Properties

Label 60.4.j.b.7.5
Level $60$
Weight $4$
Character 60.7
Analytic conductor $3.540$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [60,4,Mod(7,60)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(60, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("60.7");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 60.j (of order \(4\), 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: \(3.54011460034\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 7.5
Character \(\chi\) \(=\) 60.7
Dual form 60.4.j.b.43.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.79487 - 2.18597i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-1.55691 + 7.84704i) q^{4} +(-3.87875 - 10.4860i) q^{5} +(0.829651 - 8.44462i) q^{6} +(17.0336 - 17.0336i) q^{7} +(19.9478 - 10.6810i) q^{8} +9.00000i q^{9} +O(q^{10})\) \(q+(-1.79487 - 2.18597i) q^{2} +(2.12132 + 2.12132i) q^{3} +(-1.55691 + 7.84704i) q^{4} +(-3.87875 - 10.4860i) q^{5} +(0.829651 - 8.44462i) q^{6} +(17.0336 - 17.0336i) q^{7} +(19.9478 - 10.6810i) q^{8} +9.00000i q^{9} +(-15.9601 + 27.2997i) q^{10} -62.6605i q^{11} +(-19.9488 + 13.3434i) q^{12} +(-10.3908 + 10.3908i) q^{13} +(-67.8080 - 6.66187i) q^{14} +(14.0160 - 30.4722i) q^{15} +(-59.1521 - 24.4343i) q^{16} +(-15.8043 - 15.8043i) q^{17} +(19.6737 - 16.1538i) q^{18} +40.5175 q^{19} +(88.3226 - 14.1111i) q^{20} +72.2675 q^{21} +(-136.974 + 112.467i) q^{22} +(144.815 + 144.815i) q^{23} +(64.9736 + 19.6578i) q^{24} +(-94.9105 + 81.3449i) q^{25} +(41.3640 + 4.06385i) q^{26} +(-19.0919 + 19.0919i) q^{27} +(107.144 + 160.183i) q^{28} -97.7212i q^{29} +(-91.7680 + 24.0549i) q^{30} +3.67666i q^{31} +(52.7576 + 173.161i) q^{32} +(132.923 - 132.923i) q^{33} +(-6.18108 + 62.9143i) q^{34} +(-244.683 - 112.545i) q^{35} +(-70.6234 - 14.0122i) q^{36} +(158.710 + 158.710i) q^{37} +(-72.7235 - 88.5699i) q^{38} -44.0844 q^{39} +(-189.374 - 167.743i) q^{40} -330.103 q^{41} +(-129.711 - 157.974i) q^{42} +(59.6888 + 59.6888i) q^{43} +(491.699 + 97.5567i) q^{44} +(94.3736 - 34.9088i) q^{45} +(56.6375 - 576.486i) q^{46} +(0.929497 - 0.929497i) q^{47} +(-73.6476 - 177.313i) q^{48} -237.288i q^{49} +(348.169 + 61.4682i) q^{50} -67.0520i q^{51} +(-65.3595 - 97.7145i) q^{52} +(-385.246 + 385.246i) q^{53} +(76.0016 + 7.46686i) q^{54} +(-657.055 + 243.045i) q^{55} +(157.847 - 521.720i) q^{56} +(85.9505 + 85.9505i) q^{57} +(-213.615 + 175.396i) q^{58} -112.319 q^{59} +(217.295 + 157.426i) q^{60} +420.338 q^{61} +(8.03707 - 6.59912i) q^{62} +(153.303 + 153.303i) q^{63} +(283.831 - 426.127i) q^{64} +(149.261 + 68.6541i) q^{65} +(-529.144 - 51.9863i) q^{66} +(505.727 - 505.727i) q^{67} +(148.623 - 99.4111i) q^{68} +614.400i q^{69} +(193.154 + 736.871i) q^{70} +713.401i q^{71} +(96.1293 + 179.530i) q^{72} +(541.439 - 541.439i) q^{73} +(62.0717 - 631.798i) q^{74} +(-373.894 - 28.7771i) q^{75} +(-63.0820 + 317.942i) q^{76} +(-1067.33 - 1067.33i) q^{77} +(79.1256 + 96.3671i) q^{78} -277.290 q^{79} +(-26.7802 + 715.040i) q^{80} -81.0000 q^{81} +(592.491 + 721.595i) q^{82} +(96.5456 + 96.5456i) q^{83} +(-112.514 + 567.086i) q^{84} +(-104.422 + 227.024i) q^{85} +(23.3444 - 237.611i) q^{86} +(207.298 - 207.298i) q^{87} +(-669.279 - 1249.94i) q^{88} +370.942i q^{89} +(-245.697 - 143.641i) q^{90} +353.986i q^{91} +(-1361.84 + 910.908i) q^{92} +(-7.79938 + 7.79938i) q^{93} +(-3.70017 - 0.363527i) q^{94} +(-157.157 - 424.864i) q^{95} +(-255.414 + 479.245i) q^{96} +(701.220 + 701.220i) q^{97} +(-518.704 + 425.900i) q^{98} +563.944 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 24 q^{5} - 36 q^{6} + 84 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 24 q^{5} - 36 q^{6} + 84 q^{8} + 128 q^{10} + 24 q^{12} - 412 q^{13} - 180 q^{16} + 20 q^{17} + 52 q^{20} + 144 q^{21} - 436 q^{22} + 132 q^{25} + 704 q^{26} + 508 q^{28} + 480 q^{30} + 340 q^{32} - 96 q^{33} + 324 q^{36} + 508 q^{37} - 1792 q^{38} - 2696 q^{40} - 1696 q^{41} - 1500 q^{42} + 612 q^{45} + 2584 q^{46} + 528 q^{48} + 832 q^{50} + 504 q^{52} + 1772 q^{53} - 512 q^{56} + 720 q^{57} - 1060 q^{58} - 84 q^{60} + 2096 q^{61} - 472 q^{62} + 28 q^{65} - 648 q^{66} + 5872 q^{68} + 2956 q^{70} + 756 q^{72} - 3348 q^{73} - 3480 q^{76} - 384 q^{77} - 1032 q^{78} - 4828 q^{80} - 2268 q^{81} - 928 q^{82} - 476 q^{85} - 3616 q^{86} + 380 q^{88} - 1116 q^{90} + 472 q^{92} - 2688 q^{93} + 396 q^{96} + 8300 q^{97} + 72 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(37\) \(41\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.79487 2.18597i −0.634581 0.772856i
\(3\) 2.12132 + 2.12132i 0.408248 + 0.408248i
\(4\) −1.55691 + 7.84704i −0.194614 + 0.980880i
\(5\) −3.87875 10.4860i −0.346926 0.937892i
\(6\) 0.829651 8.44462i 0.0564506 0.574584i
\(7\) 17.0336 17.0336i 0.919729 0.919729i −0.0772807 0.997009i \(-0.524624\pi\)
0.997009 + 0.0772807i \(0.0246238\pi\)
\(8\) 19.9478 10.6810i 0.881577 0.472040i
\(9\) 9.00000i 0.333333i
\(10\) −15.9601 + 27.2997i −0.504703 + 0.863293i
\(11\) 62.6605i 1.71753i −0.512368 0.858766i \(-0.671232\pi\)
0.512368 0.858766i \(-0.328768\pi\)
\(12\) −19.9488 + 13.3434i −0.479893 + 0.320992i
\(13\) −10.3908 + 10.3908i −0.221684 + 0.221684i −0.809207 0.587523i \(-0.800103\pi\)
0.587523 + 0.809207i \(0.300103\pi\)
\(14\) −67.8080 6.66187i −1.29446 0.127176i
\(15\) 14.0160 30.4722i 0.241261 0.524525i
\(16\) −59.1521 24.4343i −0.924251 0.381785i
\(17\) −15.8043 15.8043i −0.225477 0.225477i 0.585323 0.810800i \(-0.300968\pi\)
−0.810800 + 0.585323i \(0.800968\pi\)
\(18\) 19.6737 16.1538i 0.257619 0.211527i
\(19\) 40.5175 0.489229 0.244614 0.969620i \(-0.421339\pi\)
0.244614 + 0.969620i \(0.421339\pi\)
\(20\) 88.3226 14.1111i 0.987476 0.157766i
\(21\) 72.2675 0.750955
\(22\) −136.974 + 112.467i −1.32741 + 1.08991i
\(23\) 144.815 + 144.815i 1.31287 + 1.31287i 0.919287 + 0.393587i \(0.128766\pi\)
0.393587 + 0.919287i \(0.371234\pi\)
\(24\) 64.9736 + 19.6578i 0.552612 + 0.167193i
\(25\) −94.9105 + 81.3449i −0.759284 + 0.650759i
\(26\) 41.3640 + 4.06385i 0.312006 + 0.0306533i
\(27\) −19.0919 + 19.0919i −0.136083 + 0.136083i
\(28\) 107.144 + 160.183i 0.723152 + 1.08114i
\(29\) 97.7212i 0.625737i −0.949796 0.312868i \(-0.898710\pi\)
0.949796 0.312868i \(-0.101290\pi\)
\(30\) −91.7680 + 24.0549i −0.558482 + 0.146394i
\(31\) 3.67666i 0.0213016i 0.999943 + 0.0106508i \(0.00339031\pi\)
−0.999943 + 0.0106508i \(0.996610\pi\)
\(32\) 52.7576 + 173.161i 0.291447 + 0.956587i
\(33\) 132.923 132.923i 0.701179 0.701179i
\(34\) −6.18108 + 62.9143i −0.0311778 + 0.317345i
\(35\) −244.683 112.545i −1.18168 0.543528i
\(36\) −70.6234 14.0122i −0.326960 0.0648712i
\(37\) 158.710 + 158.710i 0.705183 + 0.705183i 0.965518 0.260335i \(-0.0838332\pi\)
−0.260335 + 0.965518i \(0.583833\pi\)
\(38\) −72.7235 88.5699i −0.310455 0.378104i
\(39\) −44.0844 −0.181004
\(40\) −189.374 167.743i −0.748565 0.663062i
\(41\) −330.103 −1.25740 −0.628700 0.777648i \(-0.716413\pi\)
−0.628700 + 0.777648i \(0.716413\pi\)
\(42\) −129.711 157.974i −0.476542 0.580380i
\(43\) 59.6888 + 59.6888i 0.211685 + 0.211685i 0.804983 0.593298i \(-0.202174\pi\)
−0.593298 + 0.804983i \(0.702174\pi\)
\(44\) 491.699 + 97.5567i 1.68469 + 0.334255i
\(45\) 94.3736 34.9088i 0.312631 0.115642i
\(46\) 56.6375 576.486i 0.181538 1.84779i
\(47\) 0.929497 0.929497i 0.00288470 0.00288470i −0.705663 0.708548i \(-0.749351\pi\)
0.708548 + 0.705663i \(0.249351\pi\)
\(48\) −73.6476 177.313i −0.221461 0.533187i
\(49\) 237.288i 0.691801i
\(50\) 348.169 + 61.4682i 0.984771 + 0.173858i
\(51\) 67.0520i 0.184101i
\(52\) −65.3595 97.7145i −0.174302 0.260588i
\(53\) −385.246 + 385.246i −0.998445 + 0.998445i −0.999999 0.00155370i \(-0.999505\pi\)
0.00155370 + 0.999999i \(0.499505\pi\)
\(54\) 76.0016 + 7.46686i 0.191528 + 0.0188169i
\(55\) −657.055 + 243.045i −1.61086 + 0.595857i
\(56\) 157.847 521.720i 0.376664 1.24496i
\(57\) 85.9505 + 85.9505i 0.199727 + 0.199727i
\(58\) −213.615 + 175.396i −0.483605 + 0.397081i
\(59\) −112.319 −0.247841 −0.123921 0.992292i \(-0.539547\pi\)
−0.123921 + 0.992292i \(0.539547\pi\)
\(60\) 217.295 + 157.426i 0.467543 + 0.338728i
\(61\) 420.338 0.882274 0.441137 0.897440i \(-0.354575\pi\)
0.441137 + 0.897440i \(0.354575\pi\)
\(62\) 8.03707 6.59912i 0.0164630 0.0135176i
\(63\) 153.303 + 153.303i 0.306576 + 0.306576i
\(64\) 283.831 426.127i 0.554357 0.832279i
\(65\) 149.261 + 68.6541i 0.284823 + 0.131008i
\(66\) −529.144 51.9863i −0.986866 0.0969557i
\(67\) 505.727 505.727i 0.922155 0.922155i −0.0750268 0.997182i \(-0.523904\pi\)
0.997182 + 0.0750268i \(0.0239042\pi\)
\(68\) 148.623 99.4111i 0.265047 0.177285i
\(69\) 614.400i 1.07196i
\(70\) 193.154 + 736.871i 0.329805 + 1.25819i
\(71\) 713.401i 1.19247i 0.802811 + 0.596233i \(0.203337\pi\)
−0.802811 + 0.596233i \(0.796663\pi\)
\(72\) 96.1293 + 179.530i 0.157347 + 0.293859i
\(73\) 541.439 541.439i 0.868091 0.868091i −0.124170 0.992261i \(-0.539627\pi\)
0.992261 + 0.124170i \(0.0396268\pi\)
\(74\) 62.0717 631.798i 0.0975093 0.992501i
\(75\) −373.894 28.7771i −0.575648 0.0443053i
\(76\) −63.0820 + 317.942i −0.0952106 + 0.479875i
\(77\) −1067.33 1067.33i −1.57966 1.57966i
\(78\) 79.1256 + 96.3671i 0.114862 + 0.139890i
\(79\) −277.290 −0.394906 −0.197453 0.980312i \(-0.563267\pi\)
−0.197453 + 0.980312i \(0.563267\pi\)
\(80\) −26.7802 + 715.040i −0.0374265 + 0.999299i
\(81\) −81.0000 −0.111111
\(82\) 592.491 + 721.595i 0.797923 + 0.971790i
\(83\) 96.5456 + 96.5456i 0.127678 + 0.127678i 0.768058 0.640380i \(-0.221223\pi\)
−0.640380 + 0.768058i \(0.721223\pi\)
\(84\) −112.514 + 567.086i −0.146146 + 0.736597i
\(85\) −104.422 + 227.024i −0.133249 + 0.289697i
\(86\) 23.3444 237.611i 0.0292708 0.297934i
\(87\) 207.298 207.298i 0.255456 0.255456i
\(88\) −669.279 1249.94i −0.810743 1.51414i
\(89\) 370.942i 0.441795i 0.975297 + 0.220898i \(0.0708987\pi\)
−0.975297 + 0.220898i \(0.929101\pi\)
\(90\) −245.697 143.641i −0.287764 0.168234i
\(91\) 353.986i 0.407778i
\(92\) −1361.84 + 910.908i −1.54328 + 1.03227i
\(93\) −7.79938 + 7.79938i −0.00869632 + 0.00869632i
\(94\) −3.70017 0.363527i −0.00406004 0.000398883i
\(95\) −157.157 424.864i −0.169726 0.458844i
\(96\) −255.414 + 479.245i −0.271542 + 0.509508i
\(97\) 701.220 + 701.220i 0.734001 + 0.734001i 0.971410 0.237409i \(-0.0762982\pi\)
−0.237409 + 0.971410i \(0.576298\pi\)
\(98\) −518.704 + 425.900i −0.534663 + 0.439004i
\(99\) 563.944 0.572511
\(100\) −490.549 871.413i −0.490549 0.871413i
\(101\) 899.521 0.886195 0.443098 0.896473i \(-0.353879\pi\)
0.443098 + 0.896473i \(0.353879\pi\)
\(102\) −146.573 + 120.349i −0.142284 + 0.116827i
\(103\) 680.821 + 680.821i 0.651294 + 0.651294i 0.953305 0.302010i \(-0.0976578\pi\)
−0.302010 + 0.953305i \(0.597658\pi\)
\(104\) −96.2892 + 318.258i −0.0907879 + 0.300075i
\(105\) −280.308 757.794i −0.260526 0.704315i
\(106\) 1533.60 + 150.670i 1.40525 + 0.138060i
\(107\) 1332.72 1332.72i 1.20411 1.20411i 0.231199 0.972907i \(-0.425735\pi\)
0.972907 0.231199i \(-0.0742648\pi\)
\(108\) −120.090 179.539i −0.106997 0.159964i
\(109\) 539.045i 0.473680i −0.971549 0.236840i \(-0.923888\pi\)
0.971549 0.236840i \(-0.0761118\pi\)
\(110\) 1710.61 + 1000.07i 1.48273 + 0.866844i
\(111\) 673.349i 0.575779i
\(112\) −1423.78 + 591.370i −1.20120 + 0.498921i
\(113\) −494.603 + 494.603i −0.411755 + 0.411755i −0.882349 0.470595i \(-0.844039\pi\)
0.470595 + 0.882349i \(0.344039\pi\)
\(114\) 33.6154 342.155i 0.0276173 0.281103i
\(115\) 956.825 2080.23i 0.775864 1.68681i
\(116\) 766.822 + 152.143i 0.613773 + 0.121777i
\(117\) −93.5172 93.5172i −0.0738946 0.0738946i
\(118\) 201.597 + 245.525i 0.157275 + 0.191546i
\(119\) −538.409 −0.414755
\(120\) −45.8856 757.558i −0.0349064 0.576294i
\(121\) −2595.34 −1.94991
\(122\) −754.450 918.845i −0.559875 0.681871i
\(123\) −700.254 700.254i −0.513332 0.513332i
\(124\) −28.8509 5.72423i −0.0208943 0.00414557i
\(125\) 1221.11 + 679.711i 0.873758 + 0.486362i
\(126\) 59.9568 610.272i 0.0423919 0.431487i
\(127\) 458.103 458.103i 0.320079 0.320079i −0.528718 0.848798i \(-0.677327\pi\)
0.848798 + 0.528718i \(0.177327\pi\)
\(128\) −1440.94 + 144.395i −0.995017 + 0.0997098i
\(129\) 253.238i 0.172840i
\(130\) −117.827 449.504i −0.0794935 0.303262i
\(131\) 247.061i 0.164777i −0.996600 0.0823885i \(-0.973745\pi\)
0.996600 0.0823885i \(-0.0262548\pi\)
\(132\) 836.103 + 1250.00i 0.551314 + 0.824232i
\(133\) 690.159 690.159i 0.449958 0.449958i
\(134\) −2013.21 197.790i −1.29788 0.127511i
\(135\) 274.249 + 126.144i 0.174842 + 0.0804203i
\(136\) −484.068 146.455i −0.305209 0.0923413i
\(137\) 503.392 + 503.392i 0.313925 + 0.313925i 0.846428 0.532503i \(-0.178749\pi\)
−0.532503 + 0.846428i \(0.678749\pi\)
\(138\) 1343.06 1102.77i 0.828469 0.680244i
\(139\) −2206.57 −1.34647 −0.673234 0.739429i \(-0.735096\pi\)
−0.673234 + 0.739429i \(0.735096\pi\)
\(140\) 1264.09 1744.81i 0.763108 1.05331i
\(141\) 3.94352 0.00235535
\(142\) 1559.47 1280.46i 0.921605 0.756717i
\(143\) 651.092 + 651.092i 0.380749 + 0.380749i
\(144\) 219.908 532.369i 0.127262 0.308084i
\(145\) −1024.70 + 379.036i −0.586874 + 0.217085i
\(146\) −2155.38 211.757i −1.22178 0.120035i
\(147\) 503.364 503.364i 0.282427 0.282427i
\(148\) −1492.50 + 998.307i −0.828938 + 0.554461i
\(149\) 1256.34i 0.690758i −0.938463 0.345379i \(-0.887750\pi\)
0.938463 0.345379i \(-0.112250\pi\)
\(150\) 608.184 + 868.972i 0.331054 + 0.473008i
\(151\) 2543.35i 1.37069i 0.728217 + 0.685347i \(0.240349\pi\)
−0.728217 + 0.685347i \(0.759651\pi\)
\(152\) 808.235 432.769i 0.431293 0.230935i
\(153\) 142.239 142.239i 0.0751589 0.0751589i
\(154\) −417.436 + 4248.88i −0.218428 + 2.22328i
\(155\) 38.5533 14.2609i 0.0199786 0.00739007i
\(156\) 68.6354 345.932i 0.0352258 0.177543i
\(157\) −502.147 502.147i −0.255259 0.255259i 0.567864 0.823123i \(-0.307770\pi\)
−0.823123 + 0.567864i \(0.807770\pi\)
\(158\) 497.699 + 606.147i 0.250600 + 0.305206i
\(159\) −1634.46 −0.815227
\(160\) 1611.12 1224.86i 0.796065 0.605211i
\(161\) 4933.46 2.41498
\(162\) 145.384 + 177.063i 0.0705090 + 0.0858729i
\(163\) −794.602 794.602i −0.381828 0.381828i 0.489932 0.871761i \(-0.337022\pi\)
−0.871761 + 0.489932i \(0.837022\pi\)
\(164\) 513.940 2590.33i 0.244707 1.23336i
\(165\) −1909.40 878.249i −0.900888 0.414373i
\(166\) 37.7591 384.332i 0.0176547 0.179698i
\(167\) −2202.65 + 2202.65i −1.02064 + 1.02064i −0.0208533 + 0.999783i \(0.506638\pi\)
−0.999783 + 0.0208533i \(0.993362\pi\)
\(168\) 1441.58 771.892i 0.662025 0.354481i
\(169\) 1981.06i 0.901713i
\(170\) 683.692 179.215i 0.308451 0.0808537i
\(171\) 364.657i 0.163076i
\(172\) −561.311 + 375.451i −0.248835 + 0.166441i
\(173\) −1012.89 + 1012.89i −0.445138 + 0.445138i −0.893735 0.448596i \(-0.851924\pi\)
0.448596 + 0.893735i \(0.351924\pi\)
\(174\) −825.219 81.0745i −0.359538 0.0353232i
\(175\) −231.072 + 3002.27i −0.0998139 + 1.29686i
\(176\) −1531.06 + 3706.50i −0.655728 + 1.58743i
\(177\) −238.264 238.264i −0.101181 0.101181i
\(178\) 810.868 665.792i 0.341444 0.280355i
\(179\) −1120.88 −0.468036 −0.234018 0.972232i \(-0.575187\pi\)
−0.234018 + 0.972232i \(0.575187\pi\)
\(180\) 126.999 + 794.903i 0.0525888 + 0.329159i
\(181\) −2751.89 −1.13009 −0.565046 0.825059i \(-0.691142\pi\)
−0.565046 + 0.825059i \(0.691142\pi\)
\(182\) 773.801 635.357i 0.315154 0.258768i
\(183\) 891.671 + 891.671i 0.360187 + 0.360187i
\(184\) 4435.53 + 1341.97i 1.77713 + 0.537672i
\(185\) 1048.63 2279.82i 0.416739 0.906032i
\(186\) 31.0480 + 3.05035i 0.0122395 + 0.00120249i
\(187\) −990.305 + 990.305i −0.387264 + 0.387264i
\(188\) 5.84665 + 8.74094i 0.00226814 + 0.00339095i
\(189\) 650.407i 0.250318i
\(190\) −646.664 + 1106.12i −0.246915 + 0.422348i
\(191\) 655.307i 0.248253i 0.992266 + 0.124127i \(0.0396129\pi\)
−0.992266 + 0.124127i \(0.960387\pi\)
\(192\) 1506.05 301.855i 0.566092 0.113461i
\(193\) −110.876 + 110.876i −0.0413527 + 0.0413527i −0.727481 0.686128i \(-0.759309\pi\)
0.686128 + 0.727481i \(0.259309\pi\)
\(194\) 274.248 2791.44i 0.101494 1.03306i
\(195\) 170.993 + 462.267i 0.0627950 + 0.169762i
\(196\) 1862.01 + 369.436i 0.678574 + 0.134634i
\(197\) 1236.54 + 1236.54i 0.447209 + 0.447209i 0.894426 0.447217i \(-0.147585\pi\)
−0.447217 + 0.894426i \(0.647585\pi\)
\(198\) −1012.20 1232.76i −0.363304 0.442468i
\(199\) 3900.17 1.38932 0.694662 0.719336i \(-0.255554\pi\)
0.694662 + 0.719336i \(0.255554\pi\)
\(200\) −1024.41 + 2636.40i −0.362184 + 0.932107i
\(201\) 2145.62 0.752936
\(202\) −1614.52 1966.32i −0.562363 0.684902i
\(203\) −1664.54 1664.54i −0.575508 0.575508i
\(204\) 526.160 + 104.394i 0.180581 + 0.0358286i
\(205\) 1280.39 + 3461.45i 0.436225 + 1.17931i
\(206\) 266.270 2710.24i 0.0900578 0.916656i
\(207\) −1303.34 + 1303.34i −0.437625 + 0.437625i
\(208\) 868.528 360.746i 0.289527 0.120256i
\(209\) 2538.84i 0.840266i
\(210\) −1153.40 + 1972.88i −0.379010 + 0.648294i
\(211\) 2734.41i 0.892154i −0.894995 0.446077i \(-0.852821\pi\)
0.894995 0.446077i \(-0.147179\pi\)
\(212\) −2423.25 3622.83i −0.785044 1.17367i
\(213\) −1513.35 + 1513.35i −0.486822 + 0.486822i
\(214\) −5305.35 521.230i −1.69470 0.166498i
\(215\) 394.376 857.413i 0.125099 0.271977i
\(216\) −176.920 + 584.763i −0.0557310 + 0.184204i
\(217\) 62.6268 + 62.6268i 0.0195916 + 0.0195916i
\(218\) −1178.33 + 967.514i −0.366087 + 0.300589i
\(219\) 2297.13 0.708793
\(220\) −884.205 5534.34i −0.270969 1.69602i
\(221\) 328.439 0.0999691
\(222\) 1471.92 1208.57i 0.444995 0.365379i
\(223\) −2994.18 2994.18i −0.899127 0.899127i 0.0962315 0.995359i \(-0.469321\pi\)
−0.995359 + 0.0962315i \(0.969321\pi\)
\(224\) 3848.20 + 2050.90i 1.14785 + 0.611748i
\(225\) −732.104 854.195i −0.216920 0.253095i
\(226\) 1968.93 + 193.440i 0.579519 + 0.0569355i
\(227\) 1907.92 1907.92i 0.557856 0.557856i −0.370841 0.928696i \(-0.620930\pi\)
0.928696 + 0.370841i \(0.120930\pi\)
\(228\) −808.275 + 540.640i −0.234778 + 0.157038i
\(229\) 3801.54i 1.09700i −0.836151 0.548500i \(-0.815199\pi\)
0.836151 0.548500i \(-0.184801\pi\)
\(230\) −6264.69 + 1642.15i −1.79601 + 0.470783i
\(231\) 4528.32i 1.28979i
\(232\) −1043.76 1949.32i −0.295373 0.551635i
\(233\) −2260.08 + 2260.08i −0.635462 + 0.635462i −0.949433 0.313970i \(-0.898341\pi\)
0.313970 + 0.949433i \(0.398341\pi\)
\(234\) −36.5747 + 372.276i −0.0102178 + 0.104002i
\(235\) −13.3519 6.14137i −0.00370632 0.00170476i
\(236\) 174.870 881.369i 0.0482333 0.243103i
\(237\) −588.221 588.221i −0.161220 0.161220i
\(238\) 966.372 + 1176.94i 0.263196 + 0.320546i
\(239\) 4255.37 1.15170 0.575851 0.817555i \(-0.304671\pi\)
0.575851 + 0.817555i \(0.304671\pi\)
\(240\) −1573.64 + 1460.02i −0.423242 + 0.392683i
\(241\) −5500.15 −1.47011 −0.735053 0.678009i \(-0.762843\pi\)
−0.735053 + 0.678009i \(0.762843\pi\)
\(242\) 4658.28 + 5673.32i 1.23738 + 1.50700i
\(243\) −171.827 171.827i −0.0453609 0.0453609i
\(244\) −654.428 + 3298.41i −0.171703 + 0.865405i
\(245\) −2488.19 + 920.381i −0.648835 + 0.240004i
\(246\) −273.870 + 2787.60i −0.0709810 + 0.722482i
\(247\) −421.009 + 421.009i −0.108454 + 0.108454i
\(248\) 39.2706 + 73.3414i 0.0100552 + 0.0187790i
\(249\) 409.608i 0.104248i
\(250\) −705.909 3889.30i −0.178582 0.983925i
\(251\) 4640.95i 1.16707i −0.812089 0.583534i \(-0.801669\pi\)
0.812089 0.583534i \(-0.198331\pi\)
\(252\) −1441.65 + 964.293i −0.360378 + 0.241051i
\(253\) 9074.21 9074.21i 2.25490 2.25490i
\(254\) −1823.63 179.165i −0.450492 0.0442590i
\(255\) −703.104 + 260.078i −0.172667 + 0.0638695i
\(256\) 2901.93 + 2890.67i 0.708480 + 0.705731i
\(257\) −2138.06 2138.06i −0.518944 0.518944i 0.398308 0.917252i \(-0.369598\pi\)
−0.917252 + 0.398308i \(0.869598\pi\)
\(258\) 553.571 454.529i 0.133581 0.109681i
\(259\) 5406.81 1.29715
\(260\) −771.117 + 1064.37i −0.183933 + 0.253882i
\(261\) 879.491 0.208579
\(262\) −540.066 + 443.441i −0.127349 + 0.104564i
\(263\) 1976.57 + 1976.57i 0.463423 + 0.463423i 0.899776 0.436353i \(-0.143730\pi\)
−0.436353 + 0.899776i \(0.643730\pi\)
\(264\) 1231.77 4071.28i 0.287159 0.949128i
\(265\) 5533.94 + 2545.40i 1.28282 + 0.590047i
\(266\) −2747.41 269.922i −0.633287 0.0622180i
\(267\) −786.887 + 786.887i −0.180362 + 0.180362i
\(268\) 3181.09 + 4755.83i 0.725059 + 1.08399i
\(269\) 7921.21i 1.79541i 0.440600 + 0.897704i \(0.354766\pi\)
−0.440600 + 0.897704i \(0.645234\pi\)
\(270\) −216.494 825.912i −0.0487979 0.186161i
\(271\) 5348.23i 1.19883i −0.800440 0.599413i \(-0.795401\pi\)
0.800440 0.599413i \(-0.204599\pi\)
\(272\) 548.691 + 1321.02i 0.122313 + 0.294481i
\(273\) −750.917 + 750.917i −0.166475 + 0.166475i
\(274\) 196.877 2003.92i 0.0434080 0.441830i
\(275\) 5097.11 + 5947.14i 1.11770 + 1.30409i
\(276\) −4821.22 956.565i −1.05146 0.208618i
\(277\) 2873.27 + 2873.27i 0.623242 + 0.623242i 0.946359 0.323117i \(-0.104731\pi\)
−0.323117 + 0.946359i \(0.604731\pi\)
\(278\) 3960.51 + 4823.50i 0.854444 + 1.04063i
\(279\) −33.0900 −0.00710052
\(280\) −6082.98 + 368.449i −1.29831 + 0.0786394i
\(281\) −5533.29 −1.17469 −0.587346 0.809336i \(-0.699827\pi\)
−0.587346 + 0.809336i \(0.699827\pi\)
\(282\) −7.07809 8.62041i −0.00149466 0.00182035i
\(283\) 1302.24 + 1302.24i 0.273533 + 0.273533i 0.830521 0.556988i \(-0.188043\pi\)
−0.556988 + 0.830521i \(0.688043\pi\)
\(284\) −5598.08 1110.70i −1.16967 0.232070i
\(285\) 567.893 1234.65i 0.118032 0.256613i
\(286\) 254.643 2591.89i 0.0526481 0.535880i
\(287\) −5622.85 + 5622.85i −1.15647 + 1.15647i
\(288\) −1558.45 + 474.818i −0.318862 + 0.0971491i
\(289\) 4413.45i 0.898320i
\(290\) 2667.76 + 1559.64i 0.540194 + 0.315811i
\(291\) 2975.02i 0.599309i
\(292\) 3405.72 + 5091.67i 0.682551 + 1.02044i
\(293\) −1378.64 + 1378.64i −0.274884 + 0.274884i −0.831063 0.556179i \(-0.812267\pi\)
0.556179 + 0.831063i \(0.312267\pi\)
\(294\) −2003.81 196.866i −0.397498 0.0390526i
\(295\) 435.656 + 1177.77i 0.0859827 + 0.232449i
\(296\) 4861.11 + 1470.73i 0.954547 + 0.288799i
\(297\) 1196.31 + 1196.31i 0.233726 + 0.233726i
\(298\) −2746.31 + 2254.95i −0.533857 + 0.438342i
\(299\) −3009.50 −0.582086
\(300\) 807.935 2889.16i 0.155487 0.556019i
\(301\) 2033.43 0.389386
\(302\) 5559.68 4564.97i 1.05935 0.869816i
\(303\) 1908.17 + 1908.17i 0.361788 + 0.361788i
\(304\) −2396.69 990.014i −0.452170 0.186780i
\(305\) −1630.39 4407.64i −0.306084 0.827478i
\(306\) −566.229 55.6297i −0.105782 0.0103926i
\(307\) −4613.74 + 4613.74i −0.857720 + 0.857720i −0.991069 0.133349i \(-0.957427\pi\)
0.133349 + 0.991069i \(0.457427\pi\)
\(308\) 10037.2 6713.67i 1.85688 1.24204i
\(309\) 2888.48i 0.531779i
\(310\) −100.372 58.6800i −0.0183895 0.0107510i
\(311\) 8196.69i 1.49451i −0.664539 0.747254i \(-0.731372\pi\)
0.664539 0.747254i \(-0.268628\pi\)
\(312\) −879.388 + 470.867i −0.159569 + 0.0854410i
\(313\) −6452.49 + 6452.49i −1.16523 + 1.16523i −0.181913 + 0.983315i \(0.558229\pi\)
−0.983315 + 0.181913i \(0.941771\pi\)
\(314\) −196.390 + 1998.96i −0.0352960 + 0.359261i
\(315\) 1012.90 2202.15i 0.181176 0.393895i
\(316\) 431.716 2175.91i 0.0768541 0.387356i
\(317\) −4192.10 4192.10i −0.742750 0.742750i 0.230357 0.973106i \(-0.426011\pi\)
−0.973106 + 0.230357i \(0.926011\pi\)
\(318\) 2933.64 + 3572.88i 0.517328 + 0.630053i
\(319\) −6123.26 −1.07472
\(320\) −5569.26 1323.40i −0.972909 0.231188i
\(321\) 5654.27 0.983148
\(322\) −8854.90 10784.4i −1.53250 1.86643i
\(323\) −640.350 640.350i −0.110310 0.110310i
\(324\) 126.110 635.610i 0.0216237 0.108987i
\(325\) 140.958 1831.43i 0.0240583 0.312584i
\(326\) −310.770 + 3163.18i −0.0527974 + 0.537400i
\(327\) 1143.49 1143.49i 0.193379 0.193379i
\(328\) −6584.84 + 3525.84i −1.10850 + 0.593543i
\(329\) 31.6654i 0.00530629i
\(330\) 1507.29 + 5750.23i 0.251436 + 0.959211i
\(331\) 3549.67i 0.589449i 0.955582 + 0.294725i \(0.0952279\pi\)
−0.955582 + 0.294725i \(0.904772\pi\)
\(332\) −907.910 + 607.284i −0.150084 + 0.100389i
\(333\) −1428.39 + 1428.39i −0.235061 + 0.235061i
\(334\) 8768.38 + 861.459i 1.43648 + 0.141129i
\(335\) −7264.62 3341.44i −1.18480 0.544962i
\(336\) −4274.77 1765.80i −0.694071 0.286704i
\(337\) 4054.55 + 4054.55i 0.655388 + 0.655388i 0.954285 0.298898i \(-0.0966189\pi\)
−0.298898 + 0.954285i \(0.596619\pi\)
\(338\) 4330.54 3555.74i 0.696894 0.572210i
\(339\) −2098.42 −0.336196
\(340\) −1618.89 1172.86i −0.258226 0.187080i
\(341\) 230.381 0.0365861
\(342\) 797.129 654.511i 0.126035 0.103485i
\(343\) 1800.66 + 1800.66i 0.283459 + 0.283459i
\(344\) 1828.20 + 553.124i 0.286541 + 0.0866931i
\(345\) 6442.57 2383.11i 1.00538 0.371890i
\(346\) 4032.16 + 396.144i 0.626504 + 0.0615516i
\(347\) −5172.84 + 5172.84i −0.800266 + 0.800266i −0.983137 0.182871i \(-0.941461\pi\)
0.182871 + 0.983137i \(0.441461\pi\)
\(348\) 1303.93 + 1949.42i 0.200856 + 0.300287i
\(349\) 1490.13i 0.228553i 0.993449 + 0.114276i \(0.0364549\pi\)
−0.993449 + 0.114276i \(0.963545\pi\)
\(350\) 6977.60 4883.55i 1.06562 0.745819i
\(351\) 396.760i 0.0603347i
\(352\) 10850.3 3305.82i 1.64297 0.500570i
\(353\) 7105.54 7105.54i 1.07136 1.07136i 0.0741092 0.997250i \(-0.476389\pi\)
0.997250 0.0741092i \(-0.0236114\pi\)
\(354\) −93.1853 + 948.489i −0.0139908 + 0.142406i
\(355\) 7480.69 2767.11i 1.11841 0.413698i
\(356\) −2910.80 577.523i −0.433348 0.0859794i
\(357\) −1142.14 1142.14i −0.169323 0.169323i
\(358\) 2011.83 + 2450.21i 0.297007 + 0.361724i
\(359\) 10028.6 1.47435 0.737173 0.675704i \(-0.236160\pi\)
0.737173 + 0.675704i \(0.236160\pi\)
\(360\) 1509.69 1704.36i 0.221021 0.249522i
\(361\) −5217.33 −0.760655
\(362\) 4939.28 + 6015.55i 0.717135 + 0.873399i
\(363\) −5505.54 5505.54i −0.796049 0.796049i
\(364\) −2777.74 551.123i −0.399981 0.0793591i
\(365\) −7777.61 3577.40i −1.11534 0.513012i
\(366\) 348.734 3549.59i 0.0498049 0.506941i
\(367\) −516.439 + 516.439i −0.0734547 + 0.0734547i −0.742880 0.669425i \(-0.766541\pi\)
0.669425 + 0.742880i \(0.266541\pi\)
\(368\) −5027.68 12104.6i −0.712190 1.71466i
\(369\) 2970.93i 0.419134i
\(370\) −6865.77 + 1799.71i −0.964687 + 0.252871i
\(371\) 13124.3i 1.83660i
\(372\) −49.0591 73.3450i −0.00683763 0.0102225i
\(373\) 324.011 324.011i 0.0449777 0.0449777i −0.684260 0.729238i \(-0.739875\pi\)
0.729238 + 0.684260i \(0.239875\pi\)
\(374\) 3942.24 + 387.310i 0.545049 + 0.0535489i
\(375\) 1148.49 + 4032.26i 0.158154 + 0.555266i
\(376\) 8.61344 28.4694i 0.00118139 0.00390478i
\(377\) 1015.40 + 1015.40i 0.138716 + 0.138716i
\(378\) 1421.77 1167.39i 0.193460 0.158847i
\(379\) −9665.34 −1.30996 −0.654980 0.755646i \(-0.727323\pi\)
−0.654980 + 0.755646i \(0.727323\pi\)
\(380\) 3578.61 571.744i 0.483102 0.0771838i
\(381\) 1943.57 0.261344
\(382\) 1432.48 1176.19i 0.191864 0.157537i
\(383\) −5997.35 5997.35i −0.800131 0.800131i 0.182984 0.983116i \(-0.441424\pi\)
−0.983116 + 0.182984i \(0.941424\pi\)
\(384\) −3363.00 2750.38i −0.446920 0.365507i
\(385\) −7052.10 + 15331.9i −0.933527 + 2.02958i
\(386\) 441.381 + 43.3639i 0.0582013 + 0.00571805i
\(387\) −537.200 + 537.200i −0.0705617 + 0.0705617i
\(388\) −6594.23 + 4410.76i −0.862813 + 0.577120i
\(389\) 2994.42i 0.390291i 0.980774 + 0.195145i \(0.0625178\pi\)
−0.980774 + 0.195145i \(0.937482\pi\)
\(390\) 703.592 1203.49i 0.0913533 0.156259i
\(391\) 4577.42i 0.592046i
\(392\) −2534.48 4733.38i −0.326558 0.609877i
\(393\) 524.095 524.095i 0.0672699 0.0672699i
\(394\) 483.614 4922.48i 0.0618379 0.629418i
\(395\) 1075.54 + 2907.65i 0.137003 + 0.370379i
\(396\) −878.010 + 4425.29i −0.111418 + 0.561564i
\(397\) −626.953 626.953i −0.0792592 0.0792592i 0.666366 0.745625i \(-0.267849\pi\)
−0.745625 + 0.666366i \(0.767849\pi\)
\(398\) −7000.28 8525.64i −0.881639 1.07375i
\(399\) 2928.10 0.367389
\(400\) 7601.76 2492.65i 0.950220 0.311581i
\(401\) 3530.52 0.439665 0.219833 0.975538i \(-0.429449\pi\)
0.219833 + 0.975538i \(0.429449\pi\)
\(402\) −3851.10 4690.25i −0.477799 0.581911i
\(403\) −38.2034 38.2034i −0.00472221 0.00472221i
\(404\) −1400.47 + 7058.58i −0.172466 + 0.869251i
\(405\) 314.179 + 849.362i 0.0385474 + 0.104210i
\(406\) −651.006 + 6626.28i −0.0795785 + 0.809992i
\(407\) 9944.85 9944.85i 1.21117 1.21117i
\(408\) −716.185 1337.54i −0.0869030 0.162299i
\(409\) 10887.8i 1.31631i −0.752884 0.658153i \(-0.771338\pi\)
0.752884 0.658153i \(-0.228662\pi\)
\(410\) 5268.48 9011.72i 0.634614 1.08551i
\(411\) 2135.71i 0.256319i
\(412\) −6402.41 + 4282.45i −0.765592 + 0.512091i
\(413\) −1913.19 + 1913.19i −0.227947 + 0.227947i
\(414\) 5188.38 + 509.738i 0.615930 + 0.0605126i
\(415\) 637.896 1386.85i 0.0754532 0.164043i
\(416\) −2347.47 1251.08i −0.276669 0.147451i
\(417\) −4680.85 4680.85i −0.549694 0.549694i
\(418\) −5549.83 + 4556.89i −0.649405 + 0.533217i
\(419\) −6020.00 −0.701901 −0.350950 0.936394i \(-0.614141\pi\)
−0.350950 + 0.936394i \(0.614141\pi\)
\(420\) 6382.85 1019.77i 0.741551 0.118475i
\(421\) 5018.38 0.580952 0.290476 0.956882i \(-0.406186\pi\)
0.290476 + 0.956882i \(0.406186\pi\)
\(422\) −5977.33 + 4907.90i −0.689507 + 0.566144i
\(423\) 8.36547 + 8.36547i 0.000961567 + 0.000961567i
\(424\) −3569.99 + 11799.6i −0.408901 + 1.35151i
\(425\) 2785.59 + 214.396i 0.317932 + 0.0244700i
\(426\) 6024.40 + 591.874i 0.685172 + 0.0673154i
\(427\) 7159.87 7159.87i 0.811453 0.811453i
\(428\) 8383.01 + 12532.9i 0.946748 + 1.41542i
\(429\) 2762.35i 0.310880i
\(430\) −2582.13 + 676.848i −0.289584 + 0.0759081i
\(431\) 3250.22i 0.363242i 0.983369 + 0.181621i \(0.0581344\pi\)
−0.983369 + 0.181621i \(0.941866\pi\)
\(432\) 1595.82 662.828i 0.177729 0.0738202i
\(433\) −1386.91 + 1386.91i −0.153928 + 0.153928i −0.779870 0.625942i \(-0.784715\pi\)
0.625942 + 0.779870i \(0.284715\pi\)
\(434\) 24.4934 249.307i 0.00270904 0.0275740i
\(435\) −2977.77 1369.66i −0.328215 0.150966i
\(436\) 4229.91 + 839.244i 0.464623 + 0.0921846i
\(437\) 5867.56 + 5867.56i 0.642296 + 0.642296i
\(438\) −4123.04 5021.45i −0.449787 0.547795i
\(439\) 2636.87 0.286676 0.143338 0.989674i \(-0.454216\pi\)
0.143338 + 0.989674i \(0.454216\pi\)
\(440\) −10510.8 + 11866.2i −1.13883 + 1.28568i
\(441\) 2135.59 0.230600
\(442\) −589.503 717.956i −0.0634385 0.0772617i
\(443\) −1138.08 1138.08i −0.122059 0.122059i 0.643439 0.765498i \(-0.277507\pi\)
−0.765498 + 0.643439i \(0.777507\pi\)
\(444\) −5283.80 1048.34i −0.564770 0.112055i
\(445\) 3889.68 1438.79i 0.414357 0.153270i
\(446\) −1171.03 + 11919.4i −0.124327 + 1.26547i
\(447\) 2665.09 2665.09i 0.282001 0.282001i
\(448\) −2423.81 12093.1i −0.255612 1.27533i
\(449\) 10622.1i 1.11645i 0.829689 + 0.558225i \(0.188518\pi\)
−0.829689 + 0.558225i \(0.811482\pi\)
\(450\) −553.214 + 3133.52i −0.0579528 + 0.328257i
\(451\) 20684.4i 2.15963i
\(452\) −3111.11 4651.22i −0.323749 0.484015i
\(453\) −5395.26 + 5395.26i −0.559583 + 0.559583i
\(454\) −7595.12 746.190i −0.785147 0.0771376i
\(455\) 3711.88 1373.02i 0.382452 0.141469i
\(456\) 2632.57 + 796.485i 0.270354 + 0.0817957i
\(457\) −3598.01 3598.01i −0.368289 0.368289i 0.498564 0.866853i \(-0.333861\pi\)
−0.866853 + 0.498564i \(0.833861\pi\)
\(458\) −8310.05 + 6823.26i −0.847823 + 0.696135i
\(459\) 603.468 0.0613670
\(460\) 14834.0 + 10747.0i 1.50356 + 1.08931i
\(461\) −3947.37 −0.398801 −0.199400 0.979918i \(-0.563899\pi\)
−0.199400 + 0.979918i \(0.563899\pi\)
\(462\) −9898.75 + 8127.72i −0.996822 + 0.818476i
\(463\) 1878.89 + 1878.89i 0.188595 + 0.188595i 0.795088 0.606494i \(-0.207424\pi\)
−0.606494 + 0.795088i \(0.707424\pi\)
\(464\) −2387.74 + 5780.41i −0.238897 + 0.578338i
\(465\) 112.036 + 51.5321i 0.0111732 + 0.00513923i
\(466\) 8997.00 + 883.920i 0.894373 + 0.0878687i
\(467\) 12538.2 12538.2i 1.24239 1.24239i 0.283389 0.959005i \(-0.408541\pi\)
0.959005 0.283389i \(-0.0914587\pi\)
\(468\) 879.431 588.235i 0.0868626 0.0581008i
\(469\) 17228.7i 1.69626i
\(470\) 10.5401 + 40.2099i 0.00103442 + 0.00394626i
\(471\) 2130.43i 0.208418i
\(472\) −2240.51 + 1199.68i −0.218491 + 0.116991i
\(473\) 3740.13 3740.13i 0.363576 0.363576i
\(474\) −230.054 + 2341.61i −0.0222927 + 0.226907i
\(475\) −3845.54 + 3295.89i −0.371464 + 0.318370i
\(476\) 838.253 4224.91i 0.0807170 0.406825i
\(477\) −3467.21 3467.21i −0.332815 0.332815i
\(478\) −7637.81 9302.09i −0.730848 0.890100i
\(479\) −5432.04 −0.518155 −0.259077 0.965857i \(-0.583418\pi\)
−0.259077 + 0.965857i \(0.583418\pi\)
\(480\) 6016.03 + 819.383i 0.572069 + 0.0779157i
\(481\) −3298.25 −0.312655
\(482\) 9872.03 + 12023.1i 0.932902 + 1.13618i
\(483\) 10465.5 + 10465.5i 0.985910 + 0.985910i
\(484\) 4040.70 20365.7i 0.379480 1.91263i
\(485\) 4633.10 10072.8i 0.433770 0.943058i
\(486\) −67.2017 + 684.015i −0.00627229 + 0.0638427i
\(487\) 8299.24 8299.24i 0.772226 0.772226i −0.206269 0.978495i \(-0.566132\pi\)
0.978495 + 0.206269i \(0.0661322\pi\)
\(488\) 8384.82 4489.64i 0.777793 0.416468i
\(489\) 3371.21i 0.311762i
\(490\) 6477.89 + 3787.14i 0.597227 + 0.349154i
\(491\) 8485.31i 0.779912i 0.920834 + 0.389956i \(0.127510\pi\)
−0.920834 + 0.389956i \(0.872490\pi\)
\(492\) 6585.16 4404.69i 0.603418 0.403615i
\(493\) −1544.42 + 1544.42i −0.141089 + 0.141089i
\(494\) 1675.97 + 164.657i 0.152642 + 0.0149965i
\(495\) −2187.40 5913.50i −0.198619 0.536953i
\(496\) 89.8365 217.482i 0.00813262 0.0196880i
\(497\) 12151.8 + 12151.8i 1.09675 + 1.09675i
\(498\) 895.390 735.192i 0.0805691 0.0661541i
\(499\) 7884.62 0.707343 0.353672 0.935370i \(-0.384933\pi\)
0.353672 + 0.935370i \(0.384933\pi\)
\(500\) −7234.88 + 8523.88i −0.647108 + 0.762399i
\(501\) −9345.05 −0.833346
\(502\) −10145.0 + 8329.89i −0.901976 + 0.740600i
\(503\) 4629.69 + 4629.69i 0.410393 + 0.410393i 0.881875 0.471483i \(-0.156281\pi\)
−0.471483 + 0.881875i \(0.656281\pi\)
\(504\) 4695.48 + 1420.62i 0.414987 + 0.125555i
\(505\) −3489.02 9432.34i −0.307444 0.831156i
\(506\) −36122.9 3548.93i −3.17364 0.311797i
\(507\) −4202.47 + 4202.47i −0.368123 + 0.368123i
\(508\) 2881.53 + 4307.98i 0.251668 + 0.376251i
\(509\) 3355.70i 0.292217i −0.989269 0.146109i \(-0.953325\pi\)
0.989269 0.146109i \(-0.0466749\pi\)
\(510\) 1830.50 + 1070.16i 0.158933 + 0.0929164i
\(511\) 18445.3i 1.59682i
\(512\) 1110.33 11531.9i 0.0958404 0.995397i
\(513\) −773.555 + 773.555i −0.0665756 + 0.0665756i
\(514\) −836.199 + 8511.27i −0.0717571 + 0.730382i
\(515\) 4498.32 9779.80i 0.384893 0.836795i
\(516\) −1987.17 394.269i −0.169536 0.0336371i
\(517\) −58.2427 58.2427i −0.00495457 0.00495457i
\(518\) −9704.50 11819.1i −0.823149 1.00251i
\(519\) −4297.35 −0.363454
\(520\) 3710.72 224.760i 0.312935 0.0189546i
\(521\) 9339.67 0.785371 0.392686 0.919673i \(-0.371546\pi\)
0.392686 + 0.919673i \(0.371546\pi\)
\(522\) −1578.57 1922.54i −0.132360 0.161202i
\(523\) −11258.5 11258.5i −0.941300 0.941300i 0.0570698 0.998370i \(-0.481824\pi\)
−0.998370 + 0.0570698i \(0.981824\pi\)
\(524\) 1938.69 + 384.651i 0.161626 + 0.0320678i
\(525\) −6858.95 + 5878.59i −0.570189 + 0.488691i
\(526\) 773.037 7868.38i 0.0640799 0.652239i
\(527\) 58.1071 58.1071i 0.00480301 0.00480301i
\(528\) −11110.5 + 4614.79i −0.915766 + 0.380366i
\(529\) 29776.0i 2.44728i
\(530\) −4368.54 16665.7i −0.358032 1.36587i
\(531\) 1010.87i 0.0826138i
\(532\) 4341.19 + 6490.22i 0.353787 + 0.528922i
\(533\) 3430.03 3430.03i 0.278745 0.278745i
\(534\) 3132.47 + 307.753i 0.253849 + 0.0249396i
\(535\) −19144.2 8805.58i −1.54706 0.711586i
\(536\) 4686.46 15489.8i 0.377657 1.24824i
\(537\) −2377.74 2377.74i −0.191075 0.191075i
\(538\) 17315.5 14217.5i 1.38759 1.13933i
\(539\) −14868.6 −1.18819
\(540\) −1416.84 + 1955.65i −0.112909 + 0.155848i
\(541\) 10460.0 0.831259 0.415629 0.909534i \(-0.363561\pi\)
0.415629 + 0.909534i \(0.363561\pi\)
\(542\) −11691.1 + 9599.36i −0.926520 + 0.760752i
\(543\) −5837.65 5837.65i −0.461358 0.461358i
\(544\) 1902.89 3570.48i 0.149974 0.281403i
\(545\) −5652.40 + 2090.82i −0.444261 + 0.164332i
\(546\) 2989.27 + 293.684i 0.234302 + 0.0230193i
\(547\) 2166.76 2166.76i 0.169367 0.169367i −0.617334 0.786701i \(-0.711787\pi\)
0.786701 + 0.617334i \(0.211787\pi\)
\(548\) −4733.88 + 3166.40i −0.369017 + 0.246829i
\(549\) 3783.04i 0.294091i
\(550\) 3851.63 21816.4i 0.298607 1.69137i
\(551\) 3959.42i 0.306128i
\(552\) 6562.43 + 12255.9i 0.506006 + 0.945014i
\(553\) −4723.25 + 4723.25i −0.363206 + 0.363206i
\(554\) 1123.74 11438.0i 0.0861790 0.877175i
\(555\) 7060.71 2611.76i 0.540019 0.199753i
\(556\) 3435.44 17315.1i 0.262041 1.32072i
\(557\) −10496.9 10496.9i −0.798503 0.798503i 0.184356 0.982859i \(-0.440980\pi\)
−0.982859 + 0.184356i \(0.940980\pi\)
\(558\) 59.3921 + 72.3336i 0.00450585 + 0.00548768i
\(559\) −1240.43 −0.0938543
\(560\) 11723.6 + 12635.9i 0.884662 + 0.953506i
\(561\) −4201.51 −0.316199
\(562\) 9931.51 + 12095.6i 0.745437 + 0.907868i
\(563\) 11590.7 + 11590.7i 0.867656 + 0.867656i 0.992213 0.124556i \(-0.0397507\pi\)
−0.124556 + 0.992213i \(0.539751\pi\)
\(564\) −6.13970 + 30.9450i −0.000458383 + 0.00231032i
\(565\) 7104.82 + 3267.94i 0.529030 + 0.243333i
\(566\) 509.306 5183.99i 0.0378229 0.384981i
\(567\) −1379.72 + 1379.72i −0.102192 + 0.102192i
\(568\) 7619.86 + 14230.8i 0.562891 + 1.05125i
\(569\) 1652.56i 0.121756i −0.998145 0.0608778i \(-0.980610\pi\)
0.998145 0.0608778i \(-0.0193900\pi\)
\(570\) −3718.21 + 974.645i −0.273226 + 0.0716200i
\(571\) 25725.5i 1.88543i 0.333604 + 0.942713i \(0.391735\pi\)
−0.333604 + 0.942713i \(0.608265\pi\)
\(572\) −6122.84 + 4095.46i −0.447568 + 0.299370i
\(573\) −1390.12 + 1390.12i −0.101349 + 0.101349i
\(574\) 22383.6 + 2199.10i 1.62766 + 0.159911i
\(575\) −25524.5 1964.52i −1.85121 0.142480i
\(576\) 3835.14 + 2554.48i 0.277426 + 0.184786i
\(577\) −14294.1 14294.1i −1.03132 1.03132i −0.999493 0.0318249i \(-0.989868\pi\)
−0.0318249 0.999493i \(-0.510132\pi\)
\(578\) −9647.65 + 7921.55i −0.694273 + 0.570057i
\(579\) −470.409 −0.0337643
\(580\) −1378.95 8630.99i −0.0987202 0.617900i
\(581\) 3289.04 0.234858
\(582\) 6503.30 5339.77i 0.463180 0.380310i
\(583\) 24139.7 + 24139.7i 1.71486 + 1.71486i
\(584\) 5017.40 16583.7i 0.355516 1.17506i
\(585\) −617.887 + 1343.35i −0.0436692 + 0.0949411i
\(586\) 5488.14 + 539.188i 0.386882 + 0.0380096i
\(587\) −10178.4 + 10178.4i −0.715689 + 0.715689i −0.967719 0.252030i \(-0.918902\pi\)
0.252030 + 0.967719i \(0.418902\pi\)
\(588\) 3166.22 + 4733.61i 0.222063 + 0.331991i
\(589\) 148.969i 0.0104213i
\(590\) 1792.62 3066.27i 0.125086 0.213960i
\(591\) 5246.21i 0.365144i
\(592\) −5510.06 13266.0i −0.382538 0.920994i
\(593\) 12325.9 12325.9i 0.853564 0.853564i −0.137006 0.990570i \(-0.543748\pi\)
0.990570 + 0.137006i \(0.0437479\pi\)
\(594\) 467.877 4762.30i 0.0323186 0.328955i
\(595\) 2088.35 + 5645.73i 0.143889 + 0.388996i
\(596\) 9858.51 + 1956.00i 0.677551 + 0.134431i
\(597\) 8273.51 + 8273.51i 0.567189 + 0.567189i
\(598\) 5401.64 + 6578.66i 0.369381 + 0.449869i
\(599\) 10021.9 0.683609 0.341805 0.939771i \(-0.388962\pi\)
0.341805 + 0.939771i \(0.388962\pi\)
\(600\) −7765.74 + 3419.54i −0.528392 + 0.232670i
\(601\) −2297.81 −0.155956 −0.0779782 0.996955i \(-0.524846\pi\)
−0.0779782 + 0.996955i \(0.524846\pi\)
\(602\) −3649.74 4445.02i −0.247097 0.300939i
\(603\) 4551.54 + 4551.54i 0.307385 + 0.307385i
\(604\) −19957.8 3959.76i −1.34449 0.266756i
\(605\) 10066.7 + 27214.6i 0.676477 + 1.82881i
\(606\) 746.289 7596.12i 0.0500263 0.509194i
\(607\) −15322.1 + 15322.1i −1.02455 + 1.02455i −0.0248627 + 0.999691i \(0.507915\pi\)
−0.999691 + 0.0248627i \(0.992085\pi\)
\(608\) 2137.60 + 7016.04i 0.142584 + 0.467990i
\(609\) 7062.07i 0.469900i
\(610\) −6708.64 + 11475.1i −0.445287 + 0.761661i
\(611\) 19.3164i 0.00127898i
\(612\) 894.700 + 1337.61i 0.0590950 + 0.0883489i
\(613\) 12293.1 12293.1i 0.809974 0.809974i −0.174655 0.984630i \(-0.555881\pi\)
0.984630 + 0.174655i \(0.0558811\pi\)
\(614\) 18366.5 + 1804.44i 1.20719 + 0.118601i
\(615\) −4626.72 + 10058.9i −0.303362 + 0.659538i
\(616\) −32691.2 9890.76i −2.13826 0.646932i
\(617\) 5422.96 + 5422.96i 0.353841 + 0.353841i 0.861537 0.507695i \(-0.169502\pi\)
−0.507695 + 0.861537i \(0.669502\pi\)
\(618\) 6314.12 5184.43i 0.410989 0.337457i
\(619\) −20797.3 −1.35042 −0.675212 0.737623i \(-0.735948\pi\)
−0.675212 + 0.737623i \(0.735948\pi\)
\(620\) 51.8816 + 324.732i 0.00336067 + 0.0210348i
\(621\) −5529.60 −0.357319
\(622\) −17917.7 + 14712.0i −1.15504 + 0.948386i
\(623\) 6318.49 + 6318.49i 0.406332 + 0.406332i
\(624\) 2607.68 + 1077.17i 0.167293 + 0.0691046i
\(625\) 2391.02 15441.0i 0.153025 0.988222i
\(626\) 25686.3 + 2523.58i 1.63998 + 0.161122i
\(627\) 5385.70 5385.70i 0.343037 0.343037i
\(628\) 4722.16 3158.57i 0.300055 0.200702i
\(629\) 5016.60i 0.318005i
\(630\) −6631.84 + 1738.39i −0.419395 + 0.109935i
\(631\) 12072.4i 0.761641i −0.924649 0.380820i \(-0.875642\pi\)
0.924649 0.380820i \(-0.124358\pi\)
\(632\) −5531.33 + 2961.75i −0.348140 + 0.186411i
\(633\) 5800.56 5800.56i 0.364220 0.364220i
\(634\) −1639.53 + 16688.0i −0.102704 + 1.04537i
\(635\) −6580.52 3026.78i −0.411244 0.189156i
\(636\) 2544.71 12825.7i 0.158654 0.799640i
\(637\) 2465.61 + 2465.61i 0.153361 + 0.153361i
\(638\) 10990.4 + 13385.2i 0.681999 + 0.830606i
\(639\) −6420.61 −0.397489
\(640\) 7103.16 + 14549.5i 0.438714 + 0.898627i
\(641\) −11180.1 −0.688901 −0.344451 0.938804i \(-0.611935\pi\)
−0.344451 + 0.938804i \(0.611935\pi\)
\(642\) −10148.7 12360.0i −0.623887 0.759832i
\(643\) −10929.6 10929.6i −0.670331 0.670331i 0.287461 0.957792i \(-0.407189\pi\)
−0.957792 + 0.287461i \(0.907189\pi\)
\(644\) −7680.95 + 38713.1i −0.469987 + 2.36880i
\(645\) 2655.45 982.249i 0.162106 0.0599628i
\(646\) −250.442 + 2549.13i −0.0152531 + 0.155254i
\(647\) −9379.37 + 9379.37i −0.569925 + 0.569925i −0.932107 0.362183i \(-0.882032\pi\)
0.362183 + 0.932107i \(0.382032\pi\)
\(648\) −1615.77 + 865.164i −0.0979530 + 0.0524488i
\(649\) 7037.94i 0.425676i
\(650\) −4256.46 + 2979.05i −0.256849 + 0.179766i
\(651\) 265.703i 0.0159965i
\(652\) 7472.40 4998.15i 0.448837 0.300219i
\(653\) −14721.9 + 14721.9i −0.882256 + 0.882256i −0.993764 0.111508i \(-0.964432\pi\)
0.111508 + 0.993764i \(0.464432\pi\)
\(654\) −4552.03 447.219i −0.272169 0.0267395i
\(655\) −2590.67 + 958.287i −0.154543 + 0.0571655i
\(656\) 19526.3 + 8065.82i 1.16215 + 0.480057i
\(657\) 4872.95 + 4872.95i 0.289364 + 0.289364i
\(658\) −69.2195 + 56.8351i −0.00410100 + 0.00336727i
\(659\) 14163.0 0.837195 0.418597 0.908172i \(-0.362522\pi\)
0.418597 + 0.908172i \(0.362522\pi\)
\(660\) 9864.42 13615.8i 0.581776 0.803021i
\(661\) −20489.6 −1.20568 −0.602840 0.797862i \(-0.705964\pi\)
−0.602840 + 0.797862i \(0.705964\pi\)
\(662\) 7759.47 6371.19i 0.455560 0.374053i
\(663\) 696.723 + 696.723i 0.0408122 + 0.0408122i
\(664\) 2957.08 + 894.667i 0.172827 + 0.0522889i
\(665\) −9913.93 4560.02i −0.578114 0.265910i
\(666\) 5686.18 + 558.645i 0.330834 + 0.0325031i
\(667\) 14151.5 14151.5i 0.821514 0.821514i
\(668\) −13855.0 20713.6i −0.802492 1.19975i
\(669\) 12703.2i 0.734135i
\(670\) 5734.74 + 21877.7i 0.330675 + 1.26150i
\(671\) 26338.6i 1.51533i
\(672\) 3812.66 + 12513.9i 0.218864 + 0.718354i
\(673\) −6670.44 + 6670.44i −0.382060 + 0.382060i −0.871844 0.489784i \(-0.837076\pi\)
0.489784 + 0.871844i \(0.337076\pi\)
\(674\) 1585.74 16140.5i 0.0906238 0.922417i
\(675\) 258.994 3365.05i 0.0147684 0.191883i
\(676\) −15545.5 3084.33i −0.884472 0.175486i
\(677\) 2597.70 + 2597.70i 0.147471 + 0.147471i 0.776987 0.629517i \(-0.216747\pi\)
−0.629517 + 0.776987i \(0.716747\pi\)
\(678\) 3766.38 + 4587.08i 0.213344 + 0.259831i
\(679\) 23888.6 1.35016
\(680\) 341.858 + 5643.98i 0.0192789 + 0.318289i
\(681\) 8094.63 0.455487
\(682\) −413.504 503.606i −0.0232168 0.0282758i
\(683\) −6038.66 6038.66i −0.338306 0.338306i 0.517424 0.855729i \(-0.326891\pi\)
−0.855729 + 0.517424i \(0.826891\pi\)
\(684\) −2861.48 567.738i −0.159958 0.0317369i
\(685\) 3326.02 7231.09i 0.185519 0.403337i
\(686\) 704.240 7168.12i 0.0391953 0.398951i
\(687\) 8064.29 8064.29i 0.447848 0.447848i
\(688\) −2072.27 4989.17i −0.114832 0.276469i
\(689\) 8006.02i 0.442678i
\(690\) −16772.9 9805.90i −0.925413 0.541020i
\(691\) 14390.7i 0.792256i −0.918195 0.396128i \(-0.870354\pi\)
0.918195 0.396128i \(-0.129646\pi\)
\(692\) −6371.24 9525.21i −0.349997 0.523257i
\(693\) 9606.01 9606.01i 0.526554 0.526554i
\(694\) 20592.2 + 2023.10i 1.12632 + 0.110657i
\(695\) 8558.76 + 23138.0i 0.467125 + 1.26284i
\(696\) 1920.99 6349.30i 0.104619 0.345790i
\(697\) 5217.05 + 5217.05i 0.283515 + 0.283515i
\(698\) 3257.38 2674.59i 0.176638 0.145035i
\(699\) −9588.70 −0.518853
\(700\) −23199.1 6487.49i −1.25264 0.350292i
\(701\) −7855.35 −0.423242 −0.211621 0.977352i \(-0.567874\pi\)
−0.211621 + 0.977352i \(0.567874\pi\)
\(702\) −867.304 + 712.131i −0.0466300 + 0.0382872i
\(703\) 6430.53 + 6430.53i 0.344996 + 0.344996i
\(704\) −26701.3 17785.0i −1.42947 0.952126i
\(705\) −15.2959 41.3516i −0.000817133 0.00220906i
\(706\) −28286.0 2778.99i −1.50787 0.148142i
\(707\) 15322.1 15322.1i 0.815059 0.815059i
\(708\) 2240.62 1498.71i 0.118937 0.0795551i
\(709\) 30138.0i 1.59641i 0.602383 + 0.798207i \(0.294218\pi\)
−0.602383 + 0.798207i \(0.705782\pi\)
\(710\) −19475.6 11386.0i −1.02945 0.601842i
\(711\) 2495.61i 0.131635i
\(712\) 3962.05 + 7399.49i 0.208545 + 0.389477i
\(713\) −532.438 + 532.438i −0.0279663 + 0.0279663i
\(714\) −446.691 + 4546.66i −0.0234132 + 0.238312i
\(715\) 4301.90 9352.75i 0.225010 0.489193i
\(716\) 1745.11 8795.58i 0.0910862 0.459087i
\(717\) 9027.00 + 9027.00i 0.470180 + 0.470180i
\(718\) −18000.0 21922.2i −0.935592 1.13946i
\(719\) 8967.84 0.465152 0.232576 0.972578i \(-0.425285\pi\)
0.232576 + 0.972578i \(0.425285\pi\)
\(720\) −6435.36 241.022i −0.333100 0.0124755i
\(721\) 23193.7 1.19803
\(722\) 9364.42 + 11404.9i 0.482697 + 0.587877i
\(723\) −11667.6 11667.6i −0.600169 0.600169i
\(724\) 4284.45 21594.2i 0.219931 1.10848i
\(725\) 7949.12 + 9274.77i 0.407204 + 0.475112i
\(726\) −2153.22 + 21916.6i −0.110074 + 1.12039i
\(727\) −2346.73 + 2346.73i −0.119719 + 0.119719i −0.764428 0.644709i \(-0.776978\pi\)
0.644709 + 0.764428i \(0.276978\pi\)
\(728\) 3780.93 + 7061.24i 0.192487 + 0.359488i
\(729\) 729.000i 0.0370370i
\(730\) 6139.70 + 23422.6i 0.311289 + 1.18755i
\(731\) 1886.68i 0.0954602i
\(732\) −8385.23 + 5608.73i −0.423397 + 0.283203i
\(733\) −16978.3 + 16978.3i −0.855537 + 0.855537i −0.990809 0.135271i \(-0.956809\pi\)
0.135271 + 0.990809i \(0.456809\pi\)
\(734\) 2055.86 + 201.980i 0.103383 + 0.0101570i
\(735\) −7230.67 3325.83i −0.362867 0.166905i
\(736\) −17436.2 + 32716.5i −0.873245 + 1.63851i
\(737\) −31689.1 31689.1i −1.58383 1.58383i
\(738\) −6494.35 + 5332.42i −0.323930 + 0.265974i
\(739\) 19134.0 0.952445 0.476223 0.879325i \(-0.342006\pi\)
0.476223 + 0.879325i \(0.342006\pi\)
\(740\) 16257.2 + 11778.1i 0.807605 + 0.585097i
\(741\) −1786.19 −0.0885524
\(742\) 28689.2 23556.3i 1.41943 1.16547i
\(743\) −2604.02 2604.02i −0.128576 0.128576i 0.639890 0.768466i \(-0.278980\pi\)
−0.768466 + 0.639890i \(0.778980\pi\)
\(744\) −72.2752 + 238.886i −0.00356147 + 0.0117715i
\(745\) −13173.9 + 4873.02i −0.647857 + 0.239642i
\(746\) −1289.84 126.721i −0.0633033 0.00621929i
\(747\) −868.910 + 868.910i −0.0425593 + 0.0425593i
\(748\) −6229.15 9312.78i −0.304492 0.455226i
\(749\) 45402.2i 2.21490i
\(750\) 6753.00 9747.92i 0.328780 0.474592i
\(751\) 6788.05i 0.329826i 0.986308 + 0.164913i \(0.0527343\pi\)
−0.986308 + 0.164913i \(0.947266\pi\)
\(752\) −77.6932 + 32.2701i −0.00376753 + 0.00156485i
\(753\) 9844.94 9844.94i 0.476454 0.476454i
\(754\) 397.125 4042.14i 0.0191809 0.195234i
\(755\) 26669.4 9865.02i 1.28556 0.475530i
\(756\) −5103.77 1012.63i −0.245532 0.0487154i
\(757\) −4468.53 4468.53i −0.214546 0.214546i 0.591649 0.806195i \(-0.298477\pi\)
−0.806195 + 0.591649i \(0.798477\pi\)
\(758\) 17348.0 + 21128.1i 0.831276 + 1.01241i
\(759\) 38498.6 1.84112
\(760\) −7672.94 6796.52i −0.366219 0.324389i
\(761\) 9333.28 0.444588 0.222294 0.974980i \(-0.428646\pi\)
0.222294 + 0.974980i \(0.428646\pi\)
\(762\) −3488.44 4248.58i −0.165844 0.201981i
\(763\) −9181.88 9181.88i −0.435657 0.435657i
\(764\) −5142.22 1020.25i −0.243507 0.0483135i
\(765\) −2043.22 939.800i −0.0965656 0.0444164i
\(766\) −2345.57 + 23874.5i −0.110638 + 1.12613i
\(767\) 1167.08 1167.08i 0.0549424 0.0549424i
\(768\) 23.8880 + 12288.0i 0.00112238 + 0.577349i
\(769\) 7835.45i 0.367430i 0.982980 + 0.183715i \(0.0588123\pi\)
−0.982980 + 0.183715i \(0.941188\pi\)
\(770\) 46172.7 12103.1i 2.16097 0.566451i
\(771\) 9071.03i 0.423716i
\(772\) −697.428 1042.68i −0.0325142 0.0486098i
\(773\) −25434.6 + 25434.6i −1.18347 + 1.18347i −0.204627 + 0.978840i \(0.565598\pi\)
−0.978840 + 0.204627i \(0.934402\pi\)
\(774\) 2138.50 + 210.099i 0.0993112 + 0.00975693i
\(775\) −299.078 348.954i −0.0138622 0.0161739i
\(776\) 21477.6 + 6498.05i 0.993556 + 0.300601i
\(777\) 11469.6 + 11469.6i 0.529561 + 0.529561i
\(778\) 6545.70 5374.58i 0.301638 0.247671i
\(779\) −13374.9 −0.615157
\(780\) −3893.65 + 622.077i −0.178737 + 0.0285563i
\(781\) 44702.0 2.04810
\(782\) −10006.1 + 8215.85i −0.457566 + 0.375701i
\(783\) 1865.68 + 1865.68i 0.0851520 + 0.0851520i
\(784\) −5797.95 + 14036.1i −0.264120 + 0.639398i
\(785\) −3317.78 + 7213.19i −0.150849 + 0.327961i
\(786\) −2086.33 204.974i −0.0946782 0.00930176i
\(787\) −7277.31 + 7277.31i −0.329616 + 0.329616i −0.852441 0.522824i \(-0.824878\pi\)
0.522824 + 0.852441i \(0.324878\pi\)
\(788\) −11628.4 + 7778.02i −0.525691 + 0.351625i
\(789\) 8385.86i 0.378383i
\(790\) 4425.58 7569.94i 0.199310 0.340920i
\(791\) 16849.7i 0.757405i
\(792\) 11249.5 6023.51i 0.504712 0.270248i
\(793\) −4367.64 + 4367.64i −0.195586 + 0.195586i
\(794\) −245.202 + 2495.80i −0.0109596 + 0.111552i
\(795\) 6339.67 + 17138.9i 0.282824 + 0.764595i
\(796\) −6072.21 + 30604.8i −0.270381 + 1.36276i
\(797\) 6850.16 + 6850.16i 0.304448 + 0.304448i 0.842751 0.538303i \(-0.180934\pi\)
−0.538303 + 0.842751i \(0.680934\pi\)
\(798\) −5255.54 6400.72i −0.233138 0.283939i
\(799\) −29.3801 −0.00130087
\(800\) −19093.0 12143.2i −0.843799 0.536660i
\(801\) −3338.48 −0.147265
\(802\) −6336.82 7717.61i −0.279003 0.339798i
\(803\) −33926.8 33926.8i −1.49097 1.49097i
\(804\) −3340.53 + 16836.7i −0.146532 + 0.738540i
\(805\) −19135.7 51732.1i −0.837819 2.26499i
\(806\) −14.9414 + 152.082i −0.000652964 + 0.00664621i
\(807\) −16803.4 + 16803.4i −0.732972 + 0.732972i
\(808\) 17943.5 9607.82i 0.781250 0.418319i
\(809\) 7426.20i 0.322734i −0.986895 0.161367i \(-0.948410\pi\)
0.986895 0.161367i \(-0.0515902\pi\)
\(810\) 1292.77 2211.28i 0.0560781 0.0959214i
\(811\) 29349.5i 1.27078i −0.772192 0.635389i \(-0.780840\pi\)
0.772192 0.635389i \(-0.219160\pi\)
\(812\) 15653.3 10470.2i 0.676506 0.452503i
\(813\) 11345.3 11345.3i 0.489419 0.489419i
\(814\) −39588.8 3889.44i −1.70465 0.167475i
\(815\) −5250.10 + 11414.2i −0.225648 + 0.490580i
\(816\) −1638.37 + 3966.26i −0.0702871 + 0.170156i
\(817\) 2418.44 + 2418.44i 0.103562 + 0.103562i
\(818\) −23800.5 + 19542.2i −1.01731 + 0.835303i
\(819\) −3185.87 −0.135926
\(820\) −29155.6 + 4658.10i −1.24165 + 0.198376i
\(821\) −25338.8 −1.07714 −0.538568 0.842582i \(-0.681035\pi\)
−0.538568 + 0.842582i \(0.681035\pi\)
\(822\) 4668.60 3833.32i 0.198097 0.162655i
\(823\) 690.181 + 690.181i 0.0292323 + 0.0292323i 0.721572 0.692340i \(-0.243420\pi\)
−0.692340 + 0.721572i \(0.743420\pi\)
\(824\) 20852.8 + 6309.02i 0.881603 + 0.266730i
\(825\) −1803.19 + 23428.4i −0.0760957 + 0.988693i
\(826\) 7616.10 + 748.252i 0.320821 + 0.0315194i
\(827\) −7725.23 + 7725.23i −0.324828 + 0.324828i −0.850616 0.525788i \(-0.823771\pi\)
0.525788 + 0.850616i \(0.323771\pi\)
\(828\) −8198.17 12256.5i −0.344090 0.514425i
\(829\) 1220.68i 0.0511409i −0.999673 0.0255705i \(-0.991860\pi\)
0.999673 0.0255705i \(-0.00814022\pi\)
\(830\) −4176.55 + 1094.79i −0.174663 + 0.0457839i
\(831\) 12190.3i 0.508875i
\(832\) 1478.57 + 7377.02i 0.0616106 + 0.307395i
\(833\) −3750.17 + 3750.17i −0.155985 + 0.155985i
\(834\) −1830.69 + 18633.7i −0.0760090 + 0.773659i
\(835\) 31640.4 + 14553.4i 1.31133 + 0.603161i
\(836\) 19922.4 + 3952.75i 0.824200 + 0.163527i
\(837\) −70.1944 70.1944i −0.00289877 0.00289877i
\(838\) 10805.1 + 13159.5i 0.445413 + 0.542468i
\(839\) −25188.8 −1.03649 −0.518245 0.855232i \(-0.673415\pi\)
−0.518245 + 0.855232i \(0.673415\pi\)
\(840\) −13685.6 12122.4i −0.562139 0.497930i
\(841\) 14839.6 0.608453
\(842\) −9007.32 10970.0i −0.368661 0.448992i
\(843\) −11737.9 11737.9i −0.479566 0.479566i
\(844\) 21457.0 + 4257.23i 0.875096 + 0.173625i
\(845\) 20773.3 7684.05i 0.845709 0.312828i
\(846\) 3.27174 33.3015i 0.000132961 0.00135335i
\(847\) −44208.0 + 44208.0i −1.79339 + 1.79339i
\(848\) 32201.3 13374.9i 1.30401 0.541622i
\(849\) 5524.92i 0.223339i
\(850\) −4531.11 6474.03i −0.182842 0.261244i
\(851\) 45967.3i 1.85163i
\(852\) −9519.18 14231.5i −0.382772 0.572257i
\(853\) 22544.6 22544.6i 0.904940 0.904940i −0.0909180 0.995858i \(-0.528980\pi\)
0.995858 + 0.0909180i \(0.0289801\pi\)
\(854\) −28502.3 2800.23i −1.14207 0.112204i
\(855\) 3823.78 1414.42i 0.152948 0.0565754i
\(856\) 12350.1 40819.8i 0.493127 1.62990i
\(857\) 6661.51 + 6661.51i 0.265523 + 0.265523i 0.827293 0.561770i \(-0.189880\pi\)
−0.561770 + 0.827293i \(0.689880\pi\)
\(858\) 6038.41 4958.05i 0.240266 0.197279i
\(859\) −26306.2 −1.04489 −0.522443 0.852674i \(-0.674979\pi\)
−0.522443 + 0.852674i \(0.674979\pi\)
\(860\) 6114.14 + 4429.60i 0.242431 + 0.175637i
\(861\) −23855.7 −0.944252
\(862\) 7104.87 5833.70i 0.280734 0.230507i
\(863\) 17342.4 + 17342.4i 0.684056 + 0.684056i 0.960912 0.276855i \(-0.0892922\pi\)
−0.276855 + 0.960912i \(0.589292\pi\)
\(864\) −4313.21 2298.72i −0.169836 0.0905141i
\(865\) 14549.9 + 6692.40i 0.571922 + 0.263062i
\(866\) 5521.08 + 542.424i 0.216644 + 0.0212844i
\(867\) 9362.34 9362.34i 0.366738 0.366738i
\(868\) −588.940 + 393.931i −0.0230299 + 0.0154043i
\(869\) 17375.1i 0.678264i
\(870\) 2350.68 + 8967.68i 0.0916039 + 0.349463i
\(871\) 10509.8i 0.408853i
\(872\) −5757.56 10752.8i −0.223596 0.417586i
\(873\) −6310.98 + 6310.98i −0.244667 + 0.244667i
\(874\) 2294.81 23357.8i 0.0888136 0.903991i
\(875\) 32377.9 9222.04i 1.25094 0.356299i
\(876\) −3576.42 + 18025.7i −0.137941 + 0.695241i
\(877\) 24189.5 + 24189.5i 0.931380 + 0.931380i 0.997792 0.0664120i \(-0.0211552\pi\)
−0.0664120 + 0.997792i \(0.521155\pi\)
\(878\) −4732.82 5764.10i −0.181919 0.221559i
\(879\) −5849.07 −0.224442
\(880\) 44804.8 + 1678.06i 1.71633 + 0.0642812i
\(881\) −48795.5 −1.86602 −0.933009 0.359853i \(-0.882827\pi\)
−0.933009 + 0.359853i \(0.882827\pi\)
\(882\) −3833.10 4668.33i −0.146335 0.178221i
\(883\) 5629.19 + 5629.19i 0.214538 + 0.214538i 0.806192 0.591654i \(-0.201525\pi\)
−0.591654 + 0.806192i \(0.701525\pi\)
\(884\) −511.349 + 2577.27i −0.0194553 + 0.0980577i
\(885\) −1574.26 + 3422.59i −0.0597945 + 0.129999i
\(886\) −445.106 + 4530.52i −0.0168777 + 0.171790i
\(887\) −15762.4 + 15762.4i −0.596674 + 0.596674i −0.939426 0.342752i \(-0.888641\pi\)
0.342752 + 0.939426i \(0.388641\pi\)
\(888\) 7192.07 + 13431.9i 0.271791 + 0.507594i
\(889\) 15606.3i 0.588772i
\(890\) −10126.6 5920.28i −0.381399 0.222976i
\(891\) 5075.50i 0.190837i
\(892\) 28157.2 18833.8i 1.05692 0.706954i
\(893\) 37.6609 37.6609i 0.00141128 0.00141128i
\(894\) −10609.3 1042.32i −0.396899 0.0389937i
\(895\) 4347.61 + 11753.5i 0.162374 + 0.438967i
\(896\) −22084.8 + 27004.0i −0.823439 + 1.00685i
\(897\) −6384.10 6384.10i −0.237636 0.237636i
\(898\) 23219.5 19065.2i 0.862856 0.708479i
\(899\) 359.288 0.0133292
\(900\) 7842.72 4414.94i 0.290471 0.163516i
\(901\) 12177.1 0.450252
\(902\) 45215.5 37125.8i 1.66908 1.37046i
\(903\) 4313.56 + 4313.56i 0.158966 + 0.158966i
\(904\) −4583.37 + 15149.1i −0.168629 + 0.557358i
\(905\) 10673.9 + 28856.2i 0.392059 + 1.05990i
\(906\) 21477.6 + 2110.09i 0.787578 + 0.0773765i
\(907\) 13503.7 13503.7i 0.494357 0.494357i −0.415319 0.909676i \(-0.636330\pi\)
0.909676 + 0.415319i \(0.136330\pi\)
\(908\) 12001.1 + 17942.0i 0.438623 + 0.655756i
\(909\) 8095.69i 0.295398i
\(910\) −9663.71 5649.65i −0.352032 0.205807i
\(911\) 31606.4i 1.14947i −0.818340 0.574735i \(-0.805105\pi\)
0.818340 0.574735i \(-0.194895\pi\)
\(912\) −2984.02 7184.29i −0.108345 0.260850i
\(913\) 6049.59 6049.59i 0.219291 0.219291i
\(914\) −1407.19 + 14323.1i −0.0509252 + 0.518343i
\(915\) 5891.45 12808.6i 0.212858 0.462775i
\(916\) 29830.9 + 5918.66i 1.07603 + 0.213491i
\(917\) −4208.33 4208.33i −0.151550 0.151550i
\(918\) −1083.14 1319.16i −0.0389424 0.0474279i
\(919\) −27215.2 −0.976872 −0.488436 0.872600i \(-0.662432\pi\)
−0.488436 + 0.872600i \(0.662432\pi\)
\(920\) −3132.46 51716.0i −0.112254 1.85329i
\(921\) −19574.4 −0.700325
\(922\) 7085.00 + 8628.82i 0.253072 + 0.308216i
\(923\) −7412.80 7412.80i −0.264350 0.264350i
\(924\) 35533.9 + 7050.18i 1.26513 + 0.251011i
\(925\) −27973.5 2153.01i −0.994338 0.0765302i
\(926\) 734.836 7479.55i 0.0260780 0.265436i
\(927\) −6127.39 + 6127.39i −0.217098 + 0.217098i
\(928\) 16921.5 5155.53i 0.598572 0.182369i
\(929\) 5560.38i 0.196373i 0.995168 + 0.0981863i \(0.0313041\pi\)
−0.995168 + 0.0981863i \(0.968696\pi\)
\(930\) −88.4419 337.400i −0.00311841 0.0118965i
\(931\) 9614.31i 0.338449i
\(932\) −14216.2 21253.7i −0.499643 0.746982i
\(933\) 17387.8 17387.8i 0.610130 0.610130i
\(934\) −49912.4 4903.70i −1.74859 0.171792i
\(935\) 14225.4 + 6543.15i 0.497564 + 0.228860i
\(936\) −2864.32 866.603i −0.100025 0.0302626i
\(937\) −25303.2 25303.2i −0.882197 0.882197i 0.111560 0.993758i \(-0.464415\pi\)
−0.993758 + 0.111560i \(0.964415\pi\)
\(938\) −37661.4 + 30923.2i −1.31097 + 1.07642i
\(939\) −27375.6 −0.951404
\(940\) 68.9794 95.2117i 0.00239347 0.00330368i
\(941\) 30786.5 1.06654 0.533268 0.845946i \(-0.320964\pi\)
0.533268 + 0.845946i \(0.320964\pi\)
\(942\) −4657.05 + 3823.83i −0.161077 + 0.132258i
\(943\) −47804.0 47804.0i −1.65081 1.65081i
\(944\) 6643.88 + 2744.42i 0.229068 + 0.0946222i
\(945\) 6820.14 2522.77i 0.234772 0.0868420i
\(946\) −14888.8 1462.77i −0.511710 0.0502735i
\(947\) −25385.5 + 25385.5i −0.871087 + 0.871087i −0.992591 0.121504i \(-0.961228\pi\)
0.121504 + 0.992591i \(0.461228\pi\)
\(948\) 5531.60 3699.99i 0.189513 0.126762i
\(949\) 11252.0i 0.384883i
\(950\) 14106.9 + 2490.54i 0.481778 + 0.0850565i
\(951\) 17785.6i 0.606453i
\(952\) −10740.1 + 5750.76i −0.365639 + 0.195781i
\(953\) 9612.33 9612.33i 0.326730 0.326730i −0.524611 0.851342i \(-0.675789\pi\)
0.851342 + 0.524611i \(0.175789\pi\)
\(954\) −1356.03 + 13802.4i −0.0460201 + 0.468416i
\(955\) 6871.52 2541.78i 0.232835 0.0861256i
\(956\) −6625.22 + 33392.0i −0.224137 + 1.12968i
\(957\) −12989.4 12989.4i −0.438754 0.438754i
\(958\) 9749.78 + 11874.3i 0.328811 + 0.400459i
\(959\) 17149.2 0.577451
\(960\) −9006.82 14621.5i −0.302806 0.491571i
\(961\) 29777.5 0.999546
\(962\) 5919.91 + 7209.86i 0.198405 + 0.241637i
\(963\) 11994.5 + 11994.5i 0.401368 + 0.401368i
\(964\) 8563.23 43159.9i 0.286103 1.44200i
\(965\) 1592.71 + 732.583i 0.0531307 + 0.0244380i
\(966\) 4093.05 41661.2i 0.136327 1.38761i
\(967\) 31572.0 31572.0i 1.04993 1.04993i 0.0512489 0.998686i \(-0.483680\pi\)
0.998686 0.0512489i \(-0.0163202\pi\)
\(968\) −51771.3 + 27720.9i −1.71900 + 0.920437i
\(969\) 2716.78i 0.0900675i
\(970\) −30334.6 + 7951.55i −1.00411 + 0.263205i
\(971\) 46468.4i 1.53578i −0.640582 0.767890i \(-0.721307\pi\)
0.640582 0.767890i \(-0.278693\pi\)
\(972\) 1615.85 1080.81i 0.0533215 0.0356658i
\(973\) −37585.9 + 37585.9i −1.23839 + 1.23839i
\(974\) −33037.9 3245.84i −1.08686 0.106780i
\(975\) 4184.08 3586.04i 0.137433 0.117790i
\(976\) −24863.8 10270.6i −0.815443 0.336839i
\(977\) 20243.2 + 20243.2i 0.662885 + 0.662885i 0.956059 0.293174i \(-0.0947117\pi\)
−0.293174 + 0.956059i \(0.594712\pi\)
\(978\) −7369.36 + 6050.87i −0.240947 + 0.197838i
\(979\) 23243.4 0.758798
\(980\) −3348.38 20957.9i −0.109143 0.683138i
\(981\) 4851.41 0.157893
\(982\) 18548.6 15230.0i 0.602760 0.494917i
\(983\) 23609.1 + 23609.1i 0.766037 + 0.766037i 0.977406 0.211369i \(-0.0677922\pi\)
−0.211369 + 0.977406i \(0.567792\pi\)
\(984\) −21448.0 6489.11i −0.694855 0.210229i
\(985\) 8170.10 17762.6i 0.264285 0.574582i
\(986\) 6148.06 + 604.023i 0.198574 + 0.0195091i
\(987\) 67.1724 67.1724i 0.00216628 0.00216628i
\(988\) −2648.20 3959.15i −0.0852738 0.127487i
\(989\) 17287.7i 0.555832i
\(990\) −9000.62 + 15395.5i −0.288948 + 0.494244i
\(991\) 20637.0i 0.661510i 0.943717 + 0.330755i \(0.107303\pi\)
−0.943717 + 0.330755i \(0.892697\pi\)
\(992\) −636.654 + 193.972i −0.0203768 + 0.00620828i
\(993\) −7529.99 + 7529.99i −0.240642 + 0.240642i
\(994\) 4752.58 48374.3i 0.151653 1.54360i
\(995\) −15127.8 40897.0i −0.481993 1.30304i
\(996\) −3214.21 637.723i −0.102255 0.0202882i
\(997\) −37105.3 37105.3i −1.17867 1.17867i −0.980083 0.198591i \(-0.936364\pi\)
−0.198591 0.980083i \(-0.563636\pi\)
\(998\) −14151.8 17235.5i −0.448867 0.546675i
\(999\) −6060.15 −0.191926
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 60.4.j.b.7.5 yes 28
3.2 odd 2 180.4.k.f.127.10 28
4.3 odd 2 inner 60.4.j.b.7.3 28
5.3 odd 4 inner 60.4.j.b.43.3 yes 28
12.11 even 2 180.4.k.f.127.12 28
15.8 even 4 180.4.k.f.163.12 28
20.3 even 4 inner 60.4.j.b.43.5 yes 28
60.23 odd 4 180.4.k.f.163.10 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.4.j.b.7.3 28 4.3 odd 2 inner
60.4.j.b.7.5 yes 28 1.1 even 1 trivial
60.4.j.b.43.3 yes 28 5.3 odd 4 inner
60.4.j.b.43.5 yes 28 20.3 even 4 inner
180.4.k.f.127.10 28 3.2 odd 2
180.4.k.f.127.12 28 12.11 even 2
180.4.k.f.163.10 28 60.23 odd 4
180.4.k.f.163.12 28 15.8 even 4