Properties

Label 17.4.c.a.4.3
Level $17$
Weight $4$
Character 17.4
Analytic conductor $1.003$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [17,4,Mod(4,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.4");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 17.c (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: \(1.00303247010\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} + 46x^{6} + 561x^{4} + 836x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 4.3
Root \(1.11783i\) of defining polynomial
Character \(\chi\) \(=\) 17.4
Dual form 17.4.c.a.13.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.11783i q^{2} +(-5.92758 + 5.92758i) q^{3} +3.51478 q^{4} +(10.1567 - 10.1567i) q^{5} +(-12.5536 - 12.5536i) q^{6} +(3.21600 + 3.21600i) q^{7} +24.3864i q^{8} -43.2725i q^{9} +O(q^{10})\) \(q+2.11783i q^{2} +(-5.92758 + 5.92758i) q^{3} +3.51478 q^{4} +(10.1567 - 10.1567i) q^{5} +(-12.5536 - 12.5536i) q^{6} +(3.21600 + 3.21600i) q^{7} +24.3864i q^{8} -43.2725i q^{9} +(21.5102 + 21.5102i) q^{10} +(-34.0053 - 34.0053i) q^{11} +(-20.8341 + 20.8341i) q^{12} +49.5377 q^{13} +(-6.81095 + 6.81095i) q^{14} +120.409i q^{15} -23.5281 q^{16} +(-51.7393 - 47.2869i) q^{17} +91.6440 q^{18} +31.1112i q^{19} +(35.6985 - 35.6985i) q^{20} -38.1262 q^{21} +(72.0176 - 72.0176i) q^{22} +(-29.6163 - 29.6163i) q^{23} +(-144.552 - 144.552i) q^{24} -81.3170i q^{25} +104.913i q^{26} +(96.4567 + 96.4567i) q^{27} +(11.3035 + 11.3035i) q^{28} +(-85.8152 + 85.8152i) q^{29} -255.007 q^{30} +(118.742 - 118.742i) q^{31} +145.263i q^{32} +403.139 q^{33} +(100.146 - 109.575i) q^{34} +65.3279 q^{35} -152.093i q^{36} +(-251.954 + 251.954i) q^{37} -65.8884 q^{38} +(-293.639 + 293.639i) q^{39} +(247.685 + 247.685i) q^{40} +(-44.8038 - 44.8038i) q^{41} -80.7450i q^{42} +87.7863i q^{43} +(-119.521 - 119.521i) q^{44} +(-439.506 - 439.506i) q^{45} +(62.7224 - 62.7224i) q^{46} +281.901 q^{47} +(139.465 - 139.465i) q^{48} -322.315i q^{49} +172.216 q^{50} +(586.986 - 26.3920i) q^{51} +174.114 q^{52} -5.63254i q^{53} +(-204.279 + 204.279i) q^{54} -690.763 q^{55} +(-78.4266 + 78.4266i) q^{56} +(-184.414 - 184.414i) q^{57} +(-181.742 - 181.742i) q^{58} +134.352i q^{59} +423.212i q^{60} +(422.875 + 422.875i) q^{61} +(251.476 + 251.476i) q^{62} +(139.164 - 139.164i) q^{63} -495.867 q^{64} +(503.140 - 503.140i) q^{65} +853.781i q^{66} -951.761 q^{67} +(-181.852 - 166.203i) q^{68} +351.106 q^{69} +138.354i q^{70} +(234.945 - 234.945i) q^{71} +1055.26 q^{72} +(18.7588 - 18.7588i) q^{73} +(-533.597 - 533.597i) q^{74} +(482.013 + 482.013i) q^{75} +109.349i q^{76} -218.722i q^{77} +(-621.879 - 621.879i) q^{78} +(23.4362 + 23.4362i) q^{79} +(-238.968 + 238.968i) q^{80} +24.8476 q^{81} +(94.8869 - 94.8869i) q^{82} +283.887i q^{83} -134.005 q^{84} +(-1005.78 + 45.2217i) q^{85} -185.917 q^{86} -1017.35i q^{87} +(829.267 - 829.267i) q^{88} -191.442 q^{89} +(930.800 - 930.800i) q^{90} +(159.313 + 159.313i) q^{91} +(-104.095 - 104.095i) q^{92} +1407.70i q^{93} +597.020i q^{94} +(315.987 + 315.987i) q^{95} +(-861.056 - 861.056i) q^{96} +(203.024 - 203.024i) q^{97} +682.609 q^{98} +(-1471.50 + 1471.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 36 q^{4} + 14 q^{5} + 22 q^{6} + 2 q^{7} + 78 q^{10} - 108 q^{11} - 174 q^{12} - 88 q^{13} + 108 q^{14} + 420 q^{16} - 10 q^{17} + 428 q^{18} - 306 q^{20} - 260 q^{21} + 30 q^{22} - 22 q^{23} - 862 q^{24} + 540 q^{27} - 764 q^{28} + 46 q^{29} - 120 q^{30} + 610 q^{31} + 816 q^{33} + 1002 q^{34} + 1172 q^{35} - 574 q^{37} - 768 q^{38} - 844 q^{39} - 342 q^{40} - 968 q^{41} + 550 q^{44} - 1154 q^{45} - 944 q^{46} - 368 q^{47} + 2494 q^{48} + 468 q^{50} + 296 q^{51} + 2564 q^{52} - 1592 q^{54} - 1996 q^{55} + 684 q^{56} - 300 q^{57} + 266 q^{58} + 1258 q^{61} - 2516 q^{62} + 122 q^{63} - 3044 q^{64} + 628 q^{65} + 764 q^{67} + 1914 q^{68} + 1812 q^{69} + 1266 q^{71} + 1404 q^{72} - 1732 q^{73} + 1538 q^{74} + 1292 q^{75} - 2836 q^{78} + 914 q^{79} + 498 q^{80} + 280 q^{81} - 280 q^{82} - 2952 q^{84} - 2498 q^{85} - 4244 q^{86} + 442 q^{88} - 2156 q^{89} + 2478 q^{90} - 1632 q^{91} - 1768 q^{92} + 1484 q^{95} + 3998 q^{96} + 1836 q^{97} + 6728 q^{98} - 2088 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.11783i 0.748767i 0.927274 + 0.374384i \(0.122146\pi\)
−0.927274 + 0.374384i \(0.877854\pi\)
\(3\) −5.92758 + 5.92758i −1.14076 + 1.14076i −0.152453 + 0.988311i \(0.548717\pi\)
−0.988311 + 0.152453i \(0.951283\pi\)
\(4\) 3.51478 0.439347
\(5\) 10.1567 10.1567i 0.908443 0.908443i −0.0877040 0.996147i \(-0.527953\pi\)
0.996147 + 0.0877040i \(0.0279530\pi\)
\(6\) −12.5536 12.5536i −0.854167 0.854167i
\(7\) 3.21600 + 3.21600i 0.173648 + 0.173648i 0.788580 0.614932i \(-0.210817\pi\)
−0.614932 + 0.788580i \(0.710817\pi\)
\(8\) 24.3864i 1.07774i
\(9\) 43.2725i 1.60269i
\(10\) 21.5102 + 21.5102i 0.680212 + 0.680212i
\(11\) −34.0053 34.0053i −0.932090 0.932090i 0.0657467 0.997836i \(-0.479057\pi\)
−0.997836 + 0.0657467i \(0.979057\pi\)
\(12\) −20.8341 + 20.8341i −0.501192 + 0.501192i
\(13\) 49.5377 1.05687 0.528434 0.848974i \(-0.322779\pi\)
0.528434 + 0.848974i \(0.322779\pi\)
\(14\) −6.81095 + 6.81095i −0.130022 + 0.130022i
\(15\) 120.409i 2.07264i
\(16\) −23.5281 −0.367627
\(17\) −51.7393 47.2869i −0.738154 0.674632i
\(18\) 91.6440 1.20004
\(19\) 31.1112i 0.375653i 0.982202 + 0.187826i \(0.0601443\pi\)
−0.982202 + 0.187826i \(0.939856\pi\)
\(20\) 35.6985 35.6985i 0.399122 0.399122i
\(21\) −38.1262 −0.396182
\(22\) 72.0176 72.0176i 0.697918 0.697918i
\(23\) −29.6163 29.6163i −0.268497 0.268497i 0.559998 0.828494i \(-0.310802\pi\)
−0.828494 + 0.559998i \(0.810802\pi\)
\(24\) −144.552 144.552i −1.22944 1.22944i
\(25\) 81.3170i 0.650536i
\(26\) 104.913i 0.791349i
\(27\) 96.4567 + 96.4567i 0.687522 + 0.687522i
\(28\) 11.3035 + 11.3035i 0.0762916 + 0.0762916i
\(29\) −85.8152 + 85.8152i −0.549499 + 0.549499i −0.926296 0.376797i \(-0.877025\pi\)
0.376797 + 0.926296i \(0.377025\pi\)
\(30\) −255.007 −1.55192
\(31\) 118.742 118.742i 0.687957 0.687957i −0.273823 0.961780i \(-0.588288\pi\)
0.961780 + 0.273823i \(0.0882882\pi\)
\(32\) 145.263i 0.802470i
\(33\) 403.139 2.12659
\(34\) 100.146 109.575i 0.505143 0.552706i
\(35\) 65.3279 0.315498
\(36\) 152.093i 0.704136i
\(37\) −251.954 + 251.954i −1.11949 + 1.11949i −0.127669 + 0.991817i \(0.540750\pi\)
−0.991817 + 0.127669i \(0.959250\pi\)
\(38\) −65.8884 −0.281277
\(39\) −293.639 + 293.639i −1.20564 + 1.20564i
\(40\) 247.685 + 247.685i 0.979062 + 0.979062i
\(41\) −44.8038 44.8038i −0.170663 0.170663i 0.616608 0.787270i \(-0.288506\pi\)
−0.787270 + 0.616608i \(0.788506\pi\)
\(42\) 80.7450i 0.296648i
\(43\) 87.7863i 0.311332i 0.987810 + 0.155666i \(0.0497524\pi\)
−0.987810 + 0.155666i \(0.950248\pi\)
\(44\) −119.521 119.521i −0.409511 0.409511i
\(45\) −439.506 439.506i −1.45595 1.45595i
\(46\) 62.7224 62.7224i 0.201041 0.201041i
\(47\) 281.901 0.874884 0.437442 0.899247i \(-0.355885\pi\)
0.437442 + 0.899247i \(0.355885\pi\)
\(48\) 139.465 139.465i 0.419375 0.419375i
\(49\) 322.315i 0.939693i
\(50\) 172.216 0.487100
\(51\) 586.986 26.3920i 1.61166 0.0724630i
\(52\) 174.114 0.464332
\(53\) 5.63254i 0.0145979i −0.999973 0.00729895i \(-0.997677\pi\)
0.999973 0.00729895i \(-0.00232335\pi\)
\(54\) −204.279 + 204.279i −0.514794 + 0.514794i
\(55\) −690.763 −1.69350
\(56\) −78.4266 + 78.4266i −0.187146 + 0.187146i
\(57\) −184.414 184.414i −0.428531 0.428531i
\(58\) −181.742 181.742i −0.411447 0.411447i
\(59\) 134.352i 0.296460i 0.988953 + 0.148230i \(0.0473576\pi\)
−0.988953 + 0.148230i \(0.952642\pi\)
\(60\) 423.212i 0.910608i
\(61\) 422.875 + 422.875i 0.887599 + 0.887599i 0.994292 0.106693i \(-0.0340261\pi\)
−0.106693 + 0.994292i \(0.534026\pi\)
\(62\) 251.476 + 251.476i 0.515120 + 0.515120i
\(63\) 139.164 139.164i 0.278303 0.278303i
\(64\) −495.867 −0.968490
\(65\) 503.140 503.140i 0.960105 0.960105i
\(66\) 853.781i 1.59232i
\(67\) −951.761 −1.73546 −0.867732 0.497032i \(-0.834423\pi\)
−0.867732 + 0.497032i \(0.834423\pi\)
\(68\) −181.852 166.203i −0.324306 0.296398i
\(69\) 351.106 0.612582
\(70\) 138.354i 0.236235i
\(71\) 234.945 234.945i 0.392717 0.392717i −0.482938 0.875655i \(-0.660430\pi\)
0.875655 + 0.482938i \(0.160430\pi\)
\(72\) 1055.26 1.72727
\(73\) 18.7588 18.7588i 0.0300761 0.0300761i −0.691909 0.721985i \(-0.743230\pi\)
0.721985 + 0.691909i \(0.243230\pi\)
\(74\) −533.597 533.597i −0.838235 0.838235i
\(75\) 482.013 + 482.013i 0.742108 + 0.742108i
\(76\) 109.349i 0.165042i
\(77\) 218.722i 0.323710i
\(78\) −621.879 621.879i −0.902743 0.902743i
\(79\) 23.4362 + 23.4362i 0.0333769 + 0.0333769i 0.723598 0.690221i \(-0.242487\pi\)
−0.690221 + 0.723598i \(0.742487\pi\)
\(80\) −238.968 + 238.968i −0.333968 + 0.333968i
\(81\) 24.8476 0.0340845
\(82\) 94.8869 94.8869i 0.127787 0.127787i
\(83\) 283.887i 0.375430i 0.982224 + 0.187715i \(0.0601081\pi\)
−0.982224 + 0.187715i \(0.939892\pi\)
\(84\) −134.005 −0.174062
\(85\) −1005.78 + 45.2217i −1.28344 + 0.0577056i
\(86\) −185.917 −0.233115
\(87\) 1017.35i 1.25370i
\(88\) 829.267 829.267i 1.00455 1.00455i
\(89\) −191.442 −0.228009 −0.114005 0.993480i \(-0.536368\pi\)
−0.114005 + 0.993480i \(0.536368\pi\)
\(90\) 930.800 930.800i 1.09017 1.09017i
\(91\) 159.313 + 159.313i 0.183523 + 0.183523i
\(92\) −104.095 104.095i −0.117963 0.117963i
\(93\) 1407.70i 1.56959i
\(94\) 597.020i 0.655085i
\(95\) 315.987 + 315.987i 0.341259 + 0.341259i
\(96\) −861.056 861.056i −0.915428 0.915428i
\(97\) 203.024 203.024i 0.212515 0.212515i −0.592820 0.805335i \(-0.701985\pi\)
0.805335 + 0.592820i \(0.201985\pi\)
\(98\) 682.609 0.703612
\(99\) −1471.50 + 1471.50i −1.49385 + 1.49385i
\(100\) 285.811i 0.285811i
\(101\) 154.062 0.151780 0.0758899 0.997116i \(-0.475820\pi\)
0.0758899 + 0.997116i \(0.475820\pi\)
\(102\) 55.8938 + 1243.14i 0.0542580 + 1.20676i
\(103\) 765.082 0.731900 0.365950 0.930634i \(-0.380744\pi\)
0.365950 + 0.930634i \(0.380744\pi\)
\(104\) 1208.05i 1.13903i
\(105\) −387.236 + 387.236i −0.359909 + 0.359909i
\(106\) 11.9288 0.0109304
\(107\) −279.648 + 279.648i −0.252660 + 0.252660i −0.822060 0.569400i \(-0.807175\pi\)
0.569400 + 0.822060i \(0.307175\pi\)
\(108\) 339.024 + 339.024i 0.302061 + 0.302061i
\(109\) 620.769 + 620.769i 0.545495 + 0.545495i 0.925134 0.379640i \(-0.123952\pi\)
−0.379640 + 0.925134i \(0.623952\pi\)
\(110\) 1462.92i 1.26804i
\(111\) 2986.96i 2.55414i
\(112\) −75.6664 75.6664i −0.0638375 0.0638375i
\(113\) 1446.78 + 1446.78i 1.20444 + 1.20444i 0.972801 + 0.231641i \(0.0744095\pi\)
0.231641 + 0.972801i \(0.425590\pi\)
\(114\) 390.559 390.559i 0.320870 0.320870i
\(115\) −601.607 −0.487827
\(116\) −301.621 + 301.621i −0.241421 + 0.241421i
\(117\) 2143.62i 1.69383i
\(118\) −284.535 −0.221980
\(119\) −14.3189 318.468i −0.0110304 0.245327i
\(120\) −2936.35 −2.23376
\(121\) 981.722i 0.737582i
\(122\) −895.578 + 895.578i −0.664605 + 0.664605i
\(123\) 531.156 0.389372
\(124\) 417.351 417.351i 0.302252 0.302252i
\(125\) 443.675 + 443.675i 0.317468 + 0.317468i
\(126\) 294.727 + 294.727i 0.208384 + 0.208384i
\(127\) 2106.13i 1.47156i −0.677218 0.735782i \(-0.736815\pi\)
0.677218 0.735782i \(-0.263185\pi\)
\(128\) 111.936i 0.0772959i
\(129\) −520.361 520.361i −0.355157 0.355157i
\(130\) 1065.57 + 1065.57i 0.718895 + 0.718895i
\(131\) −983.275 + 983.275i −0.655795 + 0.655795i −0.954382 0.298587i \(-0.903485\pi\)
0.298587 + 0.954382i \(0.403485\pi\)
\(132\) 1416.94 0.934311
\(133\) −100.054 + 100.054i −0.0652313 + 0.0652313i
\(134\) 2015.67i 1.29946i
\(135\) 1959.36 1.24915
\(136\) 1153.16 1261.73i 0.727076 0.795535i
\(137\) −2309.58 −1.44030 −0.720149 0.693820i \(-0.755926\pi\)
−0.720149 + 0.693820i \(0.755926\pi\)
\(138\) 743.584i 0.458682i
\(139\) 1751.57 1751.57i 1.06882 1.06882i 0.0713691 0.997450i \(-0.477263\pi\)
0.997450 0.0713691i \(-0.0227368\pi\)
\(140\) 229.613 0.138613
\(141\) −1670.99 + 1670.99i −0.998036 + 0.998036i
\(142\) 497.576 + 497.576i 0.294054 + 0.294054i
\(143\) −1684.55 1684.55i −0.985097 0.985097i
\(144\) 1018.12i 0.589190i
\(145\) 1743.20i 0.998377i
\(146\) 39.7281 + 39.7281i 0.0225200 + 0.0225200i
\(147\) 1910.55 + 1910.55i 1.07197 + 1.07197i
\(148\) −885.563 + 885.563i −0.491843 + 0.491843i
\(149\) 1521.60 0.836607 0.418304 0.908307i \(-0.362625\pi\)
0.418304 + 0.908307i \(0.362625\pi\)
\(150\) −1020.82 + 1020.82i −0.555666 + 0.555666i
\(151\) 397.910i 0.214447i −0.994235 0.107223i \(-0.965804\pi\)
0.994235 0.107223i \(-0.0341960\pi\)
\(152\) −758.691 −0.404855
\(153\) −2046.22 + 2238.89i −1.08122 + 1.18303i
\(154\) 463.217 0.242384
\(155\) 2412.05i 1.24994i
\(156\) −1032.08 + 1032.08i −0.529694 + 0.529694i
\(157\) −1068.19 −0.543001 −0.271501 0.962438i \(-0.587520\pi\)
−0.271501 + 0.962438i \(0.587520\pi\)
\(158\) −49.6339 + 49.6339i −0.0249915 + 0.0249915i
\(159\) 33.3873 + 33.3873i 0.0166528 + 0.0166528i
\(160\) 1475.39 + 1475.39i 0.728997 + 0.728997i
\(161\) 190.492i 0.0932476i
\(162\) 52.6231i 0.0255214i
\(163\) −597.803 597.803i −0.287261 0.287261i 0.548735 0.835996i \(-0.315110\pi\)
−0.835996 + 0.548735i \(0.815110\pi\)
\(164\) −157.475 157.475i −0.0749802 0.0749802i
\(165\) 4094.56 4094.56i 1.93188 1.93188i
\(166\) −601.226 −0.281109
\(167\) −1848.05 + 1848.05i −0.856327 + 0.856327i −0.990903 0.134576i \(-0.957033\pi\)
0.134576 + 0.990903i \(0.457033\pi\)
\(168\) 929.761i 0.426980i
\(169\) 256.987 0.116972
\(170\) −95.7720 2130.07i −0.0432081 0.960994i
\(171\) 1346.26 0.602054
\(172\) 308.549i 0.136783i
\(173\) 2181.30 2181.30i 0.958620 0.958620i −0.0405576 0.999177i \(-0.512913\pi\)
0.999177 + 0.0405576i \(0.0129134\pi\)
\(174\) 2154.59 0.938728
\(175\) 261.515 261.515i 0.112964 0.112964i
\(176\) 800.081 + 800.081i 0.342661 + 0.342661i
\(177\) −796.383 796.383i −0.338191 0.338191i
\(178\) 405.443i 0.170726i
\(179\) 918.935i 0.383712i −0.981423 0.191856i \(-0.938549\pi\)
0.981423 0.191856i \(-0.0614506\pi\)
\(180\) −1544.77 1544.77i −0.639667 0.639667i
\(181\) −1526.40 1526.40i −0.626833 0.626833i 0.320437 0.947270i \(-0.396170\pi\)
−0.947270 + 0.320437i \(0.896170\pi\)
\(182\) −337.399 + 337.399i −0.137416 + 0.137416i
\(183\) −5013.25 −2.02508
\(184\) 722.234 722.234i 0.289368 0.289368i
\(185\) 5118.04i 2.03398i
\(186\) −2981.29 −1.17526
\(187\) 151.405 + 3367.41i 0.0592077 + 1.31684i
\(188\) 990.821 0.384378
\(189\) 620.409i 0.238773i
\(190\) −669.209 + 669.209i −0.255524 + 0.255524i
\(191\) 1349.67 0.511302 0.255651 0.966769i \(-0.417710\pi\)
0.255651 + 0.966769i \(0.417710\pi\)
\(192\) 2939.29 2939.29i 1.10482 1.10482i
\(193\) −2481.32 2481.32i −0.925436 0.925436i 0.0719705 0.997407i \(-0.477071\pi\)
−0.997407 + 0.0719705i \(0.977071\pi\)
\(194\) 429.971 + 429.971i 0.159124 + 0.159124i
\(195\) 5964.81i 2.19051i
\(196\) 1132.86i 0.412852i
\(197\) 2509.24 + 2509.24i 0.907492 + 0.907492i 0.996069 0.0885772i \(-0.0282320\pi\)
−0.0885772 + 0.996069i \(0.528232\pi\)
\(198\) −3116.38 3116.38i −1.11854 1.11854i
\(199\) −2172.17 + 2172.17i −0.773774 + 0.773774i −0.978764 0.204990i \(-0.934284\pi\)
0.204990 + 0.978764i \(0.434284\pi\)
\(200\) 1983.03 0.701106
\(201\) 5641.64 5641.64i 1.97976 1.97976i
\(202\) 326.278i 0.113648i
\(203\) −551.963 −0.190838
\(204\) 2063.12 92.7619i 0.708077 0.0318364i
\(205\) −910.116 −0.310075
\(206\) 1620.32i 0.548023i
\(207\) −1281.57 + 1281.57i −0.430316 + 0.430316i
\(208\) −1165.53 −0.388533
\(209\) 1057.95 1057.95i 0.350142 0.350142i
\(210\) −820.103 820.103i −0.269488 0.269488i
\(211\) 4258.19 + 4258.19i 1.38932 + 1.38932i 0.826757 + 0.562559i \(0.190183\pi\)
0.562559 + 0.826757i \(0.309817\pi\)
\(212\) 19.7971i 0.00641354i
\(213\) 2785.32i 0.895995i
\(214\) −592.249 592.249i −0.189184 0.189184i
\(215\) 891.619 + 891.619i 0.282827 + 0.282827i
\(216\) −2352.23 + 2352.23i −0.740968 + 0.740968i
\(217\) 763.748 0.238924
\(218\) −1314.69 + 1314.69i −0.408449 + 0.408449i
\(219\) 222.389i 0.0686194i
\(220\) −2427.88 −0.744035
\(221\) −2563.05 2342.48i −0.780132 0.712998i
\(222\) 6325.88 1.91246
\(223\) 3581.06i 1.07536i −0.843149 0.537680i \(-0.819301\pi\)
0.843149 0.537680i \(-0.180699\pi\)
\(224\) −467.164 + 467.164i −0.139347 + 0.139347i
\(225\) −3518.79 −1.04260
\(226\) −3064.05 + 3064.05i −0.901847 + 0.901847i
\(227\) −3001.23 3001.23i −0.877528 0.877528i 0.115751 0.993278i \(-0.463073\pi\)
−0.993278 + 0.115751i \(0.963073\pi\)
\(228\) −648.176 648.176i −0.188274 0.188274i
\(229\) 5146.73i 1.48518i −0.669748 0.742589i \(-0.733598\pi\)
0.669748 0.742589i \(-0.266402\pi\)
\(230\) 1274.10i 0.365269i
\(231\) 1296.49 + 1296.49i 0.369277 + 0.369277i
\(232\) −2092.72 2092.72i −0.592215 0.592215i
\(233\) 2013.38 2013.38i 0.566098 0.566098i −0.364935 0.931033i \(-0.618909\pi\)
0.931033 + 0.364935i \(0.118909\pi\)
\(234\) 4539.84 1.26828
\(235\) 2863.19 2863.19i 0.794782 0.794782i
\(236\) 472.218i 0.130249i
\(237\) −277.840 −0.0761504
\(238\) 674.463 30.3251i 0.183693 0.00825917i
\(239\) 3984.47 1.07839 0.539193 0.842182i \(-0.318729\pi\)
0.539193 + 0.842182i \(0.318729\pi\)
\(240\) 2833.00i 0.761957i
\(241\) −1268.92 + 1268.92i −0.339163 + 0.339163i −0.856052 0.516890i \(-0.827090\pi\)
0.516890 + 0.856052i \(0.327090\pi\)
\(242\) −2079.12 −0.552278
\(243\) −2751.62 + 2751.62i −0.726404 + 0.726404i
\(244\) 1486.31 + 1486.31i 0.389964 + 0.389964i
\(245\) −3273.65 3273.65i −0.853657 0.853657i
\(246\) 1124.90i 0.291549i
\(247\) 1541.18i 0.397016i
\(248\) 2895.69 + 2895.69i 0.741436 + 0.741436i
\(249\) −1682.76 1682.76i −0.428277 0.428277i
\(250\) −939.631 + 939.631i −0.237710 + 0.237710i
\(251\) −4658.75 −1.17154 −0.585772 0.810476i \(-0.699209\pi\)
−0.585772 + 0.810476i \(0.699209\pi\)
\(252\) 489.132 489.132i 0.122272 0.122272i
\(253\) 2014.22i 0.500526i
\(254\) 4460.43 1.10186
\(255\) 5693.78 6229.89i 1.39827 1.52993i
\(256\) −4204.00 −1.02637
\(257\) 6235.43i 1.51345i 0.653736 + 0.756723i \(0.273201\pi\)
−0.653736 + 0.756723i \(0.726799\pi\)
\(258\) 1102.04 1102.04i 0.265930 0.265930i
\(259\) −1620.57 −0.388792
\(260\) 1768.42 1768.42i 0.421819 0.421819i
\(261\) 3713.44 + 3713.44i 0.880674 + 0.880674i
\(262\) −2082.41 2082.41i −0.491038 0.491038i
\(263\) 149.037i 0.0349430i −0.999847 0.0174715i \(-0.994438\pi\)
0.999847 0.0174715i \(-0.00556163\pi\)
\(264\) 9831.10i 2.29190i
\(265\) −57.2080 57.2080i −0.0132613 0.0132613i
\(266\) −211.897 211.897i −0.0488430 0.0488430i
\(267\) 1134.79 1134.79i 0.260105 0.260105i
\(268\) −3345.23 −0.762472
\(269\) −2199.13 + 2199.13i −0.498450 + 0.498450i −0.910955 0.412505i \(-0.864654\pi\)
0.412505 + 0.910955i \(0.364654\pi\)
\(270\) 4149.60i 0.935322i
\(271\) 4725.42 1.05922 0.529610 0.848241i \(-0.322338\pi\)
0.529610 + 0.848241i \(0.322338\pi\)
\(272\) 1217.33 + 1112.57i 0.271365 + 0.248013i
\(273\) −1888.69 −0.418713
\(274\) 4891.31i 1.07845i
\(275\) −2765.21 + 2765.21i −0.606358 + 0.606358i
\(276\) 1234.06 0.269136
\(277\) −636.499 + 636.499i −0.138063 + 0.138063i −0.772761 0.634698i \(-0.781125\pi\)
0.634698 + 0.772761i \(0.281125\pi\)
\(278\) 3709.53 + 3709.53i 0.800297 + 0.800297i
\(279\) −5138.26 5138.26i −1.10258 1.10258i
\(280\) 1593.11i 0.340024i
\(281\) 9165.72i 1.94584i −0.231143 0.972920i \(-0.574246\pi\)
0.231143 0.972920i \(-0.425754\pi\)
\(282\) −3538.89 3538.89i −0.747297 0.747297i
\(283\) 2504.08 + 2504.08i 0.525979 + 0.525979i 0.919371 0.393392i \(-0.128698\pi\)
−0.393392 + 0.919371i \(0.628698\pi\)
\(284\) 825.781 825.781i 0.172539 0.172539i
\(285\) −3746.08 −0.778592
\(286\) 3567.59 3567.59i 0.737608 0.737608i
\(287\) 288.178i 0.0592704i
\(288\) 6285.87 1.28611
\(289\) 440.904 + 4893.18i 0.0897423 + 0.995965i
\(290\) −3691.80 −0.747552
\(291\) 2406.88i 0.484859i
\(292\) 65.9331 65.9331i 0.0132138 0.0132138i
\(293\) 1268.29 0.252882 0.126441 0.991974i \(-0.459645\pi\)
0.126441 + 0.991974i \(0.459645\pi\)
\(294\) −4046.22 + 4046.22i −0.802655 + 0.802655i
\(295\) 1364.57 + 1364.57i 0.269317 + 0.269317i
\(296\) −6144.25 6144.25i −1.20651 1.20651i
\(297\) 6560.08i 1.28166i
\(298\) 3222.50i 0.626424i
\(299\) −1467.12 1467.12i −0.283766 0.283766i
\(300\) 1694.17 + 1694.17i 0.326043 + 0.326043i
\(301\) −282.321 + 282.321i −0.0540621 + 0.0540621i
\(302\) 842.708 0.160571
\(303\) −913.217 + 913.217i −0.173145 + 0.173145i
\(304\) 731.988i 0.138100i
\(305\) 8590.02 1.61267
\(306\) −4741.59 4333.56i −0.885813 0.809585i
\(307\) 9924.22 1.84497 0.922484 0.386034i \(-0.126155\pi\)
0.922484 + 0.386034i \(0.126155\pi\)
\(308\) 768.760i 0.142221i
\(309\) −4535.09 + 4535.09i −0.834926 + 0.834926i
\(310\) 5108.32 0.935914
\(311\) 1031.43 1031.43i 0.188062 0.188062i −0.606796 0.794858i \(-0.707546\pi\)
0.794858 + 0.606796i \(0.207546\pi\)
\(312\) −7160.80 7160.80i −1.29936 1.29936i
\(313\) 564.173 + 564.173i 0.101882 + 0.101882i 0.756210 0.654329i \(-0.227049\pi\)
−0.654329 + 0.756210i \(0.727049\pi\)
\(314\) 2262.26i 0.406582i
\(315\) 2826.90i 0.505644i
\(316\) 82.3730 + 82.3730i 0.0146641 + 0.0146641i
\(317\) −2724.15 2724.15i −0.482661 0.482661i 0.423319 0.905981i \(-0.360865\pi\)
−0.905981 + 0.423319i \(0.860865\pi\)
\(318\) −70.7088 + 70.7088i −0.0124690 + 0.0124690i
\(319\) 5836.34 1.02436
\(320\) −5036.37 + 5036.37i −0.879817 + 0.879817i
\(321\) 3315.28i 0.576451i
\(322\) 403.430 0.0698208
\(323\) 1471.15 1609.67i 0.253428 0.277290i
\(324\) 87.3338 0.0149749
\(325\) 4028.26i 0.687531i
\(326\) 1266.05 1266.05i 0.215092 0.215092i
\(327\) −7359.32 −1.24456
\(328\) 1092.60 1092.60i 0.183929 0.183929i
\(329\) 906.595 + 906.595i 0.151922 + 0.151922i
\(330\) 8671.59 + 8671.59i 1.44653 + 1.44653i
\(331\) 8470.40i 1.40657i 0.710907 + 0.703286i \(0.248285\pi\)
−0.710907 + 0.703286i \(0.751715\pi\)
\(332\) 997.800i 0.164944i
\(333\) 10902.7 + 10902.7i 1.79418 + 1.79418i
\(334\) −3913.87 3913.87i −0.641190 0.641190i
\(335\) −9666.75 + 9666.75i −1.57657 + 1.57657i
\(336\) 897.038 0.145647
\(337\) −1359.69 + 1359.69i −0.219784 + 0.219784i −0.808407 0.588624i \(-0.799670\pi\)
0.588624 + 0.808407i \(0.299670\pi\)
\(338\) 544.256i 0.0875848i
\(339\) −17151.9 −2.74797
\(340\) −3535.09 + 158.944i −0.563874 + 0.0253528i
\(341\) −8075.71 −1.28248
\(342\) 2851.16i 0.450798i
\(343\) 2139.65 2139.65i 0.336823 0.336823i
\(344\) −2140.79 −0.335534
\(345\) 3566.08 3566.08i 0.556496 0.556496i
\(346\) 4619.63 + 4619.63i 0.717783 + 0.717783i
\(347\) 1813.08 + 1813.08i 0.280493 + 0.280493i 0.833306 0.552812i \(-0.186445\pi\)
−0.552812 + 0.833306i \(0.686445\pi\)
\(348\) 3575.77i 0.550809i
\(349\) 283.156i 0.0434298i 0.999764 + 0.0217149i \(0.00691260\pi\)
−0.999764 + 0.0217149i \(0.993087\pi\)
\(350\) 553.846 + 553.846i 0.0845838 + 0.0845838i
\(351\) 4778.25 + 4778.25i 0.726621 + 0.726621i
\(352\) 4939.70 4939.70i 0.747974 0.747974i
\(353\) 10695.1 1.61259 0.806295 0.591514i \(-0.201470\pi\)
0.806295 + 0.591514i \(0.201470\pi\)
\(354\) 1686.61 1686.61i 0.253226 0.253226i
\(355\) 4772.54i 0.713521i
\(356\) −672.877 −0.100175
\(357\) 1972.62 + 1802.87i 0.292443 + 0.267277i
\(358\) 1946.15 0.287311
\(359\) 8702.38i 1.27937i 0.768637 + 0.639685i \(0.220935\pi\)
−0.768637 + 0.639685i \(0.779065\pi\)
\(360\) 10718.0 10718.0i 1.56913 1.56913i
\(361\) 5891.09 0.858885
\(362\) 3232.67 3232.67i 0.469352 0.469352i
\(363\) −5819.24 5819.24i −0.841407 0.841407i
\(364\) 559.951 + 559.951i 0.0806303 + 0.0806303i
\(365\) 381.055i 0.0546448i
\(366\) 10617.2i 1.51632i
\(367\) −8429.92 8429.92i −1.19901 1.19901i −0.974462 0.224552i \(-0.927908\pi\)
−0.224552 0.974462i \(-0.572092\pi\)
\(368\) 696.815 + 696.815i 0.0987065 + 0.0987065i
\(369\) −1938.77 + 1938.77i −0.273519 + 0.273519i
\(370\) −10839.2 −1.52298
\(371\) 18.1142 18.1142i 0.00253489 0.00253489i
\(372\) 4947.77i 0.689597i
\(373\) −11054.6 −1.53454 −0.767270 0.641324i \(-0.778385\pi\)
−0.767270 + 0.641324i \(0.778385\pi\)
\(374\) −7131.63 + 320.651i −0.986010 + 0.0443328i
\(375\) −5259.85 −0.724313
\(376\) 6874.56i 0.942894i
\(377\) −4251.09 + 4251.09i −0.580749 + 0.580749i
\(378\) −1313.92 −0.178786
\(379\) 8166.04 8166.04i 1.10676 1.10676i 0.113185 0.993574i \(-0.463895\pi\)
0.993574 0.113185i \(-0.0361051\pi\)
\(380\) 1110.63 + 1110.63i 0.149931 + 0.149931i
\(381\) 12484.3 + 12484.3i 1.67871 + 1.67871i
\(382\) 2858.38i 0.382847i
\(383\) 10238.7i 1.36599i −0.730423 0.682995i \(-0.760677\pi\)
0.730423 0.682995i \(-0.239323\pi\)
\(384\) −663.513 663.513i −0.0881764 0.0881764i
\(385\) −2221.49 2221.49i −0.294072 0.294072i
\(386\) 5255.02 5255.02i 0.692937 0.692937i
\(387\) 3798.73 0.498968
\(388\) 713.584 713.584i 0.0933678 0.0933678i
\(389\) 4378.48i 0.570688i 0.958425 + 0.285344i \(0.0921079\pi\)
−0.958425 + 0.285344i \(0.907892\pi\)
\(390\) −12632.5 −1.64018
\(391\) 131.863 + 2932.79i 0.0170553 + 0.379328i
\(392\) 7860.09 1.01274
\(393\) 11656.9i 1.49621i
\(394\) −5314.15 + 5314.15i −0.679501 + 0.679501i
\(395\) 476.068 0.0606420
\(396\) −5171.98 + 5171.98i −0.656317 + 0.656317i
\(397\) −7110.57 7110.57i −0.898915 0.898915i 0.0964253 0.995340i \(-0.469259\pi\)
−0.995340 + 0.0964253i \(0.969259\pi\)
\(398\) −4600.30 4600.30i −0.579377 0.579377i
\(399\) 1186.15i 0.148827i
\(400\) 1913.23i 0.239154i
\(401\) −5809.87 5809.87i −0.723519 0.723519i 0.245801 0.969320i \(-0.420949\pi\)
−0.969320 + 0.245801i \(0.920949\pi\)
\(402\) 11948.1 + 11948.1i 1.48238 + 1.48238i
\(403\) 5882.20 5882.20i 0.727080 0.727080i
\(404\) 541.495 0.0666841
\(405\) 252.370 252.370i 0.0309638 0.0309638i
\(406\) 1168.97i 0.142894i
\(407\) 17135.6 2.08692
\(408\) 643.605 + 14314.5i 0.0780960 + 1.73694i
\(409\) −5402.57 −0.653154 −0.326577 0.945171i \(-0.605895\pi\)
−0.326577 + 0.945171i \(0.605895\pi\)
\(410\) 1927.48i 0.232174i
\(411\) 13690.2 13690.2i 1.64304 1.64304i
\(412\) 2689.09 0.321558
\(413\) −432.076 + 432.076i −0.0514796 + 0.0514796i
\(414\) −2714.15 2714.15i −0.322206 0.322206i
\(415\) 2883.36 + 2883.36i 0.341056 + 0.341056i
\(416\) 7195.98i 0.848105i
\(417\) 20765.1i 2.43854i
\(418\) 2240.56 + 2240.56i 0.262175 + 0.262175i
\(419\) −4458.44 4458.44i −0.519831 0.519831i 0.397689 0.917520i \(-0.369812\pi\)
−0.917520 + 0.397689i \(0.869812\pi\)
\(420\) −1361.05 + 1361.05i −0.158125 + 0.158125i
\(421\) −6492.45 −0.751598 −0.375799 0.926701i \(-0.622632\pi\)
−0.375799 + 0.926701i \(0.622632\pi\)
\(422\) −9018.13 + 9018.13i −1.04027 + 1.04027i
\(423\) 12198.6i 1.40216i
\(424\) 137.357 0.0157327
\(425\) −3845.22 + 4207.28i −0.438872 + 0.480195i
\(426\) −5898.84 −0.670892
\(427\) 2719.93i 0.308259i
\(428\) −982.902 + 982.902i −0.111006 + 0.111006i
\(429\) 19970.6 2.24753
\(430\) −1888.30 + 1888.30i −0.211772 + 0.211772i
\(431\) 9530.02 + 9530.02i 1.06507 + 1.06507i 0.997730 + 0.0673390i \(0.0214509\pi\)
0.0673390 + 0.997730i \(0.478549\pi\)
\(432\) −2269.44 2269.44i −0.252751 0.252751i
\(433\) 13237.8i 1.46921i 0.678495 + 0.734605i \(0.262633\pi\)
−0.678495 + 0.734605i \(0.737367\pi\)
\(434\) 1617.49i 0.178899i
\(435\) −10332.9 10332.9i −1.13891 1.13891i
\(436\) 2181.87 + 2181.87i 0.239662 + 0.239662i
\(437\) 921.399 921.399i 0.100862 0.100862i
\(438\) −470.983 −0.0513800
\(439\) −7247.17 + 7247.17i −0.787901 + 0.787901i −0.981150 0.193248i \(-0.938098\pi\)
0.193248 + 0.981150i \(0.438098\pi\)
\(440\) 16845.2i 1.82515i
\(441\) −13947.4 −1.50603
\(442\) 4960.99 5428.11i 0.533870 0.584137i
\(443\) −8163.30 −0.875508 −0.437754 0.899095i \(-0.644226\pi\)
−0.437754 + 0.899095i \(0.644226\pi\)
\(444\) 10498.5i 1.12215i
\(445\) −1944.42 + 1944.42i −0.207133 + 0.207133i
\(446\) 7584.09 0.805195
\(447\) −9019.42 + 9019.42i −0.954372 + 0.954372i
\(448\) −1594.71 1594.71i −0.168176 0.168176i
\(449\) −3099.02 3099.02i −0.325727 0.325727i 0.525232 0.850959i \(-0.323979\pi\)
−0.850959 + 0.525232i \(0.823979\pi\)
\(450\) 7452.21i 0.780668i
\(451\) 3047.13i 0.318146i
\(452\) 5085.13 + 5085.13i 0.529169 + 0.529169i
\(453\) 2358.65 + 2358.65i 0.244633 + 0.244633i
\(454\) 6356.11 6356.11i 0.657064 0.657064i
\(455\) 3236.19 0.333440
\(456\) 4497.20 4497.20i 0.461844 0.461844i
\(457\) 10463.4i 1.07102i −0.844530 0.535509i \(-0.820120\pi\)
0.844530 0.535509i \(-0.179880\pi\)
\(458\) 10899.9 1.11205
\(459\) −429.464 9551.73i −0.0436724 0.971322i
\(460\) −2114.52 −0.214326
\(461\) 7540.64i 0.761828i −0.924610 0.380914i \(-0.875609\pi\)
0.924610 0.380914i \(-0.124391\pi\)
\(462\) −2745.76 + 2745.76i −0.276503 + 0.276503i
\(463\) −12962.0 −1.30107 −0.650536 0.759475i \(-0.725456\pi\)
−0.650536 + 0.759475i \(0.725456\pi\)
\(464\) 2019.07 2019.07i 0.202011 0.202011i
\(465\) 14297.6 + 14297.6i 1.42589 + 1.42589i
\(466\) 4264.00 + 4264.00i 0.423876 + 0.423876i
\(467\) 12536.8i 1.24226i −0.783707 0.621130i \(-0.786674\pi\)
0.783707 0.621130i \(-0.213326\pi\)
\(468\) 7534.36i 0.744179i
\(469\) −3060.86 3060.86i −0.301359 0.301359i
\(470\) 6063.76 + 6063.76i 0.595107 + 0.595107i
\(471\) 6331.81 6331.81i 0.619436 0.619436i
\(472\) −3276.36 −0.319506
\(473\) 2985.20 2985.20i 0.290190 0.290190i
\(474\) 588.419i 0.0570189i
\(475\) 2529.87 0.244376
\(476\) −50.3278 1119.34i −0.00484616 0.107784i
\(477\) −243.734 −0.0233958
\(478\) 8438.46i 0.807460i
\(479\) 741.437 741.437i 0.0707246 0.0707246i −0.670860 0.741584i \(-0.734075\pi\)
0.741584 + 0.670860i \(0.234075\pi\)
\(480\) −17491.0 −1.66323
\(481\) −12481.2 + 12481.2i −1.18315 + 1.18315i
\(482\) −2687.36 2687.36i −0.253954 0.253954i
\(483\) 1129.16 + 1129.16i 0.106374 + 0.106374i
\(484\) 3450.54i 0.324055i
\(485\) 4124.10i 0.386115i
\(486\) −5827.47 5827.47i −0.543908 0.543908i
\(487\) 639.001 + 639.001i 0.0594577 + 0.0594577i 0.736210 0.676753i \(-0.236613\pi\)
−0.676753 + 0.736210i \(0.736613\pi\)
\(488\) −10312.4 + 10312.4i −0.956598 + 0.956598i
\(489\) 7087.06 0.655394
\(490\) 6933.05 6933.05i 0.639191 0.639191i
\(491\) 14922.5i 1.37158i 0.727800 + 0.685789i \(0.240543\pi\)
−0.727800 + 0.685789i \(0.759457\pi\)
\(492\) 1866.90 0.171069
\(493\) 8497.94 382.083i 0.776325 0.0349050i
\(494\) −3263.96 −0.297273
\(495\) 29891.1i 2.71415i
\(496\) −2793.77 + 2793.77i −0.252911 + 0.252911i
\(497\) 1511.17 0.136389
\(498\) 3563.82 3563.82i 0.320680 0.320680i
\(499\) −1858.57 1858.57i −0.166735 0.166735i 0.618807 0.785543i \(-0.287616\pi\)
−0.785543 + 0.618807i \(0.787616\pi\)
\(500\) 1559.42 + 1559.42i 0.139479 + 0.139479i
\(501\) 21909.0i 1.95373i
\(502\) 9866.45i 0.877214i
\(503\) 4596.21 + 4596.21i 0.407426 + 0.407426i 0.880840 0.473414i \(-0.156979\pi\)
−0.473414 + 0.880840i \(0.656979\pi\)
\(504\) 3393.72 + 3393.72i 0.299937 + 0.299937i
\(505\) 1564.76 1564.76i 0.137883 0.137883i
\(506\) −4265.79 −0.374777
\(507\) −1523.31 + 1523.31i −0.133437 + 0.133437i
\(508\) 7402.58i 0.646528i
\(509\) −1931.57 −0.168203 −0.0841013 0.996457i \(-0.526802\pi\)
−0.0841013 + 0.996457i \(0.526802\pi\)
\(510\) 13193.9 + 12058.5i 1.14556 + 1.04698i
\(511\) 120.657 0.0104453
\(512\) 8007.88i 0.691214i
\(513\) −3000.89 + 3000.89i −0.258270 + 0.258270i
\(514\) −13205.6 −1.13322
\(515\) 7770.70 7770.70i 0.664889 0.664889i
\(516\) −1828.95 1828.95i −0.156037 0.156037i
\(517\) −9586.14 9586.14i −0.815470 0.815470i
\(518\) 3432.10i 0.291115i
\(519\) 25859.7i 2.18712i
\(520\) 12269.8 + 12269.8i 1.03474 + 1.03474i
\(521\) 3738.53 + 3738.53i 0.314372 + 0.314372i 0.846601 0.532229i \(-0.178645\pi\)
−0.532229 + 0.846601i \(0.678645\pi\)
\(522\) −7864.44 + 7864.44i −0.659420 + 0.659420i
\(523\) 8406.61 0.702859 0.351430 0.936214i \(-0.385696\pi\)
0.351430 + 0.936214i \(0.385696\pi\)
\(524\) −3455.99 + 3455.99i −0.288122 + 0.288122i
\(525\) 3100.31i 0.257731i
\(526\) 315.635 0.0261642
\(527\) −11758.5 + 528.686i −0.971936 + 0.0437001i
\(528\) −9485.09 −0.781791
\(529\) 10412.8i 0.855819i
\(530\) 121.157 121.157i 0.00992966 0.00992966i
\(531\) 5813.75 0.475132
\(532\) −351.667 + 351.667i −0.0286592 + 0.0286592i
\(533\) −2219.48 2219.48i −0.180368 0.180368i
\(534\) 2403.30 + 2403.30i 0.194758 + 0.194758i
\(535\) 5680.61i 0.459054i
\(536\) 23210.0i 1.87037i
\(537\) 5447.06 + 5447.06i 0.437725 + 0.437725i
\(538\) −4657.39 4657.39i −0.373223 0.373223i
\(539\) −10960.4 + 10960.4i −0.875878 + 0.875878i
\(540\) 6886.72 0.548810
\(541\) −8004.01 + 8004.01i −0.636080 + 0.636080i −0.949586 0.313506i \(-0.898496\pi\)
0.313506 + 0.949586i \(0.398496\pi\)
\(542\) 10007.6i 0.793110i
\(543\) 18095.8 1.43014
\(544\) 6869.01 7515.78i 0.541372 0.592346i
\(545\) 12609.9 0.991101
\(546\) 3999.93i 0.313518i
\(547\) 849.665 849.665i 0.0664151 0.0664151i −0.673119 0.739534i \(-0.735046\pi\)
0.739534 + 0.673119i \(0.235046\pi\)
\(548\) −8117.66 −0.632791
\(549\) 18298.8 18298.8i 1.42254 1.42254i
\(550\) −5856.25 5856.25i −0.454021 0.454021i
\(551\) −2669.82 2669.82i −0.206421 0.206421i
\(552\) 8562.21i 0.660202i
\(553\) 150.742i 0.0115916i
\(554\) −1348.00 1348.00i −0.103377 0.103377i
\(555\) −30337.6 30337.6i −2.32029 2.32029i
\(556\) 6156.36 6156.36i 0.469583 0.469583i
\(557\) −5277.38 −0.401454 −0.200727 0.979647i \(-0.564330\pi\)
−0.200727 + 0.979647i \(0.564330\pi\)
\(558\) 10882.0 10882.0i 0.825575 0.825575i
\(559\) 4348.73i 0.329037i
\(560\) −1537.04 −0.115985
\(561\) −20858.1 19063.2i −1.56975 1.43467i
\(562\) 19411.5 1.45698
\(563\) 2341.00i 0.175243i 0.996154 + 0.0876213i \(0.0279265\pi\)
−0.996154 + 0.0876213i \(0.972073\pi\)
\(564\) −5873.18 + 5873.18i −0.438485 + 0.438485i
\(565\) 29389.1 2.18833
\(566\) −5303.23 + 5303.23i −0.393836 + 0.393836i
\(567\) 79.9099 + 79.9099i 0.00591869 + 0.00591869i
\(568\) 5729.47 + 5729.47i 0.423245 + 0.423245i
\(569\) 3732.25i 0.274981i 0.990503 + 0.137490i \(0.0439036\pi\)
−0.990503 + 0.137490i \(0.956096\pi\)
\(570\) 7933.58i 0.582985i
\(571\) −3185.66 3185.66i −0.233478 0.233478i 0.580665 0.814143i \(-0.302793\pi\)
−0.814143 + 0.580665i \(0.802793\pi\)
\(572\) −5920.81 5920.81i −0.432800 0.432800i
\(573\) −8000.29 + 8000.29i −0.583275 + 0.583275i
\(574\) 610.313 0.0443797
\(575\) −2408.31 + 2408.31i −0.174667 + 0.174667i
\(576\) 21457.4i 1.55218i
\(577\) −15292.7 −1.10337 −0.551685 0.834053i \(-0.686015\pi\)
−0.551685 + 0.834053i \(0.686015\pi\)
\(578\) −10362.9 + 933.761i −0.745746 + 0.0671961i
\(579\) 29416.4 2.11141
\(580\) 6126.95i 0.438634i
\(581\) −912.981 + 912.981i −0.0651925 + 0.0651925i
\(582\) −5097.37 −0.363046
\(583\) −191.536 + 191.536i −0.0136065 + 0.0136065i
\(584\) 457.460 + 457.460i 0.0324141 + 0.0324141i
\(585\) −21772.1 21772.1i −1.53875 1.53875i
\(586\) 2686.03i 0.189350i
\(587\) 11208.5i 0.788116i 0.919086 + 0.394058i \(0.128929\pi\)
−0.919086 + 0.394058i \(0.871071\pi\)
\(588\) 6715.15 + 6715.15i 0.470966 + 0.470966i
\(589\) 3694.21 + 3694.21i 0.258433 + 0.258433i
\(590\) −2889.94 + 2889.94i −0.201656 + 0.201656i
\(591\) −29747.5 −2.07047
\(592\) 5928.00 5928.00i 0.411553 0.411553i
\(593\) 10220.6i 0.707774i 0.935288 + 0.353887i \(0.115140\pi\)
−0.935288 + 0.353887i \(0.884860\pi\)
\(594\) 13893.2 0.959669
\(595\) −3380.02 3089.15i −0.232886 0.212845i
\(596\) 5348.09 0.367561
\(597\) 25751.4i 1.76539i
\(598\) 3107.12 3107.12i 0.212474 0.212474i
\(599\) 9068.76 0.618597 0.309298 0.950965i \(-0.399906\pi\)
0.309298 + 0.950965i \(0.399906\pi\)
\(600\) −11754.6 + 11754.6i −0.799797 + 0.799797i
\(601\) 10107.0 + 10107.0i 0.685980 + 0.685980i 0.961341 0.275361i \(-0.0887974\pi\)
−0.275361 + 0.961341i \(0.588797\pi\)
\(602\) −597.908 597.908i −0.0404800 0.0404800i
\(603\) 41185.1i 2.78140i
\(604\) 1398.57i 0.0942167i
\(605\) 9971.05 + 9971.05i 0.670051 + 0.670051i
\(606\) −1934.04 1934.04i −0.129645 0.129645i
\(607\) 9231.72 9231.72i 0.617304 0.617304i −0.327535 0.944839i \(-0.606218\pi\)
0.944839 + 0.327535i \(0.106218\pi\)
\(608\) −4519.30 −0.301450
\(609\) 3271.81 3271.81i 0.217702 0.217702i
\(610\) 18192.2i 1.20751i
\(611\) 13964.8 0.924638
\(612\) −7192.02 + 7869.20i −0.475033 + 0.519760i
\(613\) −15590.7 −1.02725 −0.513623 0.858016i \(-0.671697\pi\)
−0.513623 + 0.858016i \(0.671697\pi\)
\(614\) 21017.9i 1.38145i
\(615\) 5394.79 5394.79i 0.353722 0.353722i
\(616\) 5333.84 0.348874
\(617\) 18303.2 18303.2i 1.19426 1.19426i 0.218400 0.975859i \(-0.429916\pi\)
0.975859 0.218400i \(-0.0700837\pi\)
\(618\) −9604.56 9604.56i −0.625165 0.625165i
\(619\) −317.054 317.054i −0.0205872 0.0205872i 0.696738 0.717325i \(-0.254634\pi\)
−0.717325 + 0.696738i \(0.754634\pi\)
\(620\) 8477.82i 0.549157i
\(621\) 5713.38i 0.369195i
\(622\) 2184.40 + 2184.40i 0.140814 + 0.140814i
\(623\) −615.678 615.678i −0.0395933 0.0395933i
\(624\) 6908.77 6908.77i 0.443225 0.443225i
\(625\) 19177.2 1.22734
\(626\) −1194.83 + 1194.83i −0.0762857 + 0.0762857i
\(627\) 12542.1i 0.798859i
\(628\) −3754.47 −0.238566
\(629\) 24950.0 1121.80i 1.58159 0.0711114i
\(630\) 5986.91 0.378610
\(631\) 6811.18i 0.429713i −0.976646 0.214856i \(-0.931072\pi\)
0.976646 0.214856i \(-0.0689284\pi\)
\(632\) −571.524 + 571.524i −0.0359715 + 0.0359715i
\(633\) −50481.5 −3.16976
\(634\) 5769.30 5769.30i 0.361401 0.361401i
\(635\) −21391.3 21391.3i −1.33683 1.33683i
\(636\) 117.349 + 117.349i 0.00731634 + 0.00731634i
\(637\) 15966.7i 0.993132i
\(638\) 12360.4i 0.767011i
\(639\) −10166.7 10166.7i −0.629402 0.629402i
\(640\) 1136.90 + 1136.90i 0.0702189 + 0.0702189i
\(641\) −9965.73 + 9965.73i −0.614076 + 0.614076i −0.944006 0.329930i \(-0.892975\pi\)
0.329930 + 0.944006i \(0.392975\pi\)
\(642\) 7021.21 0.431628
\(643\) 6116.96 6116.96i 0.375162 0.375162i −0.494191 0.869353i \(-0.664536\pi\)
0.869353 + 0.494191i \(0.164536\pi\)
\(644\) 669.537i 0.0409681i
\(645\) −10570.3 −0.645279
\(646\) 3409.02 + 3115.66i 0.207626 + 0.189758i
\(647\) −10310.7 −0.626515 −0.313258 0.949668i \(-0.601420\pi\)
−0.313258 + 0.949668i \(0.601420\pi\)
\(648\) 605.943i 0.0367341i
\(649\) 4568.68 4568.68i 0.276327 0.276327i
\(650\) 8531.18 0.514801
\(651\) −4527.18 + 4527.18i −0.272556 + 0.272556i
\(652\) −2101.15 2101.15i −0.126207 0.126207i
\(653\) −6074.29 6074.29i −0.364020 0.364020i 0.501270 0.865291i \(-0.332866\pi\)
−0.865291 + 0.501270i \(0.832866\pi\)
\(654\) 15585.8i 0.931887i
\(655\) 19973.6i 1.19150i
\(656\) 1054.15 + 1054.15i 0.0627402 + 0.0627402i
\(657\) −811.741 811.741i −0.0482025 0.0482025i
\(658\) −1920.02 + 1920.02i −0.113754 + 0.113754i
\(659\) −4635.27 −0.273998 −0.136999 0.990571i \(-0.543746\pi\)
−0.136999 + 0.990571i \(0.543746\pi\)
\(660\) 14391.5 14391.5i 0.848768 0.848768i
\(661\) 27861.5i 1.63946i 0.572747 + 0.819732i \(0.305878\pi\)
−0.572747 + 0.819732i \(0.694122\pi\)
\(662\) −17938.9 −1.05320
\(663\) 29077.9 1307.40i 1.70331 0.0765839i
\(664\) −6922.98 −0.404614
\(665\) 2032.43i 0.118518i
\(666\) −23090.1 + 23090.1i −1.34343 + 1.34343i
\(667\) 5083.05 0.295077
\(668\) −6495.50 + 6495.50i −0.376225 + 0.376225i
\(669\) 21227.0 + 21227.0i 1.22673 + 1.22673i
\(670\) −20472.6 20472.6i −1.18048 1.18048i
\(671\) 28760.0i 1.65464i
\(672\) 5538.31i 0.317924i
\(673\) −5996.35 5996.35i −0.343451 0.343451i 0.514212 0.857663i \(-0.328084\pi\)
−0.857663 + 0.514212i \(0.828084\pi\)
\(674\) −2879.60 2879.60i −0.164567 0.164567i
\(675\) 7843.56 7843.56i 0.447258 0.447258i
\(676\) 903.253 0.0513913
\(677\) 7979.46 7979.46i 0.452992 0.452992i −0.443355 0.896346i \(-0.646212\pi\)
0.896346 + 0.443355i \(0.146212\pi\)
\(678\) 36324.8i 2.05759i
\(679\) 1305.85 0.0738054
\(680\) −1102.79 24527.3i −0.0621914 1.38320i
\(681\) 35580.1 2.00210
\(682\) 17103.0i 0.960276i
\(683\) 1637.44 1637.44i 0.0917350 0.0917350i −0.659750 0.751485i \(-0.729338\pi\)
0.751485 + 0.659750i \(0.229338\pi\)
\(684\) 4731.81 0.264511
\(685\) −23457.7 + 23457.7i −1.30843 + 1.30843i
\(686\) 4531.43 + 4531.43i 0.252202 + 0.252202i
\(687\) 30507.7 + 30507.7i 1.69424 + 1.69424i
\(688\) 2065.45i 0.114454i
\(689\) 279.023i 0.0154281i
\(690\) 7552.36 + 7552.36i 0.416686 + 0.416686i
\(691\) 5780.78 + 5780.78i 0.318251 + 0.318251i 0.848095 0.529844i \(-0.177750\pi\)
−0.529844 + 0.848095i \(0.677750\pi\)
\(692\) 7666.79 7666.79i 0.421167 0.421167i
\(693\) −9464.66 −0.518806
\(694\) −3839.80 + 3839.80i −0.210024 + 0.210024i
\(695\) 35580.2i 1.94192i
\(696\) 24809.6 1.35116
\(697\) 199.484 + 4436.74i 0.0108407 + 0.241110i
\(698\) −599.677 −0.0325188
\(699\) 23868.9i 1.29157i
\(700\) 919.168 919.168i 0.0496304 0.0496304i
\(701\) −22583.3 −1.21677 −0.608387 0.793640i \(-0.708183\pi\)
−0.608387 + 0.793640i \(0.708183\pi\)
\(702\) −10119.5 + 10119.5i −0.544070 + 0.544070i
\(703\) −7838.60 7838.60i −0.420538 0.420538i
\(704\) 16862.1 + 16862.1i 0.902719 + 0.902719i
\(705\) 33943.6i 1.81332i
\(706\) 22650.5i 1.20745i
\(707\) 495.464 + 495.464i 0.0263562 + 0.0263562i
\(708\) −2799.11 2799.11i −0.148583 0.148583i
\(709\) −16352.3 + 16352.3i −0.866183 + 0.866183i −0.992048 0.125864i \(-0.959830\pi\)
0.125864 + 0.992048i \(0.459830\pi\)
\(710\) 10107.4 0.534262
\(711\) 1014.14 1014.14i 0.0534927 0.0534927i
\(712\) 4668.58i 0.245734i
\(713\) −7033.38 −0.369428
\(714\) −3818.18 + 4177.69i −0.200129 + 0.218972i
\(715\) −34218.8 −1.78981
\(716\) 3229.85i 0.168583i
\(717\) −23618.3 + 23618.3i −1.23018 + 1.23018i
\(718\) −18430.2 −0.957951
\(719\) −24637.7 + 24637.7i −1.27793 + 1.27793i −0.336108 + 0.941823i \(0.609111\pi\)
−0.941823 + 0.336108i \(0.890889\pi\)
\(720\) 10340.7 + 10340.7i 0.535245 + 0.535245i
\(721\) 2460.50 + 2460.50i 0.127093 + 0.127093i
\(722\) 12476.4i 0.643105i
\(723\) 15043.2i 0.773809i
\(724\) −5364.97 5364.97i −0.275397 0.275397i
\(725\) 6978.23 + 6978.23i 0.357469 + 0.357469i
\(726\) 12324.2 12324.2i 0.630019 0.630019i
\(727\) 11782.3 0.601077 0.300538 0.953770i \(-0.402834\pi\)
0.300538 + 0.953770i \(0.402834\pi\)
\(728\) −3885.08 + 3885.08i −0.197789 + 0.197789i
\(729\) 31950.0i 1.62323i
\(730\) 807.012 0.0409162
\(731\) 4151.14 4542.00i 0.210035 0.229811i
\(732\) −17620.5 −0.889715
\(733\) 20099.0i 1.01279i −0.862302 0.506394i \(-0.830978\pi\)
0.862302 0.506394i \(-0.169022\pi\)
\(734\) 17853.2 17853.2i 0.897783 0.897783i
\(735\) 38809.7 1.94764
\(736\) 4302.13 4302.13i 0.215460 0.215460i
\(737\) 32364.9 + 32364.9i 1.61761 + 1.61761i
\(738\) −4106.00 4106.00i −0.204802 0.204802i
\(739\) 12538.4i 0.624132i −0.950060 0.312066i \(-0.898979\pi\)
0.950060 0.312066i \(-0.101021\pi\)
\(740\) 17988.8i 0.893623i
\(741\) −9135.48 9135.48i −0.452902 0.452902i
\(742\) 38.3629 + 38.3629i 0.00189804 + 0.00189804i
\(743\) 2329.69 2329.69i 0.115031 0.115031i −0.647248 0.762279i \(-0.724080\pi\)
0.762279 + 0.647248i \(0.224080\pi\)
\(744\) −34328.8 −1.69161
\(745\) 15454.5 15454.5i 0.760010 0.760010i
\(746\) 23411.7i 1.14901i
\(747\) 12284.5 0.601696
\(748\) 532.156 + 11835.7i 0.0260127 + 0.578552i
\(749\) −1798.70 −0.0877477
\(750\) 11139.5i 0.542342i
\(751\) −5128.04 + 5128.04i −0.249168 + 0.249168i −0.820629 0.571461i \(-0.806377\pi\)
0.571461 + 0.820629i \(0.306377\pi\)
\(752\) −6632.61 −0.321631
\(753\) 27615.1 27615.1i 1.33646 1.33646i
\(754\) −9003.10 9003.10i −0.434846 0.434846i
\(755\) −4041.46 4041.46i −0.194813 0.194813i
\(756\) 2180.60i 0.104904i
\(757\) 26725.2i 1.28315i −0.767061 0.641574i \(-0.778282\pi\)
0.767061 0.641574i \(-0.221718\pi\)
\(758\) 17294.3 + 17294.3i 0.828705 + 0.828705i
\(759\) −11939.5 11939.5i −0.570982 0.570982i
\(760\) −7705.79 + 7705.79i −0.367787 + 0.367787i
\(761\) 1638.39 0.0780443 0.0390222 0.999238i \(-0.487576\pi\)
0.0390222 + 0.999238i \(0.487576\pi\)
\(762\) −26439.6 + 26439.6i −1.25696 + 1.25696i
\(763\) 3992.79i 0.189448i
\(764\) 4743.79 0.224639
\(765\) 1956.85 + 43522.6i 0.0924840 + 2.05694i
\(766\) 21683.9 1.02281
\(767\) 6655.50i 0.313319i
\(768\) 24919.5 24919.5i 1.17084 1.17084i
\(769\) 9542.58 0.447483 0.223741 0.974649i \(-0.428173\pi\)
0.223741 + 0.974649i \(0.428173\pi\)
\(770\) 4704.76 4704.76i 0.220192 0.220192i
\(771\) −36961.0 36961.0i −1.72648 1.72648i
\(772\) −8721.28 8721.28i −0.406588 0.406588i
\(773\) 10640.1i 0.495080i −0.968878 0.247540i \(-0.920378\pi\)
0.968878 0.247540i \(-0.0796222\pi\)
\(774\) 8045.09i 0.373611i
\(775\) −9655.73 9655.73i −0.447541 0.447541i
\(776\) 4951.02 + 4951.02i 0.229035 + 0.229035i
\(777\) 9606.06 9606.06i 0.443520 0.443520i
\(778\) −9272.90 −0.427313
\(779\) 1393.90 1393.90i 0.0641100 0.0641100i
\(780\) 20965.0i 0.962393i
\(781\) −15978.8 −0.732095
\(782\) −6211.15 + 279.265i −0.284029 + 0.0127705i
\(783\) −16554.9 −0.755586
\(784\) 7583.45i 0.345456i
\(785\) −10849.3 + 10849.3i −0.493285 + 0.493285i
\(786\) 24687.4 1.12032
\(787\) −3081.73 + 3081.73i −0.139583 + 0.139583i −0.773446 0.633863i \(-0.781468\pi\)
0.633863 + 0.773446i \(0.281468\pi\)
\(788\) 8819.42 + 8819.42i 0.398704 + 0.398704i
\(789\) 883.429 + 883.429i 0.0398617 + 0.0398617i
\(790\) 1008.23i 0.0454068i
\(791\) 9305.71i 0.418297i
\(792\) −35884.5 35884.5i −1.60997 1.60997i
\(793\) 20948.3 + 20948.3i 0.938076 + 0.938076i
\(794\) 15059.0 15059.0i 0.673078 0.673078i
\(795\) 678.210 0.0302561
\(796\) −7634.70 + 7634.70i −0.339956 + 0.339956i
\(797\) 19901.9i 0.884517i 0.896888 + 0.442259i \(0.145823\pi\)
−0.896888 + 0.442259i \(0.854177\pi\)
\(798\) 2512.08 0.111437
\(799\) −14585.4 13330.2i −0.645799 0.590225i
\(800\) 11812.3 0.522035
\(801\) 8284.18i 0.365427i
\(802\) 12304.3 12304.3i 0.541747 0.541747i
\(803\) −1275.80 −0.0560672
\(804\) 19829.1 19829.1i 0.869800 0.869800i
\(805\) −1934.77 1934.77i −0.0847101 0.0847101i
\(806\) 12457.5 + 12457.5i 0.544414 + 0.544414i
\(807\) 26071.0i 1.13723i
\(808\) 3757.02i 0.163579i
\(809\) −19895.7 19895.7i −0.864641 0.864641i 0.127232 0.991873i \(-0.459391\pi\)
−0.991873 + 0.127232i \(0.959391\pi\)
\(810\) 534.477 + 534.477i 0.0231847 + 0.0231847i
\(811\) −151.038 + 151.038i −0.00653964 + 0.00653964i −0.710369 0.703829i \(-0.751472\pi\)
0.703829 + 0.710369i \(0.251472\pi\)
\(812\) −1940.03 −0.0838444
\(813\) −28010.3 + 28010.3i −1.20832 + 1.20832i
\(814\) 36290.3i 1.56262i
\(815\) −12143.4 −0.521921
\(816\) −13810.7 + 620.953i −0.592488 + 0.0266393i
\(817\) −2731.14 −0.116953
\(818\) 11441.8i 0.489061i
\(819\) 6893.89 6893.89i 0.294129 0.294129i
\(820\) −3198.86 −0.136230
\(821\) 7369.47 7369.47i 0.313272 0.313272i −0.532904 0.846176i \(-0.678899\pi\)
0.846176 + 0.532904i \(0.178899\pi\)
\(822\) 28993.6 + 28993.6i 1.23025 + 1.23025i
\(823\) 17736.3 + 17736.3i 0.751215 + 0.751215i 0.974706 0.223491i \(-0.0717453\pi\)
−0.223491 + 0.974706i \(0.571745\pi\)
\(824\) 18657.6i 0.788796i
\(825\) 32782.0i 1.38342i
\(826\) −915.066 915.066i −0.0385462 0.0385462i
\(827\) 19714.3 + 19714.3i 0.828939 + 0.828939i 0.987370 0.158431i \(-0.0506437\pi\)
−0.158431 + 0.987370i \(0.550644\pi\)
\(828\) −4504.44 + 4504.44i −0.189058 + 0.189058i
\(829\) 28128.7 1.17847 0.589235 0.807962i \(-0.299429\pi\)
0.589235 + 0.807962i \(0.299429\pi\)
\(830\) −6106.47 + 6106.47i −0.255372 + 0.255372i
\(831\) 7545.80i 0.314995i
\(832\) −24564.1 −1.02357
\(833\) −15241.3 + 16676.3i −0.633947 + 0.693638i
\(834\) −43977.0 −1.82590
\(835\) 37540.2i 1.55585i
\(836\) 3718.45 3718.45i 0.153834 0.153834i
\(837\) 22906.9 0.945971
\(838\) 9442.25 9442.25i 0.389233 0.389233i
\(839\) −27739.1 27739.1i −1.14143 1.14143i −0.988189 0.153240i \(-0.951029\pi\)
−0.153240 0.988189i \(-0.548971\pi\)
\(840\) −9443.30 9443.30i −0.387887 0.387887i
\(841\) 9660.52i 0.396101i
\(842\) 13749.9i 0.562772i
\(843\) 54330.6 + 54330.6i 2.21974 + 2.21974i
\(844\) 14966.6 + 14966.6i 0.610392 + 0.610392i
\(845\) 2610.14 2610.14i 0.106262 0.106262i
\(846\) 25834.6 1.04989
\(847\) −3157.22 + 3157.22i −0.128079 + 0.128079i
\(848\) 132.523i 0.00536657i
\(849\) −29686.3 −1.20004
\(850\) −8910.32 8143.55i −0.359555 0.328613i
\(851\) 14923.9 0.601156
\(852\) 9789.78i 0.393653i
\(853\) 27355.5 27355.5i 1.09805 1.09805i 0.103407 0.994639i \(-0.467026\pi\)
0.994639 0.103407i \(-0.0329744\pi\)
\(854\) −5760.36 −0.230814
\(855\) 13673.6 13673.6i 0.546931 0.546931i
\(856\) −6819.62 6819.62i −0.272301 0.272301i
\(857\) 6659.46 + 6659.46i 0.265441 + 0.265441i 0.827260 0.561819i \(-0.189898\pi\)
−0.561819 + 0.827260i \(0.689898\pi\)
\(858\) 42294.4i 1.68287i
\(859\) 43890.4i 1.74333i −0.490101 0.871666i \(-0.663040\pi\)
0.490101 0.871666i \(-0.336960\pi\)
\(860\) 3133.84 + 3133.84i 0.124259 + 0.124259i
\(861\) 1708.20 + 1708.20i 0.0676135 + 0.0676135i
\(862\) −20183.0 + 20183.0i −0.797489 + 0.797489i
\(863\) −6822.88 −0.269123 −0.134562 0.990905i \(-0.542963\pi\)
−0.134562 + 0.990905i \(0.542963\pi\)
\(864\) −14011.5 + 14011.5i −0.551716 + 0.551716i
\(865\) 44309.6i 1.74170i
\(866\) −28035.5 −1.10010
\(867\) −31618.2 26391.2i −1.23854 1.03379i
\(868\) 2684.40 0.104971
\(869\) 1593.91i 0.0622206i
\(870\) 21883.5 21883.5i 0.852781 0.852781i
\(871\) −47148.1 −1.83416
\(872\) −15138.3 + 15138.3i −0.587899 + 0.587899i
\(873\) −8785.35 8785.35i −0.340594 0.340594i
\(874\) 1951.37 + 1951.37i 0.0755218 + 0.0755218i
\(875\) 2853.72i 0.110255i
\(876\) 781.648i 0.0301478i
\(877\) 24429.3 + 24429.3i 0.940613 + 0.940613i 0.998333 0.0577194i \(-0.0183829\pi\)
−0.0577194 + 0.998333i \(0.518383\pi\)
\(878\) −15348.3 15348.3i −0.589955 0.589955i
\(879\) −7517.91 + 7517.91i −0.288479 + 0.288479i
\(880\) 16252.4 0.622576
\(881\) 21645.5 21645.5i 0.827760 0.827760i −0.159446 0.987207i \(-0.550971\pi\)
0.987207 + 0.159446i \(0.0509709\pi\)
\(882\) 29538.2i 1.12767i
\(883\) 42598.5 1.62350 0.811751 0.584003i \(-0.198514\pi\)
0.811751 + 0.584003i \(0.198514\pi\)
\(884\) −9008.54 8233.31i −0.342749 0.313254i
\(885\) −16177.2 −0.614454
\(886\) 17288.5i 0.655552i
\(887\) 13469.8 13469.8i 0.509888 0.509888i −0.404604 0.914492i \(-0.632591\pi\)
0.914492 + 0.404604i \(0.132591\pi\)
\(888\) 72841.1 2.75269
\(889\) 6773.31 6773.31i 0.255534 0.255534i
\(890\) −4117.96 4117.96i −0.155095 0.155095i
\(891\) −844.950 844.950i −0.0317698 0.0317698i
\(892\) 12586.6i 0.472457i
\(893\) 8770.30i 0.328653i
\(894\) −19101.6 19101.6i −0.714602 0.714602i
\(895\) −9333.34 9333.34i −0.348580 0.348580i
\(896\) −359.988 + 359.988i −0.0134223 + 0.0134223i
\(897\) 17393.0 0.647419
\(898\) 6563.20 6563.20i 0.243894 0.243894i
\(899\) 20379.7i 0.756064i
\(900\) −12367.8 −0.458065
\(901\) −266.345 + 291.423i −0.00984821 + 0.0107755i
\(902\) −6453.32 −0.238217
\(903\) 3346.96i 0.123344i
\(904\) −35281.8 + 35281.8i −1.29807 + 1.29807i
\(905\) −31006.4 −1.13888
\(906\) −4995.22 + 4995.22i −0.183174 + 0.183174i
\(907\) 5931.91 + 5931.91i 0.217162 + 0.217162i 0.807301 0.590139i \(-0.200927\pi\)
−0.590139 + 0.807301i \(0.700927\pi\)
\(908\) −10548.7 10548.7i −0.385539 0.385539i
\(909\) 6666.66i 0.243255i
\(910\) 6853.72i 0.249669i
\(911\) −7401.81 7401.81i −0.269191 0.269191i 0.559583 0.828774i \(-0.310961\pi\)
−0.828774 + 0.559583i \(0.810961\pi\)
\(912\) 4338.92 + 4338.92i 0.157540 + 0.157540i
\(913\) 9653.67 9653.67i 0.349934 0.349934i
\(914\) 22159.6 0.801943
\(915\) −50918.1 + 50918.1i −1.83967 + 1.83967i
\(916\) 18089.6i 0.652509i
\(917\) −6324.42 −0.227754
\(918\) 20229.0 909.532i 0.727294 0.0327005i
\(919\) −16180.4 −0.580787 −0.290394 0.956907i \(-0.593786\pi\)
−0.290394 + 0.956907i \(0.593786\pi\)
\(920\) 14671.0i 0.525749i
\(921\) −58826.7 + 58826.7i −2.10467 + 2.10467i
\(922\) 15969.8 0.570432
\(923\) 11638.7 11638.7i 0.415050 0.415050i
\(924\) 4556.89 + 4556.89i 0.162241 + 0.162241i
\(925\) 20488.1 + 20488.1i 0.728266 + 0.728266i
\(926\) 27451.4i 0.974201i
\(927\) 33107.0i 1.17301i
\(928\) −12465.7 12465.7i −0.440956 0.440956i
\(929\) 10051.5 + 10051.5i 0.354982 + 0.354982i 0.861959 0.506978i \(-0.169237\pi\)
−0.506978 + 0.861959i \(0.669237\pi\)
\(930\) −30280.0 + 30280.0i −1.06766 + 1.06766i
\(931\) 10027.6 0.352998
\(932\) 7076.58 7076.58i 0.248714 0.248714i
\(933\) 12227.8i 0.429068i
\(934\) 26550.9 0.930164
\(935\) 35739.6 + 32664.0i 1.25006 + 1.14249i
\(936\) 52275.2 1.82550
\(937\) 49244.5i 1.71691i 0.512887 + 0.858456i \(0.328576\pi\)
−0.512887 + 0.858456i \(0.671424\pi\)
\(938\) 6482.40 6482.40i 0.225648 0.225648i
\(939\) −6688.37 −0.232446
\(940\) 10063.5 10063.5i 0.349185 0.349185i
\(941\) −11062.8 11062.8i −0.383247 0.383247i 0.489023 0.872271i \(-0.337353\pi\)
−0.872271 + 0.489023i \(0.837353\pi\)
\(942\) 13409.7 + 13409.7i 0.463814 + 0.463814i
\(943\) 2653.84i 0.0916447i
\(944\) 3161.05i 0.108987i
\(945\) 6301.31 + 6301.31i 0.216912 + 0.216912i
\(946\) 6322.16 + 6322.16i 0.217284 + 0.217284i
\(947\) 23380.2 23380.2i 0.802273 0.802273i −0.181177 0.983450i \(-0.557991\pi\)
0.983450 + 0.181177i \(0.0579907\pi\)
\(948\) −976.546 −0.0334565
\(949\) 929.270 929.270i 0.0317865 0.0317865i
\(950\) 5357.85i 0.182981i
\(951\) 32295.3 1.10121
\(952\) 7766.29 349.187i 0.264398 0.0118878i
\(953\) −47771.2 −1.62378 −0.811890 0.583811i \(-0.801561\pi\)
−0.811890 + 0.583811i \(0.801561\pi\)
\(954\) 516.188i 0.0175180i
\(955\) 13708.2 13708.2i 0.464489 0.464489i
\(956\) 14004.5 0.473786
\(957\) −34595.4 + 34595.4i −1.16856 + 1.16856i
\(958\) 1570.24 + 1570.24i 0.0529563 + 0.0529563i
\(959\) −7427.61 7427.61i −0.250104 0.250104i
\(960\) 59707.0i 2.00733i
\(961\) 1591.73i 0.0534300i
\(962\) −26433.2 26433.2i −0.885904 0.885904i
\(963\) 12101.1 + 12101.1i 0.404935 + 0.404935i
\(964\) −4459.97 + 4459.97i −0.149010 + 0.149010i
\(965\) −50404.0 −1.68141
\(966\) −2391.37 + 2391.37i −0.0796490 + 0.0796490i
\(967\) 29494.2i 0.980837i −0.871487 0.490418i \(-0.836844\pi\)
0.871487 0.490418i \(-0.163156\pi\)
\(968\) −23940.7 −0.794919
\(969\) 821.087 + 18261.9i 0.0272210 + 0.605423i
\(970\) 8734.16 0.289110
\(971\) 32058.3i 1.05953i 0.848146 + 0.529763i \(0.177719\pi\)
−0.848146 + 0.529763i \(0.822281\pi\)
\(972\) −9671.32 + 9671.32i −0.319144 + 0.319144i
\(973\) 11266.1 0.371196
\(974\) −1353.30 + 1353.30i −0.0445200 + 0.0445200i
\(975\) 23877.8 + 23877.8i 0.784311 + 0.784311i
\(976\) −9949.44 9949.44i −0.326305 0.326305i
\(977\) 47602.0i 1.55878i 0.626542 + 0.779388i \(0.284470\pi\)
−0.626542 + 0.779388i \(0.715530\pi\)
\(978\) 15009.2i 0.490738i
\(979\) 6510.05 + 6510.05i 0.212525 + 0.212525i
\(980\) −11506.2 11506.2i −0.375052 0.375052i
\(981\) 26862.2 26862.2i 0.874256 0.874256i
\(982\) −31603.5 −1.02699
\(983\) 20407.1 20407.1i 0.662142 0.662142i −0.293743 0.955885i \(-0.594901\pi\)
0.955885 + 0.293743i \(0.0949009\pi\)
\(984\) 12953.0i 0.419640i
\(985\) 50971.2 1.64881
\(986\) 809.189 + 17997.2i 0.0261357 + 0.581287i
\(987\) −10747.8 −0.346613
\(988\) 5416.91i 0.174428i
\(989\) 2599.90 2599.90i 0.0835916 0.0835916i
\(990\) −63304.3 −2.03227
\(991\) −3326.26 + 3326.26i −0.106622 + 0.106622i −0.758405 0.651783i \(-0.774021\pi\)
0.651783 + 0.758405i \(0.274021\pi\)
\(992\) 17248.7 + 17248.7i 0.552065 + 0.552065i
\(993\) −50209.0 50209.0i −1.60457 1.60457i
\(994\) 3200.41i 0.102123i
\(995\) 44124.1i 1.40586i
\(996\) −5914.55 5914.55i −0.188162 0.188162i
\(997\) −23322.1 23322.1i −0.740842 0.740842i 0.231898 0.972740i \(-0.425506\pi\)
−0.972740 + 0.231898i \(0.925506\pi\)
\(998\) 3936.14 3936.14i 0.124846 0.124846i
\(999\) −48605.3 −1.53934
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 17.4.c.a.4.3 8
3.2 odd 2 153.4.f.a.55.2 8
4.3 odd 2 272.4.o.e.225.4 8
17.2 even 8 289.4.b.c.288.4 8
17.8 even 8 289.4.a.f.1.6 8
17.9 even 8 289.4.a.f.1.5 8
17.13 even 4 inner 17.4.c.a.13.2 yes 8
17.15 even 8 289.4.b.c.288.3 8
51.47 odd 4 153.4.f.a.64.3 8
68.47 odd 4 272.4.o.e.81.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.4.c.a.4.3 8 1.1 even 1 trivial
17.4.c.a.13.2 yes 8 17.13 even 4 inner
153.4.f.a.55.2 8 3.2 odd 2
153.4.f.a.64.3 8 51.47 odd 4
272.4.o.e.81.4 8 68.47 odd 4
272.4.o.e.225.4 8 4.3 odd 2
289.4.a.f.1.5 8 17.9 even 8
289.4.a.f.1.6 8 17.8 even 8
289.4.b.c.288.3 8 17.15 even 8
289.4.b.c.288.4 8 17.2 even 8