Properties

Label 45.4.e.b.31.2
Level $45$
Weight $4$
Character 45.31
Analytic conductor $2.655$
Analytic rank $0$
Dimension $6$
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] = [45,4,Mod(16,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.16");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 45 = 3^{2} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 45.e (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: \(2.65508595026\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.15759792.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 31.2
Root \(0.500000 + 1.98116i\) of defining polynomial
Character \(\chi\) \(=\) 45.31
Dual form 45.4.e.b.16.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0874923 + 0.151541i) q^{2} +(5.19394 - 0.151541i) q^{3} +(3.98469 - 6.90169i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(0.477395 + 0.773837i) q^{6} +(-4.23186 - 7.32979i) q^{7} +2.79440 q^{8} +(26.9541 - 1.57419i) q^{9} +O(q^{10})\) \(q+(0.0874923 + 0.151541i) q^{2} +(5.19394 - 0.151541i) q^{3} +(3.98469 - 6.90169i) q^{4} +(-2.50000 + 4.33013i) q^{5} +(0.477395 + 0.773837i) q^{6} +(-4.23186 - 7.32979i) q^{7} +2.79440 q^{8} +(26.9541 - 1.57419i) q^{9} -0.874923 q^{10} +(15.7541 + 27.2870i) q^{11} +(19.6504 - 36.4508i) q^{12} +(-13.4348 + 23.2697i) q^{13} +(0.740510 - 1.28260i) q^{14} +(-12.3287 + 22.8693i) q^{15} +(-31.6330 - 54.7900i) q^{16} -44.3307 q^{17} +(2.59683 + 3.94692i) q^{18} -90.2082 q^{19} +(19.9235 + 34.5084i) q^{20} +(-23.0908 - 37.4292i) q^{21} +(-2.75673 + 4.77480i) q^{22} +(-97.1287 + 168.232i) q^{23} +(14.5139 - 0.423466i) q^{24} +(-12.5000 - 21.6506i) q^{25} -4.70176 q^{26} +(139.759 - 12.2609i) q^{27} -67.4506 q^{28} +(-1.87186 - 3.24215i) q^{29} +(-4.54430 + 0.132587i) q^{30} +(125.832 - 217.947i) q^{31} +(16.7129 - 28.9476i) q^{32} +(85.9611 + 139.339i) q^{33} +(-3.87859 - 6.71792i) q^{34} +42.3186 q^{35} +(96.5390 - 192.301i) q^{36} -62.2293 q^{37} +(-7.89252 - 13.6703i) q^{38} +(-66.2532 + 122.898i) q^{39} +(-6.98599 + 12.1001i) q^{40} +(102.173 - 176.969i) q^{41} +(3.65180 - 6.77397i) q^{42} +(263.831 + 456.968i) q^{43} +251.101 q^{44} +(-60.5687 + 120.650i) q^{45} -33.9920 q^{46} +(-77.8637 - 134.864i) q^{47} +(-172.603 - 279.782i) q^{48} +(135.683 - 235.009i) q^{49} +(2.18731 - 3.78853i) q^{50} +(-230.251 + 6.71792i) q^{51} +(107.067 + 185.445i) q^{52} -141.694 q^{53} +(14.0859 + 20.1065i) q^{54} -157.541 q^{55} +(-11.8255 - 20.4823i) q^{56} +(-468.536 + 13.6703i) q^{57} +(0.327546 - 0.567326i) q^{58} +(246.923 - 427.683i) q^{59} +(108.711 + 176.216i) q^{60} +(379.742 + 657.732i) q^{61} +44.0373 q^{62} +(-125.604 - 190.906i) q^{63} -500.280 q^{64} +(-67.1739 - 116.349i) q^{65} +(-13.5947 + 25.2178i) q^{66} +(271.795 - 470.763i) q^{67} +(-176.644 + 305.956i) q^{68} +(-478.987 + 888.505i) q^{69} +(3.70255 + 6.41300i) q^{70} -928.207 q^{71} +(75.3203 - 4.39891i) q^{72} +608.739 q^{73} +(-5.44459 - 9.43030i) q^{74} +(-68.2052 - 110.558i) q^{75} +(-359.452 + 622.589i) q^{76} +(133.338 - 230.949i) q^{77} +(-24.4207 + 0.712510i) q^{78} +(-307.420 - 532.467i) q^{79} +316.330 q^{80} +(724.044 - 84.8617i) q^{81} +35.7573 q^{82} +(-537.655 - 931.246i) q^{83} +(-350.334 + 10.2215i) q^{84} +(110.827 - 191.957i) q^{85} +(-46.1663 + 79.9623i) q^{86} +(-10.2136 - 16.5559i) q^{87} +(44.0233 + 76.2506i) q^{88} +1505.15 q^{89} +(-23.5827 + 1.37730i) q^{90} +227.416 q^{91} +(774.055 + 1340.70i) q^{92} +(620.536 - 1151.07i) q^{93} +(13.6249 - 23.5991i) q^{94} +(225.521 - 390.613i) q^{95} +(82.4190 - 152.885i) q^{96} +(166.369 + 288.160i) q^{97} +47.4848 q^{98} +(467.593 + 710.695i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + q^{2} + 9 q^{3} - 11 q^{4} - 15 q^{5} + 84 q^{6} + 43 q^{7} - 54 q^{8} + 57 q^{9} - 10 q^{10} - 14 q^{11} + 75 q^{12} - 40 q^{13} + 27 q^{14} - 15 q^{15} + 13 q^{16} - 332 q^{17} + 3 q^{18} - 328 q^{19} - 55 q^{20} - 144 q^{21} + 376 q^{22} - 171 q^{23} - 63 q^{24} - 75 q^{25} + 868 q^{26} + 162 q^{27} - 1034 q^{28} + 335 q^{29} - 315 q^{30} + 352 q^{31} + 77 q^{32} - 708 q^{33} + 52 q^{34} - 430 q^{35} + 1086 q^{36} + 804 q^{37} + 178 q^{38} - 390 q^{39} + 135 q^{40} - 187 q^{41} + 513 q^{42} + 602 q^{43} + 1964 q^{44} + 330 q^{45} - 402 q^{46} - 665 q^{47} - 1074 q^{48} - 430 q^{49} + 25 q^{50} - 180 q^{51} + 456 q^{52} - 1460 q^{53} + 639 q^{54} + 140 q^{55} - 705 q^{56} - 486 q^{57} - 217 q^{58} + 298 q^{59} - 150 q^{60} + 1439 q^{61} - 3228 q^{62} + 2205 q^{63} - 3138 q^{64} - 200 q^{65} - 966 q^{66} + 1849 q^{67} + 710 q^{68} - 873 q^{69} + 135 q^{70} + 140 q^{71} + 261 q^{72} - 736 q^{73} + 320 q^{74} - 150 q^{75} - 204 q^{76} + 948 q^{77} - 432 q^{78} + 382 q^{79} - 130 q^{80} - 1251 q^{81} - 1150 q^{82} + 831 q^{83} - 909 q^{84} + 830 q^{85} - 1580 q^{86} + 258 q^{87} + 1428 q^{88} + 3438 q^{89} + 375 q^{90} - 1420 q^{91} + 1623 q^{92} + 2178 q^{93} + 2077 q^{94} + 820 q^{95} + 1155 q^{96} + 282 q^{97} + 4328 q^{98} - 762 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).

\(n\) \(11\) \(37\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0874923 + 0.151541i 0.0309332 + 0.0535779i 0.881078 0.472972i \(-0.156819\pi\)
−0.850144 + 0.526550i \(0.823485\pi\)
\(3\) 5.19394 0.151541i 0.999575 0.0291641i
\(4\) 3.98469 6.90169i 0.498086 0.862711i
\(5\) −2.50000 + 4.33013i −0.223607 + 0.387298i
\(6\) 0.477395 + 0.773837i 0.0324826 + 0.0526529i
\(7\) −4.23186 7.32979i −0.228499 0.395772i 0.728865 0.684658i \(-0.240048\pi\)
−0.957363 + 0.288886i \(0.906715\pi\)
\(8\) 2.79440 0.123496
\(9\) 26.9541 1.57419i 0.998299 0.0583034i
\(10\) −0.874923 −0.0276675
\(11\) 15.7541 + 27.2870i 0.431823 + 0.747939i 0.997030 0.0770098i \(-0.0245373\pi\)
−0.565208 + 0.824949i \(0.691204\pi\)
\(12\) 19.6504 36.4508i 0.472714 0.876870i
\(13\) −13.4348 + 23.2697i −0.286626 + 0.496451i −0.973002 0.230796i \(-0.925867\pi\)
0.686376 + 0.727247i \(0.259200\pi\)
\(14\) 0.740510 1.28260i 0.0141364 0.0244850i
\(15\) −12.3287 + 22.8693i −0.212216 + 0.393655i
\(16\) −31.6330 54.7900i −0.494266 0.856094i
\(17\) −44.3307 −0.632457 −0.316229 0.948683i \(-0.602417\pi\)
−0.316229 + 0.948683i \(0.602417\pi\)
\(18\) 2.59683 + 3.94692i 0.0340044 + 0.0516832i
\(19\) −90.2082 −1.08922 −0.544610 0.838689i \(-0.683322\pi\)
−0.544610 + 0.838689i \(0.683322\pi\)
\(20\) 19.9235 + 34.5084i 0.222751 + 0.385816i
\(21\) −23.0908 37.4292i −0.239944 0.388939i
\(22\) −2.75673 + 4.77480i −0.0267153 + 0.0462723i
\(23\) −97.1287 + 168.232i −0.880553 + 1.52516i −0.0298265 + 0.999555i \(0.509495\pi\)
−0.850727 + 0.525608i \(0.823838\pi\)
\(24\) 14.5139 0.423466i 0.123443 0.00360165i
\(25\) −12.5000 21.6506i −0.100000 0.173205i
\(26\) −4.70176 −0.0354650
\(27\) 139.759 12.2609i 0.996174 0.0873931i
\(28\) −67.4506 −0.455248
\(29\) −1.87186 3.24215i −0.0119860 0.0207604i 0.859970 0.510344i \(-0.170482\pi\)
−0.871956 + 0.489584i \(0.837149\pi\)
\(30\) −4.54430 + 0.132587i −0.0276557 + 0.000806898i
\(31\) 125.832 217.947i 0.729035 1.26273i −0.228257 0.973601i \(-0.573303\pi\)
0.957292 0.289124i \(-0.0933641\pi\)
\(32\) 16.7129 28.9476i 0.0923265 0.159914i
\(33\) 85.9611 + 139.339i 0.453452 + 0.735027i
\(34\) −3.87859 6.71792i −0.0195639 0.0338857i
\(35\) 42.3186 0.204376
\(36\) 96.5390 192.301i 0.446940 0.890283i
\(37\) −62.2293 −0.276498 −0.138249 0.990397i \(-0.544147\pi\)
−0.138249 + 0.990397i \(0.544147\pi\)
\(38\) −7.89252 13.6703i −0.0336931 0.0583581i
\(39\) −66.2532 + 122.898i −0.272026 + 0.504599i
\(40\) −6.98599 + 12.1001i −0.0276145 + 0.0478298i
\(41\) 102.173 176.969i 0.389188 0.674094i −0.603152 0.797626i \(-0.706089\pi\)
0.992341 + 0.123532i \(0.0394223\pi\)
\(42\) 3.65180 6.77397i 0.0134163 0.0248868i
\(43\) 263.831 + 456.968i 0.935669 + 1.62063i 0.773436 + 0.633874i \(0.218536\pi\)
0.162233 + 0.986752i \(0.448130\pi\)
\(44\) 251.101 0.860340
\(45\) −60.5687 + 120.650i −0.200646 + 0.399677i
\(46\) −33.9920 −0.108953
\(47\) −77.8637 134.864i −0.241651 0.418551i 0.719534 0.694457i \(-0.244355\pi\)
−0.961185 + 0.275906i \(0.911022\pi\)
\(48\) −172.603 279.782i −0.519023 0.841315i
\(49\) 135.683 235.009i 0.395577 0.685159i
\(50\) 2.18731 3.78853i 0.00618664 0.0107156i
\(51\) −230.251 + 6.71792i −0.632188 + 0.0184450i
\(52\) 107.067 + 185.445i 0.285529 + 0.494551i
\(53\) −141.694 −0.367230 −0.183615 0.982998i \(-0.558780\pi\)
−0.183615 + 0.982998i \(0.558780\pi\)
\(54\) 14.0859 + 20.1065i 0.0354972 + 0.0506695i
\(55\) −157.541 −0.386234
\(56\) −11.8255 20.4823i −0.0282187 0.0488762i
\(57\) −468.536 + 13.6703i −1.08876 + 0.0317661i
\(58\) 0.327546 0.567326i 0.000741533 0.00128437i
\(59\) 246.923 427.683i 0.544857 0.943721i −0.453758 0.891125i \(-0.649917\pi\)
0.998616 0.0525961i \(-0.0167496\pi\)
\(60\) 108.711 + 176.216i 0.233908 + 0.379156i
\(61\) 379.742 + 657.732i 0.797065 + 1.38056i 0.921520 + 0.388331i \(0.126948\pi\)
−0.124455 + 0.992225i \(0.539718\pi\)
\(62\) 44.0373 0.0902055
\(63\) −125.604 190.906i −0.251185 0.381776i
\(64\) −500.280 −0.977108
\(65\) −67.1739 116.349i −0.128183 0.222020i
\(66\) −13.5947 + 25.2178i −0.0253545 + 0.0470317i
\(67\) 271.795 470.763i 0.495598 0.858401i −0.504389 0.863476i \(-0.668282\pi\)
0.999987 + 0.00507574i \(0.00161566\pi\)
\(68\) −176.644 + 305.956i −0.315018 + 0.545627i
\(69\) −478.987 + 888.505i −0.835699 + 1.55019i
\(70\) 3.70255 + 6.41300i 0.00632199 + 0.0109500i
\(71\) −928.207 −1.55152 −0.775760 0.631028i \(-0.782633\pi\)
−0.775760 + 0.631028i \(0.782633\pi\)
\(72\) 75.3203 4.39891i 0.123286 0.00720024i
\(73\) 608.739 0.975993 0.487997 0.872845i \(-0.337728\pi\)
0.487997 + 0.872845i \(0.337728\pi\)
\(74\) −5.44459 9.43030i −0.00855298 0.0148142i
\(75\) −68.2052 110.558i −0.105009 0.170215i
\(76\) −359.452 + 622.589i −0.542526 + 0.939682i
\(77\) 133.338 230.949i 0.197342 0.341806i
\(78\) −24.4207 + 0.712510i −0.0354500 + 0.00103431i
\(79\) −307.420 532.467i −0.437816 0.758319i 0.559705 0.828692i \(-0.310915\pi\)
−0.997521 + 0.0703726i \(0.977581\pi\)
\(80\) 316.330 0.442085
\(81\) 724.044 84.8617i 0.993201 0.116408i
\(82\) 35.7573 0.0481553
\(83\) −537.655 931.246i −0.711028 1.23154i −0.964472 0.264186i \(-0.914897\pi\)
0.253444 0.967350i \(-0.418437\pi\)
\(84\) −350.334 + 10.2215i −0.455055 + 0.0132769i
\(85\) 110.827 191.957i 0.141422 0.244950i
\(86\) −46.1663 + 79.9623i −0.0578865 + 0.100262i
\(87\) −10.2136 16.5559i −0.0125864 0.0204020i
\(88\) 44.0233 + 76.2506i 0.0533284 + 0.0923675i
\(89\) 1505.15 1.79265 0.896324 0.443400i \(-0.146228\pi\)
0.896324 + 0.443400i \(0.146228\pi\)
\(90\) −23.5827 + 1.37730i −0.0276204 + 0.00161311i
\(91\) 227.416 0.261975
\(92\) 774.055 + 1340.70i 0.877183 + 1.51933i
\(93\) 620.536 1151.07i 0.691898 1.28345i
\(94\) 13.6249 23.5991i 0.0149501 0.0258943i
\(95\) 225.521 390.613i 0.243557 0.421853i
\(96\) 82.4190 152.885i 0.0876234 0.162539i
\(97\) 166.369 + 288.160i 0.174147 + 0.301631i 0.939866 0.341544i \(-0.110950\pi\)
−0.765719 + 0.643175i \(0.777617\pi\)
\(98\) 47.4848 0.0489458
\(99\) 467.593 + 710.695i 0.474695 + 0.721490i
\(100\) −199.235 −0.199235
\(101\) 247.493 + 428.670i 0.243826 + 0.422319i 0.961801 0.273750i \(-0.0882640\pi\)
−0.717975 + 0.696069i \(0.754931\pi\)
\(102\) −21.1632 34.3047i −0.0205438 0.0333007i
\(103\) 315.015 545.622i 0.301353 0.521959i −0.675090 0.737736i \(-0.735895\pi\)
0.976443 + 0.215777i \(0.0692284\pi\)
\(104\) −37.5421 + 65.0248i −0.0353972 + 0.0613097i
\(105\) 219.800 6.41300i 0.204289 0.00596043i
\(106\) −12.3971 21.4725i −0.0113596 0.0196754i
\(107\) −1561.00 −1.41035 −0.705175 0.709034i \(-0.749131\pi\)
−0.705175 + 0.709034i \(0.749131\pi\)
\(108\) 472.277 1013.43i 0.420786 0.902939i
\(109\) −936.140 −0.822623 −0.411311 0.911495i \(-0.634929\pi\)
−0.411311 + 0.911495i \(0.634929\pi\)
\(110\) −13.7837 23.8740i −0.0119475 0.0206936i
\(111\) −323.215 + 9.43030i −0.276381 + 0.00806382i
\(112\) −267.733 + 463.727i −0.225878 + 0.391233i
\(113\) −677.490 + 1173.45i −0.564008 + 0.976890i 0.433134 + 0.901330i \(0.357408\pi\)
−0.997141 + 0.0755602i \(0.975925\pi\)
\(114\) −43.0649 69.8065i −0.0353807 0.0573506i
\(115\) −485.643 841.159i −0.393795 0.682074i
\(116\) −29.8351 −0.0238803
\(117\) −325.491 + 648.363i −0.257194 + 0.512318i
\(118\) 86.4153 0.0674167
\(119\) 187.601 + 324.935i 0.144516 + 0.250309i
\(120\) −34.4512 + 63.9058i −0.0262079 + 0.0486148i
\(121\) 169.115 292.915i 0.127058 0.220071i
\(122\) −66.4490 + 115.093i −0.0493115 + 0.0854101i
\(123\) 503.862 934.648i 0.369363 0.685157i
\(124\) −1002.80 1736.90i −0.726244 1.25789i
\(125\) 125.000 0.0894427
\(126\) 17.9407 35.7370i 0.0126848 0.0252675i
\(127\) −1182.37 −0.826126 −0.413063 0.910702i \(-0.635541\pi\)
−0.413063 + 0.910702i \(0.635541\pi\)
\(128\) −177.474 307.393i −0.122552 0.212266i
\(129\) 1439.57 + 2333.48i 0.982535 + 1.59265i
\(130\) 11.7544 20.3592i 0.00793022 0.0137356i
\(131\) −1126.87 + 1951.80i −0.751569 + 1.30176i 0.195494 + 0.980705i \(0.437369\pi\)
−0.947062 + 0.321050i \(0.895964\pi\)
\(132\) 1304.21 38.0522i 0.859974 0.0250910i
\(133\) 381.748 + 661.207i 0.248885 + 0.431082i
\(134\) 95.1199 0.0613217
\(135\) −296.307 + 635.828i −0.188904 + 0.405358i
\(136\) −123.877 −0.0781059
\(137\) −236.856 410.246i −0.147708 0.255837i 0.782672 0.622434i \(-0.213856\pi\)
−0.930380 + 0.366597i \(0.880523\pi\)
\(138\) −176.553 + 5.15119i −0.108907 + 0.00317753i
\(139\) 68.5193 118.679i 0.0418110 0.0724188i −0.844363 0.535772i \(-0.820021\pi\)
0.886174 + 0.463353i \(0.153354\pi\)
\(140\) 168.626 292.069i 0.101797 0.176317i
\(141\) −424.857 688.675i −0.253755 0.411326i
\(142\) −81.2110 140.662i −0.0479935 0.0831272i
\(143\) −846.613 −0.495086
\(144\) −938.889 1427.02i −0.543339 0.825820i
\(145\) 18.7186 0.0107206
\(146\) 53.2600 + 92.2490i 0.0301906 + 0.0522917i
\(147\) 669.115 1241.19i 0.375426 0.696404i
\(148\) −247.965 + 429.487i −0.137720 + 0.238538i
\(149\) 71.5553 123.937i 0.0393426 0.0681433i −0.845684 0.533685i \(-0.820807\pi\)
0.885026 + 0.465541i \(0.154140\pi\)
\(150\) 10.7866 20.0089i 0.00587150 0.0108914i
\(151\) −108.421 187.790i −0.0584314 0.101206i 0.835330 0.549749i \(-0.185277\pi\)
−0.893761 + 0.448543i \(0.851943\pi\)
\(152\) −252.077 −0.134514
\(153\) −1194.89 + 69.7850i −0.631381 + 0.0368744i
\(154\) 46.6644 0.0244177
\(155\) 629.159 + 1089.74i 0.326034 + 0.564708i
\(156\) 584.202 + 946.967i 0.299831 + 0.486013i
\(157\) −674.215 + 1167.78i −0.342728 + 0.593622i −0.984938 0.172906i \(-0.944684\pi\)
0.642211 + 0.766528i \(0.278017\pi\)
\(158\) 53.7938 93.1736i 0.0270861 0.0469145i
\(159\) −735.951 + 21.4725i −0.367074 + 0.0107099i
\(160\) 83.5644 + 144.738i 0.0412897 + 0.0715158i
\(161\) 1644.14 0.804822
\(162\) 76.2083 + 102.298i 0.0369598 + 0.0496127i
\(163\) 1039.85 0.499676 0.249838 0.968288i \(-0.419623\pi\)
0.249838 + 0.968288i \(0.419623\pi\)
\(164\) −814.254 1410.33i −0.387699 0.671514i
\(165\) −818.261 + 23.8740i −0.386070 + 0.0112642i
\(166\) 94.0813 162.954i 0.0439887 0.0761907i
\(167\) 1663.52 2881.31i 0.770822 1.33510i −0.166291 0.986077i \(-0.553179\pi\)
0.937113 0.349026i \(-0.113487\pi\)
\(168\) −64.5248 104.592i −0.0296321 0.0480324i
\(169\) 737.513 + 1277.41i 0.335691 + 0.581434i
\(170\) 38.7859 0.0174985
\(171\) −2431.48 + 142.005i −1.08737 + 0.0635052i
\(172\) 4205.13 1.86418
\(173\) 597.127 + 1034.25i 0.262420 + 0.454525i 0.966885 0.255214i \(-0.0821460\pi\)
−0.704464 + 0.709740i \(0.748813\pi\)
\(174\) 1.61528 2.99630i 0.000703760 0.00130545i
\(175\) −105.796 + 183.245i −0.0456998 + 0.0791543i
\(176\) 996.702 1726.34i 0.426871 0.739362i
\(177\) 1217.69 2258.78i 0.517103 0.959210i
\(178\) 131.689 + 228.092i 0.0554523 + 0.0960463i
\(179\) 2323.70 0.970288 0.485144 0.874434i \(-0.338767\pi\)
0.485144 + 0.874434i \(0.338767\pi\)
\(180\) 591.341 + 898.779i 0.244866 + 0.372173i
\(181\) 2527.12 1.03779 0.518893 0.854839i \(-0.326344\pi\)
0.518893 + 0.854839i \(0.326344\pi\)
\(182\) 19.8972 + 34.4629i 0.00810372 + 0.0140361i
\(183\) 2072.03 + 3358.68i 0.836988 + 1.35672i
\(184\) −271.416 + 470.106i −0.108745 + 0.188352i
\(185\) 155.573 269.461i 0.0618269 0.107087i
\(186\) 228.727 6.67346i 0.0901671 0.00263076i
\(187\) −698.391 1209.65i −0.273109 0.473039i
\(188\) −1241.05 −0.481452
\(189\) −681.311 972.520i −0.262212 0.374288i
\(190\) 78.9252 0.0301360
\(191\) −1194.43 2068.82i −0.452493 0.783741i 0.546047 0.837754i \(-0.316132\pi\)
−0.998540 + 0.0540134i \(0.982799\pi\)
\(192\) −2598.42 + 75.8129i −0.976693 + 0.0284965i
\(193\) −1773.99 + 3072.64i −0.661629 + 1.14597i 0.318559 + 0.947903i \(0.396801\pi\)
−0.980188 + 0.198072i \(0.936532\pi\)
\(194\) −29.1120 + 50.4235i −0.0107738 + 0.0186608i
\(195\) −366.529 594.128i −0.134604 0.218187i
\(196\) −1081.31 1872.88i −0.394063 0.682536i
\(197\) −1239.26 −0.448192 −0.224096 0.974567i \(-0.571943\pi\)
−0.224096 + 0.974567i \(0.571943\pi\)
\(198\) −66.7887 + 133.040i −0.0239720 + 0.0477512i
\(199\) 516.657 0.184044 0.0920222 0.995757i \(-0.470667\pi\)
0.0920222 + 0.995757i \(0.470667\pi\)
\(200\) −34.9299 60.5004i −0.0123496 0.0213901i
\(201\) 1340.35 2486.30i 0.470353 0.872489i
\(202\) −43.3074 + 75.0107i −0.0150847 + 0.0261274i
\(203\) −15.8429 + 27.4406i −0.00547759 + 0.00948746i
\(204\) −871.114 + 1615.89i −0.298971 + 0.554583i
\(205\) 510.864 + 884.843i 0.174050 + 0.301464i
\(206\) 110.246 0.0372873
\(207\) −2353.18 + 4687.43i −0.790133 + 1.57391i
\(208\) 1699.93 0.566678
\(209\) −1421.15 2461.51i −0.470350 0.814670i
\(210\) 20.2027 + 32.7477i 0.00663865 + 0.0107610i
\(211\) 8.92159 15.4527i 0.00291084 0.00504173i −0.864566 0.502519i \(-0.832407\pi\)
0.867477 + 0.497477i \(0.165740\pi\)
\(212\) −564.607 + 977.928i −0.182912 + 0.316813i
\(213\) −4821.05 + 140.662i −1.55086 + 0.0452487i
\(214\) −136.575 236.555i −0.0436266 0.0755635i
\(215\) −2638.31 −0.836888
\(216\) 390.543 34.2618i 0.123024 0.0107927i
\(217\) −2130.01 −0.666334
\(218\) −81.9050 141.864i −0.0254464 0.0440744i
\(219\) 3161.76 92.2490i 0.975578 0.0284640i
\(220\) −627.753 + 1087.30i −0.192378 + 0.333208i
\(221\) 595.573 1031.56i 0.181279 0.313984i
\(222\) −29.7079 48.1554i −0.00898138 0.0145584i
\(223\) −494.777 856.978i −0.148577 0.257343i 0.782125 0.623122i \(-0.214136\pi\)
−0.930702 + 0.365779i \(0.880803\pi\)
\(224\) −282.906 −0.0843860
\(225\) −371.008 563.895i −0.109928 0.167080i
\(226\) −237.101 −0.0697863
\(227\) 1713.57 + 2967.98i 0.501028 + 0.867806i 0.999999 + 0.00118754i \(0.000378004\pi\)
−0.498971 + 0.866619i \(0.666289\pi\)
\(228\) −1772.62 + 3288.16i −0.514890 + 0.955104i
\(229\) −549.805 + 952.290i −0.158656 + 0.274800i −0.934384 0.356267i \(-0.884049\pi\)
0.775728 + 0.631067i \(0.217383\pi\)
\(230\) 84.9801 147.190i 0.0243627 0.0421974i
\(231\) 657.554 1219.74i 0.187290 0.347416i
\(232\) −5.23071 9.05985i −0.00148023 0.00256383i
\(233\) 4459.91 1.25399 0.626993 0.779025i \(-0.284285\pi\)
0.626993 + 0.779025i \(0.284285\pi\)
\(234\) −126.732 + 7.40147i −0.0354047 + 0.00206773i
\(235\) 778.637 0.216139
\(236\) −1967.82 3408.37i −0.542772 0.940109i
\(237\) −1677.41 2719.02i −0.459745 0.745228i
\(238\) −32.8273 + 56.8586i −0.00894067 + 0.0154857i
\(239\) −3272.23 + 5667.66i −0.885618 + 1.53394i −0.0406148 + 0.999175i \(0.512932\pi\)
−0.845003 + 0.534761i \(0.820402\pi\)
\(240\) 1643.00 47.9371i 0.441897 0.0128930i
\(241\) 105.162 + 182.147i 0.0281083 + 0.0486851i 0.879737 0.475460i \(-0.157718\pi\)
−0.851629 + 0.524145i \(0.824385\pi\)
\(242\) 59.1849 0.0157213
\(243\) 3747.78 550.489i 0.989384 0.145325i
\(244\) 6052.61 1.58803
\(245\) 678.414 + 1175.05i 0.176907 + 0.306412i
\(246\) 185.722 5.41871i 0.0481349 0.00140441i
\(247\) 1211.93 2099.12i 0.312199 0.540744i
\(248\) 351.624 609.031i 0.0900329 0.155942i
\(249\) −2933.67 4755.36i −0.746642 1.21028i
\(250\) 10.9365 + 18.9426i 0.00276675 + 0.00479215i
\(251\) 816.143 0.205237 0.102618 0.994721i \(-0.467278\pi\)
0.102618 + 0.994721i \(0.467278\pi\)
\(252\) −1818.07 + 106.180i −0.454474 + 0.0265425i
\(253\) −6120.71 −1.52097
\(254\) −103.448 179.177i −0.0255547 0.0442621i
\(255\) 546.538 1013.81i 0.134218 0.248970i
\(256\) −1970.06 + 3412.25i −0.480972 + 0.833069i
\(257\) 2086.17 3613.36i 0.506350 0.877023i −0.493623 0.869676i \(-0.664328\pi\)
0.999973 0.00734758i \(-0.00233883\pi\)
\(258\) −227.667 + 422.316i −0.0549378 + 0.101908i
\(259\) 263.346 + 456.128i 0.0631795 + 0.109430i
\(260\) −1070.67 −0.255385
\(261\) −55.5579 84.4425i −0.0131760 0.0200263i
\(262\) −394.371 −0.0929937
\(263\) 1408.52 + 2439.64i 0.330241 + 0.571994i 0.982559 0.185951i \(-0.0595367\pi\)
−0.652318 + 0.757945i \(0.726203\pi\)
\(264\) 240.209 + 389.370i 0.0559995 + 0.0907729i
\(265\) 354.235 613.554i 0.0821151 0.142228i
\(266\) −66.8001 + 115.701i −0.0153976 + 0.0266695i
\(267\) 7817.66 228.092i 1.79189 0.0522810i
\(268\) −2166.04 3751.69i −0.493701 0.855115i
\(269\) −102.610 −0.0232573 −0.0116287 0.999932i \(-0.503702\pi\)
−0.0116287 + 0.999932i \(0.503702\pi\)
\(270\) −122.279 + 10.7274i −0.0275616 + 0.00241795i
\(271\) −3337.27 −0.748061 −0.374031 0.927416i \(-0.622025\pi\)
−0.374031 + 0.927416i \(0.622025\pi\)
\(272\) 1402.31 + 2428.88i 0.312602 + 0.541443i
\(273\) 1181.19 34.4629i 0.261863 0.00764026i
\(274\) 41.4461 71.7867i 0.00913814 0.0158277i
\(275\) 393.853 682.174i 0.0863645 0.149588i
\(276\) 4223.57 + 6846.23i 0.921120 + 1.49310i
\(277\) −316.941 548.959i −0.0687479 0.119075i 0.829603 0.558354i \(-0.188567\pi\)
−0.898350 + 0.439280i \(0.855234\pi\)
\(278\) 23.9796 0.00517339
\(279\) 3048.59 6072.65i 0.654173 1.30308i
\(280\) 118.255 0.0252396
\(281\) 3101.20 + 5371.44i 0.658370 + 1.14033i 0.981037 + 0.193818i \(0.0620872\pi\)
−0.322667 + 0.946513i \(0.604579\pi\)
\(282\) 67.1909 124.637i 0.0141885 0.0263193i
\(283\) 3740.06 6477.98i 0.785596 1.36069i −0.143047 0.989716i \(-0.545690\pi\)
0.928642 0.370976i \(-0.120977\pi\)
\(284\) −3698.62 + 6406.19i −0.772791 + 1.33851i
\(285\) 1112.15 2063.00i 0.231150 0.428777i
\(286\) −74.0722 128.297i −0.0153146 0.0265257i
\(287\) −1729.52 −0.355716
\(288\) 404.911 806.564i 0.0828459 0.165025i
\(289\) −2947.79 −0.599998
\(290\) 1.63773 + 2.83663i 0.000331623 + 0.000574389i
\(291\) 907.780 + 1471.47i 0.182869 + 0.296424i
\(292\) 2425.64 4201.33i 0.486129 0.842000i
\(293\) 2418.26 4188.54i 0.482171 0.835144i −0.517620 0.855611i \(-0.673182\pi\)
0.999791 + 0.0204666i \(0.00651519\pi\)
\(294\) 246.633 7.19590i 0.0489250 0.00142746i
\(295\) 1234.61 + 2138.41i 0.243668 + 0.422045i
\(296\) −173.893 −0.0341464
\(297\) 2536.35 + 3620.45i 0.495535 + 0.707339i
\(298\) 25.0422 0.00486796
\(299\) −2609.81 4520.31i −0.504779 0.874303i
\(300\) −1034.81 + 30.1922i −0.199150 + 0.00581050i
\(301\) 2232.99 3867.65i 0.427599 0.740623i
\(302\) 18.9719 32.8604i 0.00361494 0.00626126i
\(303\) 1350.42 + 2188.98i 0.256039 + 0.415029i
\(304\) 2853.56 + 4942.51i 0.538365 + 0.932475i
\(305\) −3797.42 −0.712916
\(306\) −115.119 174.970i −0.0215063 0.0326874i
\(307\) −5611.86 −1.04328 −0.521638 0.853167i \(-0.674679\pi\)
−0.521638 + 0.853167i \(0.674679\pi\)
\(308\) −1062.63 1840.52i −0.196587 0.340498i
\(309\) 1553.49 2881.67i 0.286002 0.530525i
\(310\) −110.093 + 190.687i −0.0201706 + 0.0349364i
\(311\) −5460.70 + 9458.21i −0.995653 + 1.72452i −0.417163 + 0.908831i \(0.636976\pi\)
−0.578489 + 0.815690i \(0.696358\pi\)
\(312\) −185.138 + 343.424i −0.0335941 + 0.0623159i
\(313\) −2490.36 4313.44i −0.449724 0.778946i 0.548643 0.836056i \(-0.315144\pi\)
−0.998368 + 0.0571109i \(0.981811\pi\)
\(314\) −235.955 −0.0424067
\(315\) 1140.66 66.6175i 0.204028 0.0119158i
\(316\) −4899.89 −0.872280
\(317\) 1878.06 + 3252.90i 0.332752 + 0.576344i 0.983050 0.183335i \(-0.0586894\pi\)
−0.650298 + 0.759679i \(0.725356\pi\)
\(318\) −67.6440 109.648i −0.0119286 0.0193357i
\(319\) 58.9789 102.154i 0.0103517 0.0179296i
\(320\) 1250.70 2166.27i 0.218488 0.378432i
\(321\) −8107.73 + 236.555i −1.40975 + 0.0411316i
\(322\) 143.849 + 249.155i 0.0248957 + 0.0431206i
\(323\) 3998.99 0.688885
\(324\) 2299.40 5335.27i 0.394273 0.914827i
\(325\) 671.739 0.114650
\(326\) 90.9788 + 157.580i 0.0154566 + 0.0267716i
\(327\) −4862.25 + 141.864i −0.822273 + 0.0239911i
\(328\) 285.511 494.520i 0.0480632 0.0832479i
\(329\) −659.016 + 1141.45i −0.110434 + 0.191277i
\(330\) −75.2094 121.911i −0.0125459 0.0203364i
\(331\) 453.477 + 785.445i 0.0753031 + 0.130429i 0.901218 0.433366i \(-0.142674\pi\)
−0.825915 + 0.563795i \(0.809341\pi\)
\(332\) −8569.55 −1.41661
\(333\) −1677.33 + 97.9609i −0.276028 + 0.0161208i
\(334\) 582.182 0.0953759
\(335\) 1358.98 + 2353.81i 0.221638 + 0.383888i
\(336\) −1320.32 + 2449.14i −0.214372 + 0.397654i
\(337\) −4939.35 + 8555.20i −0.798408 + 1.38288i 0.122245 + 0.992500i \(0.460991\pi\)
−0.920653 + 0.390383i \(0.872343\pi\)
\(338\) −129.053 + 223.527i −0.0207680 + 0.0359712i
\(339\) −3341.02 + 6197.48i −0.535278 + 0.992923i
\(340\) −883.220 1529.78i −0.140880 0.244012i
\(341\) 7929.49 1.25925
\(342\) −234.255 356.045i −0.0370382 0.0562944i
\(343\) −5199.81 −0.818553
\(344\) 737.247 + 1276.95i 0.115551 + 0.200141i
\(345\) −2649.87 4295.34i −0.413520 0.670299i
\(346\) −104.488 + 180.979i −0.0162350 + 0.0281199i
\(347\) 1754.86 3039.50i 0.271486 0.470228i −0.697757 0.716335i \(-0.745818\pi\)
0.969243 + 0.246107i \(0.0791516\pi\)
\(348\) −154.962 + 4.52124i −0.0238702 + 0.000696448i
\(349\) 5196.48 + 9000.57i 0.797024 + 1.38049i 0.921546 + 0.388269i \(0.126927\pi\)
−0.124522 + 0.992217i \(0.539740\pi\)
\(350\) −37.0255 −0.00565456
\(351\) −1592.33 + 3416.88i −0.242143 + 0.519600i
\(352\) 1053.19 0.159475
\(353\) −4042.70 7002.16i −0.609550 1.05577i −0.991315 0.131512i \(-0.958017\pi\)
0.381765 0.924259i \(-0.375316\pi\)
\(354\) 448.836 13.0955i 0.0673881 0.00196615i
\(355\) 2320.52 4019.26i 0.346930 0.600901i
\(356\) 5997.56 10388.1i 0.892893 1.54654i
\(357\) 1023.63 + 1659.26i 0.151754 + 0.245987i
\(358\) 203.306 + 352.136i 0.0300141 + 0.0519860i
\(359\) −8189.49 −1.20397 −0.601984 0.798508i \(-0.705623\pi\)
−0.601984 + 0.798508i \(0.705623\pi\)
\(360\) −169.253 + 337.144i −0.0247789 + 0.0493585i
\(361\) 1278.52 0.186400
\(362\) 221.103 + 382.962i 0.0321020 + 0.0556024i
\(363\) 833.983 1547.01i 0.120586 0.223683i
\(364\) 906.184 1569.56i 0.130486 0.226008i
\(365\) −1521.85 + 2635.92i −0.218239 + 0.378001i
\(366\) −327.691 + 607.856i −0.0467996 + 0.0868119i
\(367\) 4497.33 + 7789.60i 0.639669 + 1.10794i 0.985505 + 0.169645i \(0.0542621\pi\)
−0.345836 + 0.938295i \(0.612405\pi\)
\(368\) 12289.9 1.74091
\(369\) 2475.39 4930.86i 0.349224 0.695638i
\(370\) 54.4459 0.00765001
\(371\) 599.629 + 1038.59i 0.0839116 + 0.145339i
\(372\) −5471.71 8869.42i −0.762621 1.23618i
\(373\) 464.934 805.288i 0.0645398 0.111786i −0.831950 0.554851i \(-0.812775\pi\)
0.896490 + 0.443064i \(0.146109\pi\)
\(374\) 122.208 211.670i 0.0168963 0.0292652i
\(375\) 649.243 18.9426i 0.0894047 0.00260852i
\(376\) −217.582 376.863i −0.0298429 0.0516894i
\(377\) 100.592 0.0137420
\(378\) 87.7673 188.335i 0.0119425 0.0256267i
\(379\) 3449.71 0.467546 0.233773 0.972291i \(-0.424893\pi\)
0.233773 + 0.972291i \(0.424893\pi\)
\(380\) −1797.26 3112.94i −0.242625 0.420238i
\(381\) −6141.14 + 179.177i −0.825775 + 0.0240932i
\(382\) 209.007 362.012i 0.0279941 0.0484872i
\(383\) 2673.07 4629.89i 0.356625 0.617692i −0.630770 0.775970i \(-0.717261\pi\)
0.987395 + 0.158278i \(0.0505941\pi\)
\(384\) −968.370 1569.69i −0.128690 0.208601i
\(385\) 666.692 + 1154.75i 0.0882540 + 0.152860i
\(386\) −620.841 −0.0818652
\(387\) 7830.66 + 11901.8i 1.02857 + 1.56332i
\(388\) 2651.72 0.346960
\(389\) −3861.72 6688.70i −0.503334 0.871801i −0.999993 0.00385448i \(-0.998773\pi\)
0.496658 0.867946i \(-0.334560\pi\)
\(390\) 57.9664 107.526i 0.00752627 0.0139610i
\(391\) 4305.78 7457.83i 0.556912 0.964600i
\(392\) 379.151 656.709i 0.0488521 0.0846144i
\(393\) −5557.14 + 10308.3i −0.713284 + 1.32312i
\(394\) −108.426 187.799i −0.0138640 0.0240132i
\(395\) 3074.20 0.391594
\(396\) 6768.20 395.282i 0.858876 0.0501607i
\(397\) 7125.03 0.900744 0.450372 0.892841i \(-0.351291\pi\)
0.450372 + 0.892841i \(0.351291\pi\)
\(398\) 45.2035 + 78.2948i 0.00569308 + 0.00986071i
\(399\) 2082.98 + 3376.42i 0.261352 + 0.423640i
\(400\) −790.826 + 1369.75i −0.0988532 + 0.171219i
\(401\) 896.547 1552.86i 0.111649 0.193382i −0.804786 0.593565i \(-0.797720\pi\)
0.916435 + 0.400183i \(0.131053\pi\)
\(402\) 494.047 14.4146i 0.0612956 0.00178839i
\(403\) 3381.05 + 5856.15i 0.417921 + 0.723860i
\(404\) 3944.73 0.485786
\(405\) −1442.65 + 3347.36i −0.177002 + 0.410695i
\(406\) −5.54451 −0.000677757
\(407\) −980.369 1698.05i −0.119398 0.206804i
\(408\) −643.412 + 18.7725i −0.0780727 + 0.00227789i
\(409\) −1569.87 + 2719.09i −0.189792 + 0.328729i −0.945181 0.326548i \(-0.894115\pi\)
0.755389 + 0.655277i \(0.227448\pi\)
\(410\) −89.3934 + 154.834i −0.0107679 + 0.0186505i
\(411\) −1292.38 2094.90i −0.155106 0.251420i
\(412\) −2510.48 4348.27i −0.300200 0.519961i
\(413\) −4179.77 −0.497997
\(414\) −916.224 + 53.5100i −0.108768 + 0.00635235i
\(415\) 5376.55 0.635962
\(416\) 449.068 + 777.808i 0.0529263 + 0.0916711i
\(417\) 337.900 626.795i 0.0396812 0.0736074i
\(418\) 248.680 430.726i 0.0290989 0.0504007i
\(419\) −1228.70 + 2128.17i −0.143260 + 0.248133i −0.928722 0.370776i \(-0.879092\pi\)
0.785463 + 0.618909i \(0.212425\pi\)
\(420\) 831.575 1542.55i 0.0966112 0.179211i
\(421\) 1339.33 + 2319.80i 0.155048 + 0.268551i 0.933076 0.359678i \(-0.117113\pi\)
−0.778029 + 0.628229i \(0.783780\pi\)
\(422\) 3.12228 0.000360167
\(423\) −2311.04 3512.56i −0.265643 0.403750i
\(424\) −395.949 −0.0453514
\(425\) 554.134 + 959.787i 0.0632457 + 0.109545i
\(426\) −443.121 718.281i −0.0503974 0.0816921i
\(427\) 3214.03 5566.86i 0.364257 0.630911i
\(428\) −6220.09 + 10773.5i −0.702476 + 1.21672i
\(429\) −4397.26 + 128.297i −0.494876 + 0.0144388i
\(430\) −230.831 399.812i −0.0258876 0.0448387i
\(431\) −9472.42 −1.05863 −0.529316 0.848425i \(-0.677551\pi\)
−0.529316 + 0.848425i \(0.677551\pi\)
\(432\) −5092.79 7269.57i −0.567192 0.809623i
\(433\) −4238.21 −0.470382 −0.235191 0.971949i \(-0.575572\pi\)
−0.235191 + 0.971949i \(0.575572\pi\)
\(434\) −186.360 322.784i −0.0206119 0.0357008i
\(435\) 97.2231 2.83663i 0.0107161 0.000312658i
\(436\) −3730.23 + 6460.94i −0.409737 + 0.709686i
\(437\) 8761.80 15175.9i 0.959116 1.66124i
\(438\) 290.609 + 471.065i 0.0317028 + 0.0513889i
\(439\) −2429.47 4207.96i −0.264128 0.457483i 0.703207 0.710985i \(-0.251751\pi\)
−0.967335 + 0.253503i \(0.918417\pi\)
\(440\) −440.233 −0.0476984
\(441\) 3287.25 6548.05i 0.354957 0.707057i
\(442\) 208.432 0.0224301
\(443\) −1167.88 2022.82i −0.125254 0.216946i 0.796578 0.604535i \(-0.206641\pi\)
−0.921832 + 0.387589i \(0.873308\pi\)
\(444\) −1222.83 + 2268.31i −0.130705 + 0.242453i
\(445\) −3762.88 + 6517.49i −0.400848 + 0.694289i
\(446\) 86.5783 149.958i 0.00919193 0.0159209i
\(447\) 352.873 654.568i 0.0373385 0.0692617i
\(448\) 2117.11 + 3666.94i 0.223268 + 0.386712i
\(449\) 13290.5 1.39692 0.698460 0.715649i \(-0.253869\pi\)
0.698460 + 0.715649i \(0.253869\pi\)
\(450\) 52.9930 105.559i 0.00555136 0.0110580i
\(451\) 6438.58 0.672241
\(452\) 5399.17 + 9351.64i 0.561849 + 0.973151i
\(453\) −591.588 958.941i −0.0613582 0.0994591i
\(454\) −299.848 + 519.351i −0.0309968 + 0.0536880i
\(455\) −568.541 + 984.742i −0.0585794 + 0.101462i
\(456\) −1309.28 + 38.2001i −0.134457 + 0.00392299i
\(457\) −2587.31 4481.35i −0.264834 0.458706i 0.702686 0.711500i \(-0.251984\pi\)
−0.967520 + 0.252794i \(0.918650\pi\)
\(458\) −192.415 −0.0196309
\(459\) −6195.63 + 543.534i −0.630037 + 0.0552724i
\(460\) −7740.55 −0.784576
\(461\) −3170.44 5491.37i −0.320309 0.554791i 0.660243 0.751052i \(-0.270453\pi\)
−0.980552 + 0.196261i \(0.937120\pi\)
\(462\) 242.372 7.07157i 0.0244073 0.000712119i
\(463\) −1591.40 + 2756.38i −0.159737 + 0.276673i −0.934774 0.355243i \(-0.884398\pi\)
0.775036 + 0.631916i \(0.217731\pi\)
\(464\) −118.425 + 205.118i −0.0118486 + 0.0205223i
\(465\) 3432.96 + 5564.68i 0.342365 + 0.554959i
\(466\) 390.208 + 675.860i 0.0387898 + 0.0671859i
\(467\) −8576.23 −0.849808 −0.424904 0.905238i \(-0.639692\pi\)
−0.424904 + 0.905238i \(0.639692\pi\)
\(468\) 3177.82 + 4829.96i 0.313877 + 0.477062i
\(469\) −4600.79 −0.452974
\(470\) 68.1247 + 117.995i 0.00668587 + 0.0115803i
\(471\) −3324.87 + 6167.53i −0.325269 + 0.603365i
\(472\) 690.000 1195.11i 0.0672877 0.116546i
\(473\) −8312.84 + 14398.3i −0.808086 + 1.39965i
\(474\) 265.282 492.090i 0.0257064 0.0476845i
\(475\) 1127.60 + 1953.06i 0.108922 + 0.188658i
\(476\) 2990.13 0.287925
\(477\) −3819.23 + 223.054i −0.366605 + 0.0214107i
\(478\) −1145.18 −0.109580
\(479\) −1458.82 2526.76i −0.139155 0.241024i 0.788022 0.615647i \(-0.211105\pi\)
−0.927177 + 0.374623i \(0.877772\pi\)
\(480\) 455.962 + 739.096i 0.0433578 + 0.0702812i
\(481\) 836.037 1448.06i 0.0792516 0.137268i
\(482\) −18.4018 + 31.8729i −0.00173896 + 0.00301197i
\(483\) 8539.56 249.155i 0.804479 0.0234719i
\(484\) −1347.74 2334.35i −0.126572 0.219229i
\(485\) −1663.69 −0.155761
\(486\) 411.324 + 519.779i 0.0383910 + 0.0485137i
\(487\) −14061.0 −1.30834 −0.654172 0.756346i \(-0.726983\pi\)
−0.654172 + 0.756346i \(0.726983\pi\)
\(488\) 1061.15 + 1837.96i 0.0984343 + 0.170493i
\(489\) 5400.92 157.580i 0.499464 0.0145726i
\(490\) −118.712 + 205.615i −0.0109446 + 0.0189566i
\(491\) 466.331 807.709i 0.0428620 0.0742391i −0.843799 0.536660i \(-0.819686\pi\)
0.886661 + 0.462421i \(0.153019\pi\)
\(492\) −4442.91 7201.78i −0.407118 0.659921i
\(493\) 82.9806 + 143.727i 0.00758065 + 0.0131301i
\(494\) 424.137 0.0386292
\(495\) −4246.38 + 248.000i −0.385577 + 0.0225187i
\(496\) −15921.8 −1.44135
\(497\) 3928.04 + 6803.57i 0.354521 + 0.614048i
\(498\) 463.959 860.629i 0.0417480 0.0774412i
\(499\) 7215.39 12497.4i 0.647305 1.12117i −0.336459 0.941698i \(-0.609229\pi\)
0.983764 0.179467i \(-0.0574374\pi\)
\(500\) 498.086 862.711i 0.0445502 0.0771632i
\(501\) 8203.60 15217.4i 0.731557 1.35701i
\(502\) 71.4062 + 123.679i 0.00634864 + 0.0109962i
\(503\) −3230.55 −0.286368 −0.143184 0.989696i \(-0.545734\pi\)
−0.143184 + 0.989696i \(0.545734\pi\)
\(504\) −350.988 533.467i −0.0310203 0.0471478i
\(505\) −2474.93 −0.218085
\(506\) −535.515 927.539i −0.0470485 0.0814904i
\(507\) 4024.18 + 6523.03i 0.352505 + 0.571397i
\(508\) −4711.36 + 8160.32i −0.411482 + 0.712708i
\(509\) 180.378 312.424i 0.0157075 0.0272062i −0.858065 0.513541i \(-0.828333\pi\)
0.873772 + 0.486335i \(0.161667\pi\)
\(510\) 201.452 5.87766i 0.0174911 0.000510328i
\(511\) −2576.10 4461.93i −0.223013 0.386270i
\(512\) −3529.04 −0.304615
\(513\) −12607.4 + 1106.03i −1.08505 + 0.0951903i
\(514\) 730.096 0.0626521
\(515\) 1575.08 + 2728.11i 0.134769 + 0.233427i
\(516\) 21841.2 637.250i 1.86338 0.0543670i
\(517\) 2453.35 4249.33i 0.208701 0.361480i
\(518\) −46.0814 + 79.8154i −0.00390869 + 0.00677005i
\(519\) 3258.18 + 5281.37i 0.275565 + 0.446679i
\(520\) −187.710 325.124i −0.0158301 0.0274185i
\(521\) −11698.8 −0.983747 −0.491873 0.870667i \(-0.663688\pi\)
−0.491873 + 0.870667i \(0.663688\pi\)
\(522\) 7.93562 15.8074i 0.000665388 0.00132542i
\(523\) 18557.3 1.55154 0.775770 0.631015i \(-0.217362\pi\)
0.775770 + 0.631015i \(0.217362\pi\)
\(524\) 8980.49 + 15554.7i 0.748692 + 1.29677i
\(525\) −521.731 + 967.795i −0.0433719 + 0.0804534i
\(526\) −246.470 + 426.899i −0.0204308 + 0.0353872i
\(527\) −5578.21 + 9661.75i −0.461083 + 0.798619i
\(528\) 4915.20 9117.54i 0.405126 0.751496i
\(529\) −12784.5 22143.3i −1.05075 1.81995i
\(530\) 123.971 0.0101603
\(531\) 5982.32 11916.5i 0.488909 0.973883i
\(532\) 6084.59 0.495866
\(533\) 2745.34 + 4755.07i 0.223103 + 0.386426i
\(534\) 718.551 + 1164.74i 0.0582298 + 0.0943882i
\(535\) 3902.50 6759.32i 0.315364 0.546226i
\(536\) 759.503 1315.50i 0.0612044 0.106009i
\(537\) 12069.2 352.136i 0.969875 0.0282976i
\(538\) −8.97756 15.5496i −0.000719424 0.00124608i
\(539\) 8550.26 0.683276
\(540\) 3207.59 + 4578.60i 0.255616 + 0.364873i
\(541\) 22755.3 1.80837 0.904185 0.427140i \(-0.140479\pi\)
0.904185 + 0.427140i \(0.140479\pi\)
\(542\) −291.985 505.733i −0.0231399 0.0400795i
\(543\) 13125.7 382.962i 1.03734 0.0302661i
\(544\) −740.893 + 1283.26i −0.0583925 + 0.101139i
\(545\) 2340.35 4053.60i 0.183944 0.318601i
\(546\) 108.567 + 175.983i 0.00850962 + 0.0137937i
\(547\) −2899.05 5021.30i −0.226608 0.392496i 0.730193 0.683241i \(-0.239430\pi\)
−0.956801 + 0.290745i \(0.906097\pi\)
\(548\) −3775.18 −0.294284
\(549\) 11271.0 + 17130.8i 0.876200 + 1.33174i
\(550\) 137.837 0.0106861
\(551\) 168.857 + 292.468i 0.0130554 + 0.0226127i
\(552\) −1338.48 + 2482.84i −0.103205 + 0.191443i
\(553\) −2601.92 + 4506.65i −0.200081 + 0.346550i
\(554\) 55.4599 96.0593i 0.00425318 0.00736673i
\(555\) 767.204 1423.14i 0.0586775 0.108845i
\(556\) −546.056 945.797i −0.0416510 0.0721416i
\(557\) 15740.3 1.19738 0.598688 0.800982i \(-0.295689\pi\)
0.598688 + 0.800982i \(0.295689\pi\)
\(558\) 1186.98 69.3231i 0.0900521 0.00525929i
\(559\) −14178.0 −1.07275
\(560\) −1338.66 2318.64i −0.101016 0.174965i
\(561\) −3810.72 6177.01i −0.286789 0.464873i
\(562\) −542.662 + 939.919i −0.0407310 + 0.0705482i
\(563\) −1909.56 + 3307.45i −0.142946 + 0.247589i −0.928605 0.371071i \(-0.878991\pi\)
0.785659 + 0.618660i \(0.212324\pi\)
\(564\) −6445.94 + 188.070i −0.481247 + 0.0140411i
\(565\) −3387.45 5867.23i −0.252232 0.436878i
\(566\) 1308.91 0.0972040
\(567\) −3686.07 4947.97i −0.273016 0.366482i
\(568\) −2593.78 −0.191607
\(569\) −4445.56 7699.93i −0.327535 0.567308i 0.654487 0.756073i \(-0.272885\pi\)
−0.982022 + 0.188766i \(0.939551\pi\)
\(570\) 409.933 11.9604i 0.0301232 0.000878889i
\(571\) −4193.31 + 7263.03i −0.307329 + 0.532309i −0.977777 0.209647i \(-0.932768\pi\)
0.670448 + 0.741956i \(0.266102\pi\)
\(572\) −3373.49 + 5843.06i −0.246596 + 0.427116i
\(573\) −6517.33 10564.3i −0.475158 0.770211i
\(574\) −151.320 262.094i −0.0110034 0.0190585i
\(575\) 4856.43 0.352221
\(576\) −13484.6 + 787.536i −0.975446 + 0.0569687i
\(577\) 16922.3 1.22095 0.610473 0.792037i \(-0.290979\pi\)
0.610473 + 0.792037i \(0.290979\pi\)
\(578\) −257.909 446.711i −0.0185599 0.0321466i
\(579\) −8748.35 + 16227.9i −0.627926 + 1.16478i
\(580\) 74.5877 129.190i 0.00533980 0.00924880i
\(581\) −4550.56 + 7881.80i −0.324938 + 0.562809i
\(582\) −143.565 + 266.309i −0.0102250 + 0.0189671i
\(583\) −2232.27 3866.40i −0.158578 0.274666i
\(584\) 1701.06 0.120531
\(585\) −1993.77 3030.32i −0.140909 0.214168i
\(586\) 846.315 0.0596603
\(587\) −7619.29 13197.0i −0.535744 0.927936i −0.999127 0.0417777i \(-0.986698\pi\)
0.463383 0.886158i \(-0.346635\pi\)
\(588\) −5900.07 9563.77i −0.413800 0.670754i
\(589\) −11351.1 + 19660.6i −0.794079 + 1.37539i
\(590\) −216.038 + 374.189i −0.0150748 + 0.0261104i
\(591\) −6436.66 + 187.799i −0.448002 + 0.0130711i
\(592\) 1968.50 + 3409.55i 0.136664 + 0.236709i
\(593\) −16960.2 −1.17449 −0.587245 0.809409i \(-0.699787\pi\)
−0.587245 + 0.809409i \(0.699787\pi\)
\(594\) −326.735 + 701.123i −0.0225692 + 0.0484300i
\(595\) −1876.01 −0.129259
\(596\) −570.252 987.705i −0.0391920 0.0678825i
\(597\) 2683.49 78.2948i 0.183966 0.00536749i
\(598\) 456.676 790.986i 0.0312289 0.0540900i
\(599\) 12456.1 21574.5i 0.849651 1.47164i −0.0318690 0.999492i \(-0.510146\pi\)
0.881520 0.472147i \(-0.156521\pi\)
\(600\) −190.592 308.942i −0.0129682 0.0210209i
\(601\) 2175.63 + 3768.31i 0.147664 + 0.255761i 0.930364 0.366638i \(-0.119491\pi\)
−0.782700 + 0.622399i \(0.786158\pi\)
\(602\) 781.476 0.0529080
\(603\) 6584.91 13116.8i 0.444707 0.885835i
\(604\) −1728.09 −0.116416
\(605\) 845.573 + 1464.58i 0.0568222 + 0.0984190i
\(606\) −213.569 + 396.164i −0.0143163 + 0.0265562i
\(607\) −13911.8 + 24096.0i −0.930254 + 1.61125i −0.147369 + 0.989082i \(0.547081\pi\)
−0.782885 + 0.622166i \(0.786253\pi\)
\(608\) −1507.64 + 2611.31i −0.100564 + 0.174182i
\(609\) −78.1285 + 144.926i −0.00519856 + 0.00964317i
\(610\) −332.245 575.465i −0.0220528 0.0381965i
\(611\) 4184.33 0.277054
\(612\) −4279.64 + 8524.84i −0.282670 + 0.563066i
\(613\) 20034.6 1.32005 0.660024 0.751244i \(-0.270546\pi\)
0.660024 + 0.751244i \(0.270546\pi\)
\(614\) −490.994 850.427i −0.0322719 0.0558965i
\(615\) 2787.49 + 4518.40i 0.182768 + 0.296260i
\(616\) 372.600 645.363i 0.0243709 0.0422117i
\(617\) −3776.95 + 6541.86i −0.246441 + 0.426848i −0.962536 0.271155i \(-0.912595\pi\)
0.716095 + 0.698003i \(0.245928\pi\)
\(618\) 572.609 16.7067i 0.0372714 0.00108745i
\(619\) −6192.54 10725.8i −0.402099 0.696456i 0.591880 0.806026i \(-0.298386\pi\)
−0.993979 + 0.109570i \(0.965053\pi\)
\(620\) 10028.0 0.649573
\(621\) −11512.0 + 24702.8i −0.743896 + 1.59628i
\(622\) −1911.08 −0.123195
\(623\) −6369.58 11032.4i −0.409618 0.709479i
\(624\) 8829.35 257.610i 0.566437 0.0165267i
\(625\) −312.500 + 541.266i −0.0200000 + 0.0346410i
\(626\) 435.775 754.785i 0.0278228 0.0481906i
\(627\) −7754.40 12569.6i −0.493909 0.800606i
\(628\) 5373.08 + 9306.45i 0.341416 + 0.591350i
\(629\) 2758.67 0.174873
\(630\) 109.894 + 167.028i 0.00694966 + 0.0105628i
\(631\) −1325.17 −0.0836043 −0.0418022 0.999126i \(-0.513310\pi\)
−0.0418022 + 0.999126i \(0.513310\pi\)
\(632\) −859.053 1487.92i −0.0540685 0.0936494i
\(633\) 43.9965 81.6122i 0.00276257 0.00512447i
\(634\) −328.632 + 569.207i −0.0205862 + 0.0356563i
\(635\) 2955.91 5119.79i 0.184727 0.319957i
\(636\) −2784.34 + 5164.86i −0.173595 + 0.322013i
\(637\) 3645.74 + 6314.60i 0.226765 + 0.392769i
\(638\) 20.6408 0.00128084
\(639\) −25019.0 + 1461.18i −1.54888 + 0.0904589i
\(640\) 1774.74 0.109613
\(641\) 11255.8 + 19495.6i 0.693568 + 1.20129i 0.970661 + 0.240451i \(0.0772955\pi\)
−0.277094 + 0.960843i \(0.589371\pi\)
\(642\) −745.212 1207.96i −0.0458118 0.0742590i
\(643\) −2807.31 + 4862.40i −0.172176 + 0.298218i −0.939180 0.343424i \(-0.888413\pi\)
0.767004 + 0.641642i \(0.221747\pi\)
\(644\) 6551.38 11347.3i 0.400871 0.694328i
\(645\) −13703.2 + 399.812i −0.836532 + 0.0244071i
\(646\) 349.881 + 606.012i 0.0213094 + 0.0369090i
\(647\) −11753.6 −0.714188 −0.357094 0.934068i \(-0.616232\pi\)
−0.357094 + 0.934068i \(0.616232\pi\)
\(648\) 2023.27 237.137i 0.122656 0.0143760i
\(649\) 15560.2 0.941127
\(650\) 58.7720 + 101.796i 0.00354650 + 0.00614273i
\(651\) −11063.2 + 322.784i −0.666051 + 0.0194330i
\(652\) 4143.48 7176.71i 0.248882 0.431076i
\(653\) 12929.1 22393.9i 0.774816 1.34202i −0.160082 0.987104i \(-0.551176\pi\)
0.934898 0.354916i \(-0.115491\pi\)
\(654\) −446.908 724.420i −0.0267209 0.0433135i
\(655\) −5634.37 9759.02i −0.336112 0.582163i
\(656\) −12928.1 −0.769450
\(657\) 16408.0 958.272i 0.974333 0.0569037i
\(658\) −230.635 −0.0136643
\(659\) 8847.75 + 15324.8i 0.523004 + 0.905869i 0.999642 + 0.0267695i \(0.00852201\pi\)
−0.476638 + 0.879100i \(0.658145\pi\)
\(660\) −3095.74 + 5742.51i −0.182578 + 0.338677i
\(661\) −3115.05 + 5395.42i −0.183300 + 0.317485i −0.943002 0.332786i \(-0.892011\pi\)
0.759702 + 0.650271i \(0.225345\pi\)
\(662\) −79.3515 + 137.441i −0.00465873 + 0.00806916i
\(663\) 2937.05 5448.13i 0.172044 0.319137i
\(664\) −1502.42 2602.27i −0.0878091 0.152090i
\(665\) −3817.48 −0.222610
\(666\) −161.599 245.614i −0.00940214 0.0142903i
\(667\) 727.243 0.0422174
\(668\) −13257.2 22962.2i −0.767872 1.32999i
\(669\) −2699.71 4376.12i −0.156019 0.252901i
\(670\) −237.800 + 411.881i −0.0137120 + 0.0237498i
\(671\) −11965.0 + 20724.0i −0.688381 + 1.19231i
\(672\) −1469.40 + 42.8719i −0.0843501 + 0.00246104i
\(673\) 3025.84 + 5240.91i 0.173310 + 0.300182i 0.939575 0.342343i \(-0.111220\pi\)
−0.766265 + 0.642524i \(0.777887\pi\)
\(674\) −1728.62 −0.0987892
\(675\) −2012.45 2872.62i −0.114754 0.163803i
\(676\) 11755.0 0.668812
\(677\) −14049.3 24334.1i −0.797576 1.38144i −0.921190 0.389112i \(-0.872782\pi\)
0.123614 0.992330i \(-0.460551\pi\)
\(678\) −1231.49 + 35.9305i −0.0697566 + 0.00203525i
\(679\) 1408.10 2438.90i 0.0795846 0.137845i
\(680\) 309.694 536.405i 0.0174650 0.0302503i
\(681\) 9349.93 + 15155.9i 0.526124 + 0.852825i
\(682\) 693.769 + 1201.64i 0.0389528 + 0.0674682i
\(683\) −8335.71 −0.466994 −0.233497 0.972358i \(-0.575017\pi\)
−0.233497 + 0.972358i \(0.575017\pi\)
\(684\) −8708.61 + 17347.1i −0.486816 + 0.969714i
\(685\) 2368.56 0.132114
\(686\) −454.944 787.986i −0.0253205 0.0438563i
\(687\) −2711.34 + 5029.46i −0.150574 + 0.279310i
\(688\) 16691.5 28910.6i 0.924939 1.60204i
\(689\) 1903.63 3297.18i 0.105258 0.182312i
\(690\) 419.076 777.374i 0.0231217 0.0428900i
\(691\) 8442.55 + 14622.9i 0.464790 + 0.805039i 0.999192 0.0401909i \(-0.0127966\pi\)
−0.534402 + 0.845230i \(0.679463\pi\)
\(692\) 9517.46 0.522832
\(693\) 3230.46 6434.92i 0.177078 0.352731i
\(694\) 614.146 0.0335917
\(695\) 342.596 + 593.394i 0.0186984 + 0.0323867i
\(696\) −28.5409 46.2637i −0.00155437 0.00251957i
\(697\) −4529.39 + 7845.14i −0.246145 + 0.426335i
\(698\) −909.305 + 1574.96i −0.0493090 + 0.0854057i
\(699\) 23164.5 675.860i 1.25345 0.0365714i
\(700\) 843.132 + 1460.35i 0.0455248 + 0.0788514i
\(701\) 16875.2 0.909226 0.454613 0.890689i \(-0.349778\pi\)
0.454613 + 0.890689i \(0.349778\pi\)
\(702\) −657.115 + 57.6479i −0.0353293 + 0.00309940i
\(703\) 5613.59 0.301167
\(704\) −7881.47 13651.1i −0.421938 0.730817i
\(705\) 4044.19 117.995i 0.216047 0.00630350i
\(706\) 707.410 1225.27i 0.0377106 0.0653168i
\(707\) 2094.71 3628.14i 0.111428 0.192999i
\(708\) −10737.3 17404.6i −0.569959 0.923879i
\(709\) 9503.71 + 16460.9i 0.503412 + 0.871936i 0.999992 + 0.00394482i \(0.00125568\pi\)
−0.496580 + 0.867991i \(0.665411\pi\)
\(710\) 812.110 0.0429267
\(711\) −9124.43 13868.2i −0.481284 0.731503i
\(712\) 4205.99 0.221385
\(713\) 24443.8 + 42337.9i 1.28391 + 2.22379i
\(714\) −161.887 + 300.295i −0.00848524 + 0.0157398i
\(715\) 2116.53 3665.94i 0.110705 0.191746i
\(716\) 9259.23 16037.4i 0.483287 0.837078i
\(717\) −16136.9 + 29933.4i −0.840506 + 1.55911i
\(718\) −716.517 1241.04i −0.0372426 0.0645061i
\(719\) 17588.1 0.912275 0.456138 0.889909i \(-0.349233\pi\)
0.456138 + 0.889909i \(0.349233\pi\)
\(720\) 8526.39 497.965i 0.441333 0.0257751i
\(721\) −5332.40 −0.275435
\(722\) 111.861 + 193.748i 0.00576596 + 0.00998693i
\(723\) 573.810 + 930.123i 0.0295162 + 0.0478446i
\(724\) 10069.8 17441.4i 0.516907 0.895309i
\(725\) −46.7964 + 81.0537i −0.00239721 + 0.00415208i
\(726\) 307.403 8.96895i 0.0157146 0.000458497i
\(727\) −2802.69 4854.40i −0.142979 0.247648i 0.785638 0.618687i \(-0.212335\pi\)
−0.928617 + 0.371039i \(0.879002\pi\)
\(728\) 635.491 0.0323528
\(729\) 19382.3 3427.15i 0.984725 0.174117i
\(730\) −532.600 −0.0270033
\(731\) −11695.8 20257.7i −0.591771 1.02498i
\(732\) 31436.9 917.220i 1.58735 0.0463134i
\(733\) −7460.04 + 12921.2i −0.375911 + 0.651097i −0.990463 0.137779i \(-0.956004\pi\)
0.614552 + 0.788877i \(0.289337\pi\)
\(734\) −786.963 + 1363.06i −0.0395740 + 0.0685443i
\(735\) 3701.71 + 6000.32i 0.185768 + 0.301123i
\(736\) 3246.60 + 5623.27i 0.162597 + 0.281626i
\(737\) 17127.6 0.856042
\(738\) 963.806 56.2889i 0.0480734 0.00280762i
\(739\) −27418.8 −1.36484 −0.682421 0.730959i \(-0.739073\pi\)
−0.682421 + 0.730959i \(0.739073\pi\)
\(740\) −1239.82 2147.44i −0.0615903 0.106677i
\(741\) 5976.58 11086.4i 0.296296 0.549619i
\(742\) −104.926 + 181.737i −0.00519131 + 0.00899161i
\(743\) 12272.1 21255.9i 0.605948 1.04953i −0.385953 0.922518i \(-0.626127\pi\)
0.991901 0.127014i \(-0.0405394\pi\)
\(744\) 1734.02 3216.56i 0.0854467 0.158501i
\(745\) 357.777 + 619.687i 0.0175945 + 0.0304746i
\(746\) 162.712 0.00798569
\(747\) −15957.9 24254.5i −0.781621 1.18799i
\(748\) −11131.5 −0.544128
\(749\) 6605.92 + 11441.8i 0.322263 + 0.558176i
\(750\) 59.6743 + 96.7296i 0.00290533 + 0.00470942i
\(751\) −767.283 + 1328.97i −0.0372817 + 0.0645738i −0.884064 0.467365i \(-0.845203\pi\)
0.846782 + 0.531939i \(0.178537\pi\)
\(752\) −4926.13 + 8532.30i −0.238880 + 0.413752i
\(753\) 4239.00 123.679i 0.205150 0.00598555i
\(754\) 8.80102 + 15.2438i 0.000425085 + 0.000736269i
\(755\) 1084.21 0.0522627
\(756\) −9426.85 + 827.005i −0.453507 + 0.0397856i
\(757\) −18051.1 −0.866681 −0.433341 0.901230i \(-0.642665\pi\)
−0.433341 + 0.901230i \(0.642665\pi\)
\(758\) 301.823 + 522.773i 0.0144627 + 0.0250501i
\(759\) −31790.6 + 927.539i −1.52032 + 0.0443578i
\(760\) 630.194 1091.53i 0.0300783 0.0520972i
\(761\) −6462.29 + 11193.0i −0.307829 + 0.533176i −0.977887 0.209133i \(-0.932936\pi\)
0.670058 + 0.742309i \(0.266269\pi\)
\(762\) −564.455 914.958i −0.0268347 0.0434980i
\(763\) 3961.61 + 6861.71i 0.187968 + 0.325571i
\(764\) −19037.8 −0.901522
\(765\) 2685.05 5348.50i 0.126900 0.252778i
\(766\) 935.491 0.0441262
\(767\) 6634.70 + 11491.6i 0.312341 + 0.540990i
\(768\) −9715.30 + 18021.6i −0.456472 + 0.846741i
\(769\) 1686.16 2920.51i 0.0790695 0.136952i −0.823779 0.566911i \(-0.808138\pi\)
0.902849 + 0.429958i \(0.141472\pi\)
\(770\) −116.661 + 202.063i −0.00545996 + 0.00945692i
\(771\) 10287.9 19083.7i 0.480557 0.891418i
\(772\) 14137.6 + 24487.0i 0.659097 + 1.14159i
\(773\) −27152.6 −1.26341 −0.631703 0.775211i \(-0.717644\pi\)
−0.631703 + 0.775211i \(0.717644\pi\)
\(774\) −1118.49 + 2227.99i −0.0519424 + 0.103467i
\(775\) −6291.59 −0.291614
\(776\) 464.901 + 805.232i 0.0215064 + 0.0372502i
\(777\) 1436.92 + 2329.19i 0.0663441 + 0.107541i
\(778\) 675.742 1170.42i 0.0311395 0.0539352i
\(779\) −9216.83 + 15964.0i −0.423912 + 0.734236i
\(780\) −5560.99 + 162.250i −0.255276 + 0.00744807i
\(781\) −14623.1 25327.9i −0.669982 1.16044i
\(782\) 1506.89 0.0689083
\(783\) −301.361 430.170i −0.0137545 0.0196335i
\(784\) −17168.2 −0.782080
\(785\) −3371.08 5838.88i −0.153272 0.265476i
\(786\) −2048.34 + 59.7635i −0.0929541 + 0.00271208i
\(787\) 12606.0 21834.3i 0.570974 0.988957i −0.425492 0.904962i \(-0.639899\pi\)
0.996466 0.0839943i \(-0.0267677\pi\)
\(788\) −4938.08 + 8553.01i −0.223238 + 0.386660i
\(789\) 7685.50 + 12457.9i 0.346782 + 0.562120i
\(790\) 268.969 + 465.868i 0.0121133 + 0.0209808i
\(791\) 11468.2 0.515500
\(792\) 1306.64 + 1985.96i 0.0586230 + 0.0891011i
\(793\) −20407.0 −0.913838
\(794\) 623.386 + 1079.74i 0.0278629 + 0.0482599i
\(795\) 1746.90 3240.44i 0.0779322 0.144562i
\(796\) 2058.72 3565.80i 0.0916700 0.158777i
\(797\) −19588.5 + 33928.2i −0.870588 + 1.50790i −0.00919851 + 0.999958i \(0.502928\pi\)
−0.861390 + 0.507945i \(0.830405\pi\)
\(798\) −329.422 + 611.068i −0.0146133 + 0.0271072i
\(799\) 3451.75 + 5978.61i 0.152834 + 0.264716i
\(800\) −835.644 −0.0369306
\(801\) 40569.9 2369.40i 1.78960 0.104517i
\(802\) 313.764 0.0138147
\(803\) 9590.16 + 16610.6i 0.421456 + 0.729983i
\(804\) −11818.8 19157.8i −0.518430 0.840353i
\(805\) −4110.35 + 7119.33i −0.179964 + 0.311706i
\(806\) −591.631 + 1024.74i −0.0258552 + 0.0447826i
\(807\) −532.949 + 15.5496i −0.0232474 + 0.000678279i
\(808\) 691.593 + 1197.87i 0.0301116 + 0.0521548i
\(809\) −36739.0 −1.59663 −0.798316 0.602239i \(-0.794275\pi\)
−0.798316 + 0.602239i \(0.794275\pi\)
\(810\) −633.483 + 74.2475i −0.0274794 + 0.00322073i
\(811\) −29660.0 −1.28422 −0.642111 0.766611i \(-0.721941\pi\)
−0.642111 + 0.766611i \(0.721941\pi\)
\(812\) 126.258 + 218.685i 0.00545662 + 0.00945115i
\(813\) −17333.6 + 505.733i −0.747743 + 0.0218165i
\(814\) 171.549 297.132i 0.00738674 0.0127942i
\(815\) −2599.62 + 4502.68i −0.111731 + 0.193524i
\(816\) 7651.61 + 12402.9i 0.328260 + 0.532096i
\(817\) −23799.7 41222.2i −1.01915 1.76522i
\(818\) −549.405 −0.0234835
\(819\) 6129.80 357.997i 0.261529 0.0152740i
\(820\) 8142.54 0.346768
\(821\) −10056.6 17418.6i −0.427501 0.740453i 0.569149 0.822234i \(-0.307273\pi\)
−0.996650 + 0.0817808i \(0.973939\pi\)
\(822\) 204.390 379.137i 0.00867265 0.0160875i
\(823\) −2687.02 + 4654.06i −0.113808 + 0.197121i −0.917303 0.398191i \(-0.869638\pi\)
0.803495 + 0.595312i \(0.202971\pi\)
\(824\) 880.277 1524.68i 0.0372159 0.0644598i
\(825\) 1942.27 3602.86i 0.0819652 0.152043i
\(826\) −365.697 633.406i −0.0154046 0.0266816i
\(827\) 27865.2 1.17167 0.585833 0.810432i \(-0.300767\pi\)
0.585833 + 0.810432i \(0.300767\pi\)
\(828\) 22974.5 + 34918.9i 0.964273 + 1.46560i
\(829\) 24363.1 1.02070 0.510352 0.859965i \(-0.329515\pi\)
0.510352 + 0.859965i \(0.329515\pi\)
\(830\) 470.407 + 814.768i 0.0196724 + 0.0340735i
\(831\) −1729.36 2803.23i −0.0721913 0.117019i
\(832\) 6721.15 11641.4i 0.280065 0.485086i
\(833\) −6014.91 + 10418.1i −0.250185 + 0.433333i
\(834\) 124.549 3.63390i 0.00517119 0.000150877i
\(835\) 8317.61 + 14406.5i 0.344722 + 0.597076i
\(836\) −22651.4 −0.937099
\(837\) 14914.0 32003.0i 0.615892 1.32161i
\(838\) −430.007 −0.0177259
\(839\) 17765.3 + 30770.4i 0.731020 + 1.26616i 0.956448 + 0.291903i \(0.0942886\pi\)
−0.225428 + 0.974260i \(0.572378\pi\)
\(840\) 614.209 17.9205i 0.0252288 0.000736089i
\(841\) 12187.5 21109.4i 0.499713 0.865528i
\(842\) −234.363 + 405.928i −0.00959226 + 0.0166143i
\(843\) 16921.4 + 27429.0i 0.691347 + 1.12065i
\(844\) −71.0996 123.148i −0.00289970 0.00502243i
\(845\) −7375.13 −0.300251
\(846\) 330.098 657.540i 0.0134149 0.0267219i
\(847\) −2862.68 −0.116131
\(848\) 4482.22 + 7763.42i 0.181509 + 0.314383i
\(849\) 18444.0 34213.0i 0.745578 1.38302i
\(850\) −96.9648 + 167.948i −0.00391278 + 0.00677714i
\(851\) 6044.25 10468.9i 0.243471 0.421705i
\(852\) −18239.6 + 33833.9i −0.733426 + 1.36048i
\(853\) −17223.8 29832.4i −0.691360 1.19747i −0.971392 0.237480i \(-0.923679\pi\)
0.280032 0.959991i \(-0.409655\pi\)
\(854\) 1124.81 0.0450705
\(855\) 5463.80 10883.6i 0.218547 0.435336i
\(856\) −4362.05 −0.174173
\(857\) −10003.4 17326.4i −0.398729 0.690618i 0.594841 0.803844i \(-0.297215\pi\)
−0.993569 + 0.113225i \(0.963882\pi\)
\(858\) −404.169 655.141i −0.0160817 0.0260678i
\(859\) −893.190 + 1547.05i −0.0354776 + 0.0614490i −0.883219 0.468961i \(-0.844629\pi\)
0.847741 + 0.530410i \(0.177962\pi\)
\(860\) −10512.8 + 18208.8i −0.416842 + 0.721992i
\(861\) −8983.04 + 262.094i −0.355565 + 0.0103741i
\(862\) −828.764 1435.46i −0.0327469 0.0567192i
\(863\) 12151.9 0.479322 0.239661 0.970857i \(-0.422964\pi\)
0.239661 + 0.970857i \(0.422964\pi\)
\(864\) 1980.86 4250.61i 0.0779978 0.167371i
\(865\) −5971.27 −0.234716
\(866\) −370.811 642.263i −0.0145504 0.0252021i
\(867\) −15310.7 + 446.711i −0.599743 + 0.0174984i
\(868\) −8487.43 + 14700.7i −0.331892 + 0.574854i
\(869\) 9686.27 16777.1i 0.378118 0.654919i
\(870\) 8.93614 + 14.4851i 0.000348234 + 0.000564473i
\(871\) 7303.02 + 12649.2i 0.284102 + 0.492080i
\(872\) −2615.94 −0.101591
\(873\) 4937.94 + 7505.18i 0.191436 + 0.290964i
\(874\) 3066.36 0.118674
\(875\) −528.982 916.224i −0.0204376 0.0353989i
\(876\) 11961.9 22189.0i 0.461366 0.855819i
\(877\) 9436.64 16344.7i 0.363344 0.629330i −0.625165 0.780493i \(-0.714968\pi\)
0.988509 + 0.151163i \(0.0483017\pi\)
\(878\) 425.119 736.328i 0.0163406 0.0283028i
\(879\) 11925.5 22121.5i 0.457609 0.848851i
\(880\) 4983.51 + 8631.69i 0.190902 + 0.330653i
\(881\) 23587.2 0.902014 0.451007 0.892520i \(-0.351065\pi\)
0.451007 + 0.892520i \(0.351065\pi\)
\(882\) 1279.91 74.7502i 0.0488625 0.00285371i
\(883\) −29504.5 −1.12447 −0.562234 0.826978i \(-0.690058\pi\)
−0.562234 + 0.826978i \(0.690058\pi\)
\(884\) −4746.35 8220.92i −0.180585 0.312782i
\(885\) 6736.57 + 10919.7i 0.255873 + 0.414759i
\(886\) 204.360 353.963i 0.00774901 0.0134217i
\(887\) −1238.02 + 2144.31i −0.0468643 + 0.0811714i −0.888506 0.458865i \(-0.848256\pi\)
0.841642 + 0.540036i \(0.181590\pi\)
\(888\) −903.192 + 26.3520i −0.0341319 + 0.000995850i
\(889\) 5003.60 + 8666.49i 0.188769 + 0.326957i
\(890\) −1316.89 −0.0495981
\(891\) 13722.3 + 18420.0i 0.515953 + 0.692586i
\(892\) −7886.13 −0.296017
\(893\) 7023.94 + 12165.8i 0.263211 + 0.455894i
\(894\) 130.068 3.79492i 0.00486589 0.000141970i
\(895\) −5809.25 + 10061.9i −0.216963 + 0.375791i
\(896\) −1502.09 + 2601.69i −0.0560058 + 0.0970048i
\(897\) −14240.2 23082.8i −0.530063 0.859210i
\(898\) 1162.82 + 2014.06i 0.0432112 + 0.0748440i
\(899\) −942.157 −0.0349529
\(900\) −5370.18 + 313.633i −0.198896 + 0.0116160i
\(901\) 6281.40 0.232257
\(902\) 563.326 + 975.709i 0.0207946 + 0.0360173i
\(903\) 11011.9 20426.7i 0.405817 0.752778i
\(904\) −1893.17 + 3279.07i −0.0696527 + 0.120642i
\(905\) −6317.80 + 10942.7i −0.232056 + 0.401933i
\(906\) 93.5595 173.550i 0.00343080 0.00636403i
\(907\) 13375.5 + 23167.1i 0.489666 + 0.848126i 0.999929 0.0118922i \(-0.00378549\pi\)
−0.510264 + 0.860018i \(0.670452\pi\)
\(908\) 27312.1 0.998221
\(909\) 7345.75 + 11164.8i 0.268034 + 0.407385i
\(910\) −198.972 −0.00724819
\(911\) −6334.11 10971.0i −0.230360 0.398996i 0.727554 0.686051i \(-0.240657\pi\)
−0.957914 + 0.287055i \(0.907324\pi\)
\(912\) 15570.2 + 25238.7i 0.565330 + 0.916377i
\(913\) 16940.6 29341.9i 0.614076 1.06361i
\(914\) 452.739 784.167i 0.0163843 0.0283785i
\(915\) −19723.6 + 575.465i −0.712613 + 0.0207916i
\(916\) 4381.61 + 7589.16i 0.158048 + 0.273748i
\(917\) 19075.1 0.686930
\(918\) −624.437 891.337i −0.0224504 0.0320463i
\(919\) 46565.5 1.67144 0.835721 0.549155i \(-0.185050\pi\)
0.835721 + 0.549155i \(0.185050\pi\)
\(920\) −1357.08 2350.53i −0.0486322 0.0842334i
\(921\) −29147.7 + 850.427i −1.04283 + 0.0304262i
\(922\) 554.779 960.905i 0.0198163 0.0343229i
\(923\) 12470.3 21599.1i 0.444706 0.770253i
\(924\) −5798.13 9398.53i −0.206433 0.334620i
\(925\) 777.866 + 1347.30i 0.0276498 + 0.0478909i
\(926\) −556.940 −0.0197648
\(927\) 7632.03 15202.6i 0.270408 0.538641i
\(928\) −125.136 −0.00442651
\(929\) −2305.46 3993.17i −0.0814205 0.141024i 0.822440 0.568852i \(-0.192612\pi\)
−0.903860 + 0.427828i \(0.859279\pi\)
\(930\) −542.921 + 1007.10i −0.0191431 + 0.0355098i
\(931\) −12239.7 + 21199.8i −0.430870 + 0.746289i
\(932\) 17771.4 30780.9i 0.624593 1.08183i
\(933\) −26929.3 + 49952.9i −0.944935 + 1.75283i
\(934\) −750.354 1299.65i −0.0262873 0.0455309i
\(935\) 6983.91 0.244276
\(936\) −909.551 + 1811.78i −0.0317624 + 0.0632692i
\(937\) −6625.43 −0.230996 −0.115498 0.993308i \(-0.536846\pi\)
−0.115498 + 0.993308i \(0.536846\pi\)
\(938\) −402.534 697.209i −0.0140119 0.0242694i
\(939\) −13588.5 22026.4i −0.472250 0.765498i
\(940\) 3102.63 5373.91i 0.107656 0.186465i
\(941\) 21721.3 37622.4i 0.752491 1.30335i −0.194121 0.980978i \(-0.562185\pi\)
0.946612 0.322375i \(-0.104481\pi\)
\(942\) −1225.53 + 35.7568i −0.0423886 + 0.00123675i
\(943\) 19847.8 + 34377.4i 0.685402 + 1.18715i
\(944\) −31243.7 −1.07722
\(945\) 5914.42 518.864i 0.203594 0.0178610i
\(946\) −2909.24 −0.0999868
\(947\) −16461.2 28511.7i −0.564855 0.978357i −0.997063 0.0765835i \(-0.975599\pi\)
0.432208 0.901774i \(-0.357735\pi\)
\(948\) −25449.8 + 742.536i −0.871909 + 0.0254393i
\(949\) −8178.28 + 14165.2i −0.279745 + 0.484533i
\(950\) −197.313 + 341.756i −0.00673861 + 0.0116716i
\(951\) 10247.5 + 16610.8i 0.349419 + 0.566394i
\(952\) 524.232 + 907.996i 0.0178471 + 0.0309121i
\(953\) 20253.5 0.688430 0.344215 0.938891i \(-0.388145\pi\)
0.344215 + 0.938891i \(0.388145\pi\)
\(954\) −367.955 559.255i −0.0124874 0.0189796i
\(955\) 11944.3 0.404722
\(956\) 26077.6 + 45167.8i 0.882229 + 1.52806i
\(957\) 290.853 539.522i 0.00982437 0.0182239i
\(958\) 255.272 442.144i 0.00860904 0.0149113i
\(959\) −2004.68 + 3472.20i −0.0675020 + 0.116917i
\(960\) 6167.78 11441.0i 0.207359 0.384644i
\(961\) −16771.8 29049.7i −0.562983 0.975116i
\(962\) 292.587 0.00980602
\(963\) −42075.3 + 2457.31i −1.40795 + 0.0822282i
\(964\) 1676.16 0.0560015
\(965\) −8869.93 15363.2i −0.295889 0.512496i
\(966\) 784.903 + 1272.30i 0.0261427 + 0.0423762i
\(967\) −1618.56 + 2803.43i −0.0538257 + 0.0932289i −0.891683 0.452661i \(-0.850475\pi\)
0.837857 + 0.545890i \(0.183808\pi\)
\(968\) 472.573 818.521i 0.0156912 0.0271780i
\(969\) 20770.5 606.012i 0.688592 0.0200907i
\(970\) −145.560 252.118i −0.00481820 0.00834537i
\(971\) −1731.06 −0.0572114 −0.0286057 0.999591i \(-0.509107\pi\)
−0.0286057 + 0.999591i \(0.509107\pi\)
\(972\) 11134.4 28059.5i 0.367425 0.925936i
\(973\) −1159.86 −0.0382151
\(974\) −1230.23 2130.81i −0.0404712 0.0700982i
\(975\) 3488.97 101.796i 0.114602 0.00334368i
\(976\) 24024.8 41612.1i 0.787924 1.36472i
\(977\) −17273.4 + 29918.5i −0.565636 + 0.979710i 0.431354 + 0.902183i \(0.358036\pi\)
−0.996990 + 0.0775275i \(0.975297\pi\)
\(978\) 496.418 + 804.674i 0.0162308 + 0.0263094i
\(979\) 23712.3 + 41071.0i 0.774106 + 1.34079i
\(980\) 10813.1 0.352460
\(981\) −25232.8 + 1473.66i −0.821224 + 0.0479617i
\(982\) 163.201 0.00530343
\(983\) −10226.6 17713.0i −0.331818 0.574726i 0.651050 0.759035i \(-0.274329\pi\)
−0.982868 + 0.184309i \(0.940995\pi\)
\(984\) 1407.99 2611.78i 0.0456149 0.0846142i
\(985\) 3098.16 5366.17i 0.100219 0.173584i
\(986\) −14.5203 + 25.1500i −0.000468987 + 0.000812310i
\(987\) −3249.91 + 6028.49i −0.104808 + 0.194416i
\(988\) −9658.31 16728.7i −0.311004 0.538675i
\(989\) −102502. −3.29563
\(990\) −409.108 621.803i −0.0131336 0.0199618i
\(991\) −5387.77 −0.172703 −0.0863513 0.996265i \(-0.527521\pi\)
−0.0863513 + 0.996265i \(0.527521\pi\)
\(992\) −4206.03 7285.05i −0.134618 0.233166i
\(993\) 2474.36 + 4010.84i 0.0790750 + 0.128177i
\(994\) −687.347 + 1190.52i −0.0219329 + 0.0379889i
\(995\) −1291.64 + 2237.19i −0.0411536 + 0.0712801i
\(996\) −44509.8 + 1298.64i −1.41601 + 0.0413142i
\(997\) 10922.4 + 18918.2i 0.346958 + 0.600949i 0.985707 0.168466i \(-0.0538813\pi\)
−0.638750 + 0.769415i \(0.720548\pi\)
\(998\) 2525.16 0.0800929
\(999\) −8697.13 + 762.988i −0.275440 + 0.0241640i
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 45.4.e.b.31.2 yes 6
3.2 odd 2 135.4.e.b.91.2 6
5.2 odd 4 225.4.k.c.49.3 12
5.3 odd 4 225.4.k.c.49.4 12
5.4 even 2 225.4.e.c.76.2 6
9.2 odd 6 135.4.e.b.46.2 6
9.4 even 3 405.4.a.h.1.2 3
9.5 odd 6 405.4.a.j.1.2 3
9.7 even 3 inner 45.4.e.b.16.2 6
45.4 even 6 2025.4.a.s.1.2 3
45.7 odd 12 225.4.k.c.124.4 12
45.14 odd 6 2025.4.a.q.1.2 3
45.34 even 6 225.4.e.c.151.2 6
45.43 odd 12 225.4.k.c.124.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.4.e.b.16.2 6 9.7 even 3 inner
45.4.e.b.31.2 yes 6 1.1 even 1 trivial
135.4.e.b.46.2 6 9.2 odd 6
135.4.e.b.91.2 6 3.2 odd 2
225.4.e.c.76.2 6 5.4 even 2
225.4.e.c.151.2 6 45.34 even 6
225.4.k.c.49.3 12 5.2 odd 4
225.4.k.c.49.4 12 5.3 odd 4
225.4.k.c.124.3 12 45.43 odd 12
225.4.k.c.124.4 12 45.7 odd 12
405.4.a.h.1.2 3 9.4 even 3
405.4.a.j.1.2 3 9.5 odd 6
2025.4.a.q.1.2 3 45.14 odd 6
2025.4.a.s.1.2 3 45.4 even 6