i
\(486\) −2666.88 + 4619.16i −0.248913 + 0.431131i
\(487\) −10696.1 −0.995250 −0.497625 0.867392i \(-0.665795\pi\)
−0.497625 + 0.867392i \(0.665795\pi\)
\(488\) 2424.49 4199.34i 0.224901 0.389539i
\(489\) 15189.2 1.40466
\(490\) −280.203 485.325i −0.0258332 0.0447444i
\(491\) −2824.19 −0.259580 −0.129790 0.991541i \(-0.541430\pi\)
−0.129790 + 0.991541i \(0.541430\pi\)
\(492\) 8365.21 0.766530
\(493\) 2768.01 + 4794.34i 0.252870 + 0.437984i
\(494\) 4538.58 7861.05i 0.413361 0.715963i
\(495\) 2690.00 0.244255
\(496\) 2171.04 + 3760.35i 0.196537 + 0.340413i
\(497\) −6114.27 10590.2i −0.551836 0.955809i
\(498\) −7866.75 13625.6i −0.707866 1.22606i
\(499\) −8289.68 + 14358.1i −0.743681 + 1.28809i 0.207127 + 0.978314i \(0.433589\pi\)
−0.950808 + 0.309780i \(0.899745\pi\)
\(500\) 2510.66 4348.59i 0.224560 0.388949i
\(501\) 387.549 + 671.255i 0.0345597 + 0.0598592i
\(502\) 3414.91 + 5914.80i 0.303615 + 0.525877i
\(503\) 5577.78 + 9661.00i 0.494435 + 0.856387i 0.999979 0.00641365i \(-0.00204154\pi\)
−0.505544 + 0.862801i \(0.668708\pi\)
\(504\) 6522.75 0.576481
\(505\) −3399.75 + 5888.54i −0.299578 + 0.518884i
\(506\) −667.662 1156.42i −0.0586584 0.101599i
\(507\) 17924.9 1.57016
\(508\) 6873.61 0.600329
\(509\) 5068.07 + 8778.16i 0.441333 + 0.764411i 0.997789 0.0664665i \(-0.0211725\pi\)
−0.556456 + 0.830877i \(0.687839\pi\)
\(510\) 2419.90 0.210108
\(511\) −754.216 + 1306.34i −0.0652927 + 0.113090i
\(512\) −512.000 −0.0441942
\(513\) −6140.09 + 10635.0i −0.528444 + 0.915292i
\(514\) 1024.38 1774.28i 0.0879054 0.152257i
\(515\) −3920.78 + 6790.99i −0.335476 + 0.581062i
\(516\) −3266.90 5658.44i −0.278716 0.482750i
\(517\) 4947.77 0.420895
\(518\) 7108.30 3030.61i 0.602936 0.257060i
\(519\) 32710.5 2.76653
\(520\) 1517.46 + 2628.31i 0.127971 + 0.221652i
\(521\) 10618.9 18392.4i 0.892940 1.54662i 0.0566057 0.998397i \(-0.481972\pi\)
0.836334 0.548220i \(-0.184694\pi\)
\(522\) 10883.8 18851.3i 0.912588 1.58065i
\(523\) 9472.09 16406.1i 0.791942 1.37168i −0.132821 0.991140i \(-0.542404\pi\)
0.924763 0.380543i \(-0.124263\pi\)
\(524\) 769.890 0.0641847
\(525\) −6765.88 + 11718.9i −0.562452 + 0.974196i
\(526\) −2774.71 −0.230006
\(527\) −3277.97 5677.62i −0.270950 0.469300i
\(528\) 1347.86 0.111094
\(529\) −7487.62 −0.615404
\(530\) −2126.48 3683.16i −0.174280 0.301861i
\(531\) −21111.0 + 36565.3i −1.72531 + 2.98832i
\(532\) −4767.31 −0.388513
\(533\) −7920.14 13718.1i −0.643638 1.11481i
\(534\) 6399.36 + 11084.0i 0.518591 + 0.898225i
\(535\) 4127.26 + 7148.63i 0.333527 + 0.577686i
\(536\) 1006.50 1743.31i 0.0811086 0.140484i
\(537\) 15503.2 26852.4i 1.24584 2.15785i
\(538\) −2176.91 3770.52i −0.174449 0.302154i
\(539\) 235.643 + 408.146i 0.0188309 + 0.0326161i
\(540\) −2052.92 3555.76i −0.163599 0.283362i
\(541\) 1085.07 0.0862304 0.0431152 0.999070i \(-0.486272\pi\)
0.0431152 + 0.999070i \(0.486272\pi\)
\(542\) 5613.86 9723.49i 0.444900 0.770590i
\(543\) 1282.67 + 2221.65i 0.101371 + 0.175580i
\(544\) 773.050 0.0609269
\(545\) −10783.5 −0.847551
\(546\) −9686.54 16777.6i −0.759241 1.31504i
\(547\) 10779.7 0.842608 0.421304 0.906920i \(-0.361573\pi\)
0.421304 + 0.906920i \(0.361573\pi\)
\(548\) −184.440 + 319.460i −0.0143775 + 0.0249026i
\(549\) 28787.3 2.23791
\(550\) −891.364 + 1543.89i −0.0691052 + 0.119694i
\(551\) −7954.69 + 13777.9i −0.615029 + 1.06526i
\(552\) −2361.65 + 4090.50i −0.182099 + 0.315404i
\(553\) 3721.62 + 6446.03i 0.286183 + 0.495684i
\(554\) −3430.46 −0.263080
\(555\) −9013.21 6769.57i −0.689351 0.517752i
\(556\) −2494.58 −0.190276
\(557\) −1075.60 1862.99i −0.0818213 0.141719i 0.822211 0.569183i \(-0.192740\pi\)
−0.904032 + 0.427464i \(0.859407\pi\)
\(558\) −12889.0 + 22324.3i −0.977838 + 1.69366i
\(559\) −6186.18 + 10714.8i −0.468063 + 0.810710i
\(560\) 796.965 1380.38i 0.0601392 0.104164i
\(561\) −2035.08 −0.153157
\(562\) −3933.49 + 6813.01i −0.295239 + 0.511369i
\(563\) 7635.94 0.571610 0.285805 0.958288i \(-0.407739\pi\)
0.285805 + 0.958288i \(0.407739\pi\)
\(564\) −8750.62 15156.5i −0.653311 1.13157i
\(565\) 4074.66 0.303402
\(566\) 8735.51 0.648729
\(567\) 2097.45 + 3632.89i 0.155352 + 0.269078i
\(568\) −2849.28 + 4935.09i −0.210481 + 0.364563i
\(569\) 1746.95 0.128710 0.0643549 0.997927i \(-0.479501\pi\)
0.0643549 + 0.997927i \(0.479501\pi\)
\(570\) 3477.15 + 6022.60i 0.255512 + 0.442560i
\(571\) −3220.40 5577.90i −0.236024 0.408805i 0.723546 0.690276i \(-0.242511\pi\)
−0.959570 + 0.281471i \(0.909178\pi\)
\(572\) −1276.14 2210.34i −0.0932836 0.161572i
\(573\) −12366.1 + 21418.6i −0.901570 + 1.56156i
\(574\) −4159.64 + 7204.71i −0.302474 + 0.523900i
\(575\) −3123.61 5410.26i −0.226546 0.392388i
\(576\) −1519.81 2632.40i −0.109940 0.190422i
\(577\) −4957.97 8587.46i −0.357718 0.619585i 0.629862 0.776707i \(-0.283112\pi\)
−0.987579 + 0.157122i \(0.949778\pi\)
\(578\) 8658.80 0.623112
\(579\) 20759.4 35956.4i 1.49004 2.58082i
\(580\) −2659.62 4606.60i −0.190405 0.329790i
\(581\) 15647.1 1.11730
\(582\) −23875.0 −1.70043
\(583\) 1788.31 + 3097.45i 0.127040 + 0.220040i
\(584\) 702.935 0.0498077
\(585\) −9008.80 + 15603.7i −0.636698 + 1.10279i
\(586\) 17063.9 1.20291
\(587\) −6992.60 + 12111.5i −0.491679 + 0.851613i −0.999954 0.00958162i \(-0.996950\pi\)
0.508275 + 0.861195i \(0.330283\pi\)
\(588\) 833.516 1443.69i 0.0584586 0.101253i
\(589\) 9420.21 16316.3i 0.659003 1.14143i
\(590\) 5158.78 + 8935.28i 0.359973 + 0.623491i
\(591\) −3669.77 −0.255422
\(592\) −2879.31 2162.57i −0.199897 0.150137i
\(593\) −11166.1 −0.773252 −0.386626 0.922236i \(-0.626360\pi\)
−0.386626 + 0.922236i \(0.626360\pi\)
\(594\) 1726.45 + 2990.30i 0.119254 + 0.206555i
\(595\) −1203.31 + 2084.19i −0.0829090 + 0.143603i
\(596\) −117.664 + 203.800i −0.00808676 + 0.0140067i
\(597\) 1049.43 1817.66i 0.0719435 0.124610i
\(598\) 8944.00 0.611617
\(599\) 7696.15 13330.1i 0.524969 0.909272i −0.474609 0.880197i \(-0.657410\pi\)
0.999577 0.0290754i \(-0.00925630\pi\)
\(600\) 6305.86 0.429059
\(601\) −1141.95 1977.92i −0.0775062 0.134245i 0.824667 0.565618i \(-0.191362\pi\)
−0.902173 + 0.431374i \(0.858029\pi\)
\(602\) 6497.94 0.439927
\(603\) 11950.7 0.807084
\(604\) −3028.38 5245.31i −0.204012 0.353359i
\(605\) 3585.46 6210.21i 0.240942 0.417324i
\(606\) −20226.4 −1.35585
\(607\) 1113.58 + 1928.78i 0.0744628 + 0.128973i 0.900853 0.434125i \(-0.142942\pi\)
−0.826390 + 0.563099i \(0.809609\pi\)
\(608\) 1110.79 + 1923.95i 0.0740930 + 0.128333i
\(609\) 16977.4 + 29405.8i 1.12965 + 1.95662i
\(610\) 3517.30 6092.15i 0.233461 0.404367i
\(611\) −16570.1 + 28700.2i −1.09714 + 1.90031i
\(612\) 2294.71 + 3974.56i 0.151566 + 0.262520i
\(613\) 14749.7 + 25547.3i 0.971838 + 1.68327i 0.689999 + 0.723810i \(0.257611\pi\)
0.281838 + 0.959462i \(0.409056\pi\)
\(614\) −2528.60 4379.67i −0.166199 0.287865i
\(615\) 12135.7 0.795707
\(616\) −670.228 + 1160.87i −0.0438380 + 0.0759297i
\(617\) −10116.8 17522.8i −0.660109 1.14334i −0.980587 0.196086i \(-0.937177\pi\)
0.320478 0.947256i \(-0.396156\pi\)
\(618\) −23326.2 −1.51831
\(619\) −12667.8 −0.822554 −0.411277 0.911510i \(-0.634917\pi\)
−0.411277 + 0.911510i \(0.634917\pi\)
\(620\) 3149.61 + 5455.29i 0.204018 + 0.353370i
\(621\) −12100.0 −0.781896
\(622\) −6340.44 + 10982.0i −0.408727 + 0.707936i
\(623\) −12728.4 −0.818547
\(624\) −4513.97 + 7818.42i −0.289589 + 0.501582i
\(625\) −2065.55 + 3577.63i −0.132195 + 0.228969i
\(626\) 2541.15 4401.40i 0.162244 0.281015i
\(627\) −2924.19 5064.85i −0.186254 0.322601i
\(628\) −4554.92 −0.289428
\(629\) 4347.37 + 3265.19i 0.275582 + 0.206982i
\(630\) 9462.81 0.598424
\(631\) −2369.66 4104.37i −0.149500 0.258942i 0.781543 0.623852i \(-0.214433\pi\)
−0.931043 + 0.364910i \(0.881100\pi\)
\(632\) 1734.29 3003.88i 0.109156 0.189063i
\(633\) −8608.23 + 14909.9i −0.540516 + 0.936201i
\(634\) −2692.50 + 4663.54i −0.168663 + 0.292134i
\(635\) 9971.82 0.623181
\(636\) 6325.61 10956.3i 0.394382 0.683089i
\(637\) −3156.68 −0.196346
\(638\) 2236.67 + 3874.03i 0.138794 + 0.240399i
\(639\) −33831.0 −2.09442
\(640\) −742.778 −0.0458764
\(641\) −6554.62 11352.9i −0.403888 0.699554i 0.590303 0.807181i \(-0.299008\pi\)
−0.994191 + 0.107627i \(0.965675\pi\)
\(642\) −12277.3 + 21265.0i −0.754747 + 1.30726i
\(643\) 27918.1 1.71226 0.856130 0.516761i \(-0.172862\pi\)
0.856130 + 0.516761i \(0.172862\pi\)
\(644\) −2348.68 4068.04i −0.143713 0.248918i
\(645\) −4739.43 8208.93i −0.289325 0.501126i
\(646\) −1677.14 2904.90i −0.102146 0.176922i
\(647\) 1084.15 1877.80i 0.0658767 0.114102i −0.831206 0.555965i \(-0.812349\pi\)
0.897083 + 0.441863i \(0.145682\pi\)
\(648\) 977.421 1692.94i 0.0592542 0.102631i
\(649\) −4338.40 7514.34i −0.262400 0.454489i
\(650\) −5970.36 10341.0i −0.360272 0.624009i
\(651\) −20105.2 34823.3i −1.21042 2.09652i
\(652\) 7039.38 0.422827
\(653\) 9783.46 16945.4i 0.586304 1.01551i −0.408408 0.912800i \(-0.633916\pi\)
0.994712 0.102708i \(-0.0327508\pi\)
\(654\) −16038.8 27780.1i −0.958972 1.66099i
\(655\) 1116.91 0.0666278
\(656\) 3876.82 0.230738
\(657\) 2086.58 + 3614.07i 0.123905 + 0.214609i
\(658\) 17405.1 1.03119
\(659\) −8235.94 + 14265.1i −0.486839 + 0.843230i −0.999886 0.0151310i \(-0.995183\pi\)
0.513047 + 0.858361i \(0.328517\pi\)
\(660\) 1955.39 0.115323
\(661\) 83.0511 143.849i 0.00488701 0.00846455i −0.863572 0.504226i \(-0.831778\pi\)
0.868459 + 0.495762i \(0.165111\pi\)
\(662\) 5240.87 9077.46i 0.307692 0.532939i
\(663\) 6815.48 11804.8i 0.399233 0.691491i
\(664\) −3645.81 6314.73i −0.213080 0.369065i
\(665\) −6916.12 −0.403302
\(666\) 2571.72 21223.1i 0.149628 1.23480i
\(667\) −15676.0 −0.910009
\(668\) 179.608 + 311.090i 0.0104031 + 0.0180186i
\(669\) −382.478 + 662.471i −0.0221038 + 0.0382849i
\(670\) 1460.17 2529.09i 0.0841959 0.145832i
\(671\) −2957.96 + 5123.34i −0.170180 + 0.294761i
\(672\) 4741.45 0.272181
\(673\) 1696.38 2938.21i 0.0971628 0.168291i −0.813346 0.581780i \(-0.802357\pi\)
0.910509 + 0.413489i \(0.135690\pi\)
\(674\) 19483.1 1.11344
\(675\) 8077.09 + 13989.9i 0.460574 + 0.797738i
\(676\) 8307.21 0.472645
\(677\) 5580.22 0.316787 0.158394 0.987376i \(-0.449368\pi\)
0.158394 + 0.987376i \(0.449368\pi\)
\(678\) 6060.43 + 10497.0i 0.343288 + 0.594592i
\(679\) 11872.0 20562.8i 0.670993 1.16219i
\(680\) 1121.49 0.0632461
\(681\) −17472.3 30262.9i −0.983173 1.70291i
\(682\) −2648.74 4587.76i −0.148718 0.257587i
\(683\) 6641.24 + 11503.0i 0.372065 + 0.644435i 0.989883 0.141886i \(-0.0453167\pi\)
−0.617818 + 0.786321i \(0.711983\pi\)
\(684\) −6594.52 + 11422.0i −0.368637 + 0.638498i
\(685\) −267.574 + 463.453i −0.0149248 + 0.0258505i
\(686\) 6717.30 + 11634.7i 0.373860 + 0.647544i
\(687\) −15497.7 26842.7i −0.860659 1.49070i
\(688\) −1514.03 2622.38i −0.0838982 0.145316i
\(689\) −23956.2 −1.32461
\(690\) −3426.14 + 5934.24i −0.189030 + 0.327410i
\(691\) −6948.98 12036.0i −0.382564 0.662620i 0.608864 0.793274i \(-0.291625\pi\)
−0.991428 + 0.130655i \(0.958292\pi\)
\(692\) 15159.5 0.832773
\(693\) −7957.98 −0.436217
\(694\) 8864.95 + 15354.5i 0.484883 + 0.839842i
\(695\) −3618.98 −0.197519
\(696\) 7911.55 13703.2i 0.430871 0.746291i
\(697\) −5853.47 −0.318100
\(698\) −594.163 + 1029.12i −0.0322198 + 0.0558063i
\(699\) −26100.2 + 45206.8i −1.41230 + 2.44618i
\(700\) −3135.62 + 5431.05i −0.169307 + 0.293249i
\(701\) 4649.93 + 8053.91i 0.250535 + 0.433940i 0.963673 0.267084i \(-0.0860600\pi\)
−0.713138 + 0.701024i \(0.752727\pi\)
\(702\) −23127.5 −1.24344
\(703\) −1879.60 + 15511.4i −0.100840 + 0.832180i
\(704\) 624.658 0.0334413
\(705\) −12694.9 21988.1i −0.678179 1.17464i
\(706\) −3009.17 + 5212.04i −0.160413 + 0.277844i
\(707\) 10057.7 17420.4i 0.535019 0.926679i
\(708\) −15345.8 + 26579.7i −0.814591 + 1.41091i
\(709\) 29471.3 1.56110 0.780550 0.625094i \(-0.214939\pi\)
0.780550 + 0.625094i \(0.214939\pi\)
\(710\) −4133.56 + 7159.53i −0.218492 + 0.378440i
\(711\) 20592.2 1.08617
\(712\) 2965.75 + 5136.84i 0.156104 + 0.270381i
\(713\) 18564.0 0.975074
\(714\) −7158.95 −0.375234
\(715\) −1851.35 3206.63i −0.0968344 0.167722i
\(716\) 7184.91 12444.6i 0.375018 0.649550i
\(717\) 1657.21 0.0863177
\(718\) 2508.18 + 4344.29i 0.130368 + 0.225804i
\(719\) 13186.0 + 22838.8i 0.683942 + 1.18462i 0.973768 + 0.227543i \(0.0730693\pi\)
−0.289826 + 0.957079i \(0.593597\pi\)
\(720\) −2204.85 3818.92i −0.114125 0.197670i
\(721\) 11599.1 20090.2i 0.599129 1.03772i
\(722\) −2039.24 + 3532.06i −0.105114 + 0.182063i
\(723\) 5459.06 + 9455.37i 0.280809 + 0.486375i
\(724\) 594.448 + 1029.61i 0.0305145 + 0.0528526i
\(725\) 10464.1 + 18124.4i 0.536039 + 0.928446i
\(726\) 21331.3 1.09047
\(727\) −10798.3 + 18703.3i −0.550878 + 0.954149i 0.447333 + 0.894367i \(0.352374\pi\)
−0.998211 + 0.0597816i \(0.980960\pi\)
\(728\) −4489.18 7775.50i −0.228544 0.395850i
\(729\) −29615.4 −1.50462
\(730\) 1019.78 0.0517036
\(731\) 2285.98 + 3959.44i 0.115664 + 0.200335i
\(732\) 20925.8 1.05661
\(733\) −9413.89 + 16305.3i −0.474366 + 0.821625i −0.999569 0.0293513i \(-0.990656\pi\)
0.525204 + 0.850977i \(0.323989\pi\)
\(734\) −19275.4 −0.969303
\(735\) 1209.21 2094.42i 0.0606838 0.105107i
\(736\) −1094.50 + 1895.72i −0.0548148 + 0.0949420i
\(737\) −1227.97 + 2126.90i −0.0613741 + 0.106303i
\(738\) 11507.9 + 19932.3i 0.573999 + 0.994196i
\(739\) −6510.06 −0.324055 −0.162027 0.986786i \(-0.551803\pi\)
−0.162027 + 0.986786i \(0.551803\pi\)
\(740\) −4177.13 3137.33i −0.207506 0.155852i
\(741\) 39172.5 1.94202
\(742\) 6290.88 + 10896.1i 0.311247 + 0.539096i
\(743\) 4517.91 7825.26i 0.223077 0.386381i −0.732664 0.680591i \(-0.761723\pi\)
0.955741 + 0.294210i \(0.0950565\pi\)
\(744\) −9369.12 + 16227.8i −0.461678 + 0.799650i
\(745\) −170.700 + 295.661i −0.00839457 + 0.0145398i
\(746\) −22205.3 −1.08981
\(747\) 21644.4 37489.1i 1.06014 1.83622i
\(748\) −943.148 −0.0461028
\(749\) −12209.9 21148.2i −0.595649 1.03169i
\(750\) 21669.5 1.05501
\(751\) −12387.2 −0.601884 −0.300942 0.953642i \(-0.597301\pi\)
−0.300942 + 0.953642i \(0.597301\pi\)
\(752\) −4055.44 7024.22i −0.196658 0.340621i
\(753\) −14737.0 + 25525.3i −0.713211 + 1.23532i
\(754\) −29962.5 −1.44717
\(755\) −4393.39 7609.58i −0.211777 0.366809i
\(756\) 6073.27 + 10519.2i 0.292173 + 0.506058i
\(757\) 8643.24 + 14970.5i 0.414985 + 0.718776i 0.995427 0.0955263i \(-0.0304534\pi\)
−0.580442 + 0.814302i \(0.697120\pi\)
\(758\) 7380.51 12783.4i 0.353657 0.612553i
\(759\) 2881.29 4990.55i 0.137792 0.238663i
\(760\) 1611.47 + 2791.15i 0.0769133 + 0.133218i
\(761\) 9167.51 + 15878.6i 0.436691 + 0.756371i 0.997432 0.0716201i \(-0.0228169\pi\)
−0.560741 + 0.827991i \(0.689484\pi\)
\(762\) 14831.5 + 25689.0i 0.705105 + 1.22128i
\(763\) 31901.5 1.51365
\(764\) −5731.00 + 9926.38i −0.271388 + 0.470057i
\(765\) 3329.03 + 5766.05i 0.157335 + 0.272512i
\(766\) −7449.10 −0.351367
\(767\) 58117.3 2.73598
\(768\) −1104.77 1913.51i −0.0519074 0.0899063i
\(769\) −27200.0 −1.27550 −0.637748 0.770245i \(-0.720134\pi\)
−0.637748 + 0.770245i \(0.720134\pi\)
\(770\) −972.325 + 1684.12i −0.0455067 + 0.0788199i
\(771\) 8841.41 0.412990
\(772\) 9620.87 16663.8i 0.448527 0.776871i
\(773\) −13160.6 + 22794.9i −0.612360 + 1.06064i 0.378481 + 0.925609i \(0.376446\pi\)
−0.990841 + 0.135030i \(0.956887\pi\)
\(774\) 8988.47 15568.5i 0.417421 0.722994i
\(775\) −12392.0 21463.5i −0.574365 0.994830i
\(776\) −11064.8 −0.511858
\(777\) 26664.3 + 20026.8i 1.23112 + 0.924656i
\(778\) −6539.27 −0.301342
\(779\) −8410.82 14568.0i −0.386841 0.670028i
\(780\) −6548.59 + 11342.5i −0.300612 + 0.520675i
\(781\) 3476.22 6020.98i 0.159269 0.275861i
\(782\) 1652.54 2862.28i 0.0755687 0.130889i
\(783\) 40535.2 1.85008
\(784\) 386.290 669.073i 0.0175970 0.0304789i
\(785\) −6608.00 −0.300445
\(786\) 1661.23 + 2877.33i 0.0753869 + 0.130574i
\(787\) −36881.0 −1.67048 −0.835239 0.549887i \(-0.814671\pi\)
−0.835239 + 0.549887i \(0.814671\pi\)
\(788\) −1700.74 −0.0768863
\(789\) −5987.14 10370.0i −0.270149 0.467912i
\(790\) 2516.00 4357.84i 0.113311 0.196260i
\(791\) −12054.3 −0.541848
\(792\) 1854.23 + 3211.61i 0.0831907 + 0.144091i
\(793\) −19812.4 34316.1i −0.887213 1.53670i
\(794\) 12159.0 + 21060.1i 0.543461 + 0.941303i
\(795\) 9176.81 15894.7i 0.409393 0.709090i
\(796\) 486.353 842.389i 0.0216562 0.0375096i
\(797\) −10624.1 18401.5i −0.472178 0.817835i 0.527316 0.849669i \(-0.323199\pi\)
−0.999493 + 0.0318340i \(0.989865\pi\)
\(798\) −10286.7 17817.0i −0.456320 0.790370i
\(799\) 6123.15 + 10605.6i 0.271116 + 0.469587i
\(800\) 2922.42 0.129154
\(801\) −17607.0 + 30496.2i −0.776671 + 1.34523i
\(802\) −179.867 311.539i −0.00791937 0.0137168i
\(803\) −857.605 −0.0376890
\(804\) 8687.11 0.381058
\(805\) −3407.33 5901.66i −0.149183 0.258393i
\(806\) 35482.6 1.55064
\(807\) 9394.47 16271.7i 0.409791 0.709778i
\(808\) −9373.84 −0.408132
\(809\) −3592.39 + 6222.20i −0.156121 + 0.270409i −0.933467 0.358665i \(-0.883232\pi\)
0.777346 + 0.629073i \(0.216566\pi\)
\(810\) 1417.98 2456.02i 0.0615097 0.106538i
\(811\) 13130.3 22742.3i 0.568515 0.984697i −0.428198 0.903685i \(-0.640852\pi\)
0.996713 0.0810118i \(-0.0258151\pi\)
\(812\) 7868.11 + 13628.0i 0.340045 + 0.588975i
\(813\) 48453.3 2.09020
\(814\) 3512.86 + 2638.41i 0.151260 + 0.113607i
\(815\) 10212.3 0.438922
\(816\) 1668.05 + 2889.15i 0.0715606 + 0.123947i
\(817\) −6569.44 + 11378.6i −0.281316 + 0.487254i
\(818\) −4545.35 + 7872.78i −0.194284 + 0.336510i
\(819\) 26651.3 46161.4i 1.13708 1.96949i
\(820\) 5624.25 0.239521
\(821\) 14746.3 25541.3i 0.626855 1.08574i −0.361324 0.932440i \(-0.617675\pi\)
0.988179 0.153304i \(-0.0489914\pi\)
\(822\) −1591.90 −0.0675474
\(823\) 12857.6 + 22270.0i 0.544579 + 0.943238i 0.998633 + 0.0522641i \(0.0166438\pi\)
−0.454055 + 0.890974i \(0.650023\pi\)
\(824\) −10810.4 −0.457038
\(825\) −7693.36 −0.324665
\(826\) −15261.5 26433.8i −0.642877 1.11350i
\(827\) −15481.9 + 26815.4i −0.650976 + 1.12752i 0.331911 + 0.943311i \(0.392307\pi\)
−0.982886 + 0.184212i \(0.941027\pi\)
\(828\) −12995.6 −0.545443
\(829\) −10660.9 18465.3i −0.446646 0.773614i 0.551519 0.834162i \(-0.314048\pi\)
−0.998165 + 0.0605482i \(0.980715\pi\)
\(830\) −5289.12 9161.02i −0.221190 0.383113i
\(831\) −7402.08 12820.8i −0.308995 0.535196i
\(832\) −2091.98 + 3623.41i −0.0871710 + 0.150985i
\(833\) −583.245 + 1010.21i −0.0242596 + 0.0420188i
\(834\) −5382.67 9323.06i −0.223485 0.387088i
\(835\) 260.564 + 451.311i 0.0107990 + 0.0187045i
\(836\) −1355.20 2347.28i −0.0560655 0.0971082i
\(837\) −48003.1 −1.98236
\(838\) 835.045 1446.34i 0.0344226 0.0596217i
\(839\) −15727.2 27240.3i −0.647156 1.12091i −0.983799 0.179274i \(-0.942625\pi\)
0.336643 0.941632i \(-0.390708\pi\)
\(840\) 6878.61 0.282541
\(841\) 28125.6 1.15321
\(842\) −16250.4 28146.5i −0.665113 1.15201i
\(843\) −33950.0 −1.38707
\(844\) −3989.45 + 6909.93i −0.162704 + 0.281812i
\(845\) 12051.6 0.490636
\(846\) 24076.2 41701.2i 0.978436 1.69470i
\(847\) −10607.1 + 18372.0i −0.430300 + 0.745301i
\(848\) 2931.58 5077.64i 0.118715 0.205621i
\(849\) 18849.0 + 32647.5i 0.761952 + 1.31974i
\(850\) −4412.46 −0.178054
\(851\) −14162.2 + 6038.00i −0.570474 + 0.243220i
\(852\) −24592.1 −0.988864
\(853\) 23005.2 + 39846.2i 0.923427 + 1.59942i 0.794072 + 0.607824i \(0.207958\pi\)
0.129356 + 0.991598i \(0.458709\pi\)
\(854\) −10405.4 + 18022.8i −0.416940 + 0.722162i
\(855\) −9566.93 + 16570.4i −0.382669 + 0.662802i
\(856\) −5689.88 + 9855.16i −0.227192 + 0.393507i
\(857\) −16592.5 −0.661365 −0.330682 0.943742i \(-0.607279\pi\)
−0.330682 + 0.943742i \(0.607279\pi\)
\(858\) 5507.20 9538.74i 0.219129 0.379542i
\(859\) −9563.88 −0.379878 −0.189939 0.981796i \(-0.560829\pi\)
−0.189939 + 0.981796i \(0.560829\pi\)
\(860\) −2196.47 3804.39i −0.0870917 0.150847i
\(861\) −35901.9 −1.42106
\(862\) −21229.5 −0.838840
\(863\) 13590.1 + 23538.7i 0.536051 + 0.928467i 0.999112 + 0.0421407i \(0.0134178\pi\)
−0.463061 + 0.886326i \(0.653249\pi\)
\(864\) 2830.17 4901.99i 0.111440 0.193020i
\(865\) 21992.5 0.864472
\(866\) 12682.2 + 21966.2i 0.497642 + 0.861941i
\(867\) 18683.5 + 32360.8i 0.731864 + 1.26763i
\(868\) −9317.68 16138.7i −0.364358 0.631087i
\(869\) −2115.89 + 3664.83i −0.0825969 + 0.143062i
\(870\) 11477.6 19879.8i 0.447272 0.774698i
\(871\) −8224.91 14246.0i −0.319966 0.554198i
\(872\) −7433.12 12874.5i −0.288667 0.499985i
\(873\) −32844.5 56888.4i −1.27333 2.20548i
\(874\) 9498.11 0.367595
\(875\) −10775.3 + 18663.3i −0.416309 + 0.721068i
\(876\) 1516.76 + 2627.10i 0.0585006 + 0.101326i
\(877\) −17764.9 −0.684013 −0.342006 0.939698i \(-0.611106\pi\)
−0.342006 + 0.939698i \(0.611106\pi\)
\(878\) 25211.5 0.969073
\(879\) 36819.6 + 63773.5i 1.41285 + 2.44713i
\(880\) 906.215 0.0347142
\(881\) 12642.6 21897.7i 0.483474 0.837401i −0.516346 0.856380i \(-0.672708\pi\)
0.999820 + 0.0189787i \(0.00604146\pi\)
\(882\) 4586.63 0.175102
\(883\) −2921.85 + 5060.80i −0.111357 + 0.192876i −0.916318 0.400452i \(-0.868853\pi\)
0.804961 + 0.593328i \(0.202186\pi\)
\(884\) 3158.60 5470.86i 0.120176 0.208150i
\(885\) −22262.7 + 38560.2i −0.845597 + 1.46462i
\(886\) 6136.72 + 10629.1i 0.232694 + 0.403039i
\(887\) 30297.4 1.14688 0.573442 0.819246i \(-0.305608\pi\)
0.573442 + 0.819246i \(0.305608\pi\)
\(888\) 1869.41 15427.2i 0.0706454 0.583001i
\(889\) −29500.2 −1.11294
\(890\) 4302.54 + 7452.21i 0.162046 + 0.280673i
\(891\) −1192.49 + 2065.45i −0.0448371 + 0.0776601i
\(892\) −177.258 + 307.019i −0.00665362 + 0.0115244i
\(893\) −17596.7 + 30478.3i −0.659406 + 1.14213i
\(894\) −1015.56 −0.0379926
\(895\) 10423.4 18053.9i 0.389293 0.674275i
\(896\) 2197.41 0.0819310
\(897\) 19298.9 + 33426.7i 0.718363 + 1.24424i
\(898\) 7235.10 0.268862
\(899\) −62189.6 −2.30716
\(900\) 8674.88 + 15025.3i 0.321292 + 0.556494i
\(901\) −4426.28 + 7666.54i −0.163663 + 0.283473i
\(902\) −4729.85 −0.174597
\(903\) 14020.9 + 24285.0i 0.516708 + 0.894964i
\(904\) 2808.68 + 4864.77i 0.103335 + 0.178982i
\(905\) 862.389 + 1493.70i 0.0316760 + 0.0548644i
\(906\) 13069.0 22636.2i 0.479236 0.830062i
\(907\) −4720.79 + 8176.64i −0.172824 + 0.299340i −0.939406 0.342807i \(-0.888622\pi\)
0.766582 + 0.642146i \(0.221956\pi\)
\(908\) −8097.47 14025.2i −0.295952 0.512603i
\(909\) −27825.2 48194.7i −1.01530 1.75854i
\(910\) −6512.64 11280.2i −0.237244 0.410918i
\(911\) −5048.65 −0.183611 −0.0918053 0.995777i \(-0.529264\pi\)
−0.0918053 + 0.995777i \(0.529264\pi\)
\(912\) −4793.62 + 8302.80i −0.174049 + 0.301462i
\(913\) 4448.01 + 7704.19i 0.161235 + 0.279268i
\(914\) 19852.2 0.718437
\(915\) 30357.8 1.09683
\(916\) −7182.32 12440.1i −0.259073 0.448727i
\(917\) −3304.22 −0.118991
\(918\) −4273.17 + 7401.34i −0.153633 + 0.266101i
\(919\) −18619.3 −0.668329 −0.334164 0.942515i \(-0.608454\pi\)
−0.334164 + 0.942515i \(0.608454\pi\)
\(920\) −1587.83 + 2750.20i −0.0569013 + 0.0985559i
\(921\) 10912.2 18900.5i 0.390411 0.676212i
\(922\) −748.892 + 1297.12i −0.0267500 + 0.0463323i
\(923\) 23283.7 + 40328.5i 0.830327 + 1.43817i
\(924\) −5784.73 −0.205957
\(925\) 16434.7 + 12343.6i 0.584184 + 0.438764i
\(926\) −25666.8 −0.910868
\(927\) −32089.6 55580.7i −1.13696 1.96927i
\(928\) 3666.57 6350.69i 0.129699 0.224646i
\(929\) 7802.23 13513.9i 0.275547 0.477261i −0.694726 0.719274i \(-0.744474\pi\)
0.970273 + 0.242013i \(0.0778078\pi\)
\(930\) −13592.1 + 23542.3i −0.479252 + 0.830088i
\(931\) −3352.25 −0.118008
\(932\) −12096.0 + 20950.9i −0.425127 + 0.736341i
\(933\) −54724.3 −1.92025
\(934\) −10067.2 17437.0i −0.352688 0.610873i
\(935\) −1368.26 −0.0478577
\(936\) −24839.2 −0.867409
\(937\) −16509.9 28596.0i −0.575619 0.997002i −0.995974 0.0896420i \(-0.971428\pi\)
0.420355 0.907360i \(-0.361906\pi\)
\(938\) −4319.71 + 7481.95i −0.150366 + 0.260442i
\(939\) 21932.7 0.762242
\(940\) −5883.38 10190.3i −0.204143 0.353586i
\(941\) −12483.6 21622.3i −0.432471 0.749062i 0.564614 0.825355i \(-0.309025\pi\)
−0.997085 + 0.0762931i \(0.975692\pi\)
\(942\) −9828.38 17023.2i −0.339943 0.588798i
\(943\) 8287.43 14354.2i 0.286189 0.495693i
\(944\) −7111.94 + 12318.2i −0.245205 + 0.424708i
\(945\) 8810.72 + 15260.6i 0.303294 + 0.525321i
\(946\) 1847.17 + 3199.40i 0.0634849 + 0.109959i
\(947\) 19195.4 + 33247.4i 0.658676 + 1.14086i 0.980959 + 0.194217i \(0.0622166\pi\)
−0.322282 + 0.946644i \(0.604450\pi\)
\(948\) 14968.7 0.512826
\(949\) 2872.12 4974.66i 0.0982434 0.170163i
\(950\) −6340.24 10981.6i −0.216531 0.375043i
\(951\) −23238.9 −0.792402
\(952\) −3317.78 −0.112952
\(953\) −9401.17 16283.3i −0.319553 0.553482i 0.660842 0.750525i \(-0.270199\pi\)
−0.980395 + 0.197043i \(0.936866\pi\)
\(954\) 34808.2 1.18130
\(955\) −8314.18 + 14400.6i −0.281718 + 0.487950i
\(956\) 768.029 0.0259831
\(957\) −9652.36 + 16718.4i −0.326036 + 0.564711i
\(958\) 9061.80 15695.5i 0.305609 0.529330i
\(959\) 791.581 1371.06i 0.0266543 0.0461666i
\(960\) −1602.73 2776.01i −0.0538832 0.0933285i
\(961\) 43856.0 1.47212
\(962\) −27069.1 + 11540.8i −0.907215 + 0.386789i
\(963\) −67559.0 −2.26071
\(964\) 2529.98 + 4382.05i 0.0845281 + 0.146407i
\(965\) 13957.4 24174.9i 0.465600 0.806442i
\(966\) 10135.7 17555.6i 0.337590 0.584724i
\(967\) 23828.6 41272.4i 0.792428 1.37253i −0.132032 0.991245i \(-0.542150\pi\)
0.924460 0.381280i \(-0.124517\pi\)
\(968\) 9885.90 0.328249
\(969\) 7237.72 12536.1i 0.239947 0.415601i
\(970\) −16052.1 −0.531342
\(971\) 21568.8 + 37358.3i 0.712848 + 1.23469i 0.963784 + 0.266686i \(0.0859286\pi\)
−0.250935 + 0.968004i \(0.580738\pi\)
\(972\) −10667.5 −0.352017
\(973\) 10706.2 0.352750
\(974\) −10696.1 18526.2i −0.351874 0.609464i
\(975\) 25765.1 44626.4i 0.846300 1.46584i
\(976\) 9697.96 0.318058
\(977\) −11799.4 20437.1i −0.386383 0.669234i 0.605577 0.795786i \(-0.292942\pi\)
−0.991960 + 0.126552i \(0.959609\pi\)
\(978\) 15189.2 + 26308.5i 0.496623 + 0.860177i
\(979\) −3618.32 6267.12i −0.118123 0.204594i
\(980\) 560.405 970.651i 0.0182668 0.0316391i
\(981\) 44128.8 76433.3i 1.43621 2.48759i
\(982\) −2824.19 4891.64i −0.0917755 0.158960i
\(983\) 10344.4 + 17917.0i 0.335640 + 0.581346i 0.983608 0.180322i \(-0.0577141\pi\)
−0.647967 + 0.761668i \(0.724381\pi\)
\(984\) 8365.21 + 14489.0i 0.271009 + 0.469402i
\(985\) −2467.33 −0.0798129
\(986\) −5536.02 + 9588.68i −0.178806 + 0.309701i
\(987\) 37556.0 + 65048.8i 1.21116 + 2.09780i
\(988\) 18154.3 0.584581
\(989\) −12946.1 −0.416241
\(990\) 2690.00 + 4659.21i 0.0863573 + 0.149575i
\(991\) −367.111 −0.0117676 −0.00588378 0.999983i \(-0.501873\pi\)
−0.00588378 + 0.999983i \(0.501873\pi\)
\(992\) −4342.08 + 7520.70i −0.138973 + 0.240708i
\(993\) 45234.0 1.44558
\(994\) 12228.5 21180.5i 0.390207 0.675859i
\(995\) 705.572 1222.09i 0.0224805 0.0389374i
\(996\) 15733.5 27251.2i 0.500537 0.866956i
\(997\) −7544.87 13068.1i −0.239667 0.415116i 0.720951 0.692986i \(-0.243705\pi\)
−0.960619 + 0.277870i \(0.910372\pi\)
\(998\) −33158.7 −1.05172
\(999\) 36620.8 15613.2i 1.15979 0.494473i
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 74.4.c.a.63.1 yes 8
3.2 odd 2 666.4.f.a.433.3 8
37.10 even 3 inner 74.4.c.a.47.1 8
111.47 odd 6 666.4.f.a.343.3 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.4.c.a.47.1 8 37.10 even 3 inner
74.4.c.a.63.1 yes 8 1.1 even 1 trivial
666.4.f.a.343.3 8 111.47 odd 6
666.4.f.a.433.3 8 3.2 odd 2