Properties

Label 197.3.c.a.14.19
Level $197$
Weight $3$
Character 197.14
Analytic conductor $5.368$
Analytic rank $0$
Dimension $64$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [197,3,Mod(14,197)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(197, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("197.14");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 197 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 197.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: \(5.36786120790\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(32\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 14.19
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.19

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.667408 - 0.667408i) q^{2} +(2.53367 - 2.53367i) q^{3} +3.10913i q^{4} +(-6.79914 + 6.79914i) q^{5} -3.38198i q^{6} +5.78196i q^{7} +(4.74469 + 4.74469i) q^{8} -3.83893i q^{9} +O(q^{10})\) \(q+(0.667408 - 0.667408i) q^{2} +(2.53367 - 2.53367i) q^{3} +3.10913i q^{4} +(-6.79914 + 6.79914i) q^{5} -3.38198i q^{6} +5.78196i q^{7} +(4.74469 + 4.74469i) q^{8} -3.83893i q^{9} +9.07559i q^{10} +(1.00971 - 1.00971i) q^{11} +(7.87751 + 7.87751i) q^{12} +(-3.79947 + 3.79947i) q^{13} +(3.85893 + 3.85893i) q^{14} +34.4535i q^{15} -6.10325 q^{16} +(2.05428 + 2.05428i) q^{17} +(-2.56213 - 2.56213i) q^{18} -21.0491i q^{19} +(-21.1394 - 21.1394i) q^{20} +(14.6496 + 14.6496i) q^{21} -1.34778i q^{22} +30.3445 q^{23} +24.0429 q^{24} -67.4565i q^{25} +5.07159i q^{26} +(13.0764 + 13.0764i) q^{27} -17.9769 q^{28} -22.3251 q^{29} +(22.9945 + 22.9945i) q^{30} +(18.3286 - 18.3286i) q^{31} +(-23.0521 + 23.0521i) q^{32} -5.11656i q^{33} +2.74208 q^{34} +(-39.3123 - 39.3123i) q^{35} +11.9357 q^{36} +58.7681 q^{37} +(-14.0483 - 14.0483i) q^{38} +19.2532i q^{39} -64.5196 q^{40} +3.61067i q^{41} +19.5545 q^{42} +58.1181i q^{43} +(3.13934 + 3.13934i) q^{44} +(26.1014 + 26.1014i) q^{45} +(20.2521 - 20.2521i) q^{46} +54.1791i q^{47} +(-15.4636 + 15.4636i) q^{48} +15.5689 q^{49} +(-45.0210 - 45.0210i) q^{50} +10.4097 q^{51} +(-11.8131 - 11.8131i) q^{52} +0.486855 q^{53} +17.4546 q^{54} +13.7304i q^{55} +(-27.4336 + 27.4336i) q^{56} +(-53.3315 - 53.3315i) q^{57} +(-14.8999 + 14.8999i) q^{58} -41.0327 q^{59} -107.121 q^{60} -22.5942 q^{61} -24.4653i q^{62} +22.1965 q^{63} +6.35733i q^{64} -51.6663i q^{65} +(-3.41483 - 3.41483i) q^{66} +(36.7245 - 36.7245i) q^{67} +(-6.38702 + 6.38702i) q^{68} +(76.8827 - 76.8827i) q^{69} -52.4747 q^{70} +(61.5039 + 61.5039i) q^{71} +(18.2145 - 18.2145i) q^{72} +(55.0929 - 55.0929i) q^{73} +(39.2223 - 39.2223i) q^{74} +(-170.912 - 170.912i) q^{75} +65.4445 q^{76} +(5.83813 + 5.83813i) q^{77} +(12.8497 + 12.8497i) q^{78} +(-80.3629 - 80.3629i) q^{79} +(41.4968 - 41.4968i) q^{80} +100.813 q^{81} +(2.40979 + 2.40979i) q^{82} +82.9292i q^{83} +(-45.5474 + 45.5474i) q^{84} -27.9346 q^{85} +(38.7885 + 38.7885i) q^{86} +(-56.5643 + 56.5643i) q^{87} +9.58157 q^{88} +(-104.173 - 104.173i) q^{89} +34.8406 q^{90} +(-21.9684 - 21.9684i) q^{91} +94.3450i q^{92} -92.8771i q^{93} +(36.1595 + 36.1595i) q^{94} +(143.116 + 143.116i) q^{95} +116.813i q^{96} -94.0182i q^{97} +(10.3908 - 10.3908i) q^{98} +(-3.87622 - 3.87622i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 2 q^{2} - 2 q^{3} - 10 q^{5} - 6 q^{8} + 10 q^{11} + 68 q^{12} + 2 q^{13} - 2 q^{14} - 280 q^{16} - 30 q^{17} - 68 q^{18} + 114 q^{20} - 20 q^{21} + 48 q^{23} + 60 q^{24} + 22 q^{27} + 392 q^{28} + 56 q^{29} - 70 q^{30} - 64 q^{31} - 156 q^{32} - 52 q^{34} - 92 q^{35} - 36 q^{36} - 160 q^{37} + 40 q^{38} + 52 q^{40} + 80 q^{42} + 140 q^{44} + 324 q^{45} + 214 q^{46} + 216 q^{48} - 836 q^{49} + 126 q^{50} + 124 q^{51} - 10 q^{52} - 16 q^{53} + 400 q^{54} - 40 q^{56} + 68 q^{57} - 266 q^{58} - 364 q^{59} - 68 q^{60} - 168 q^{61} - 12 q^{63} + 238 q^{66} - 112 q^{67} - 148 q^{68} - 48 q^{69} + 48 q^{70} + 150 q^{71} - 474 q^{72} + 18 q^{73} + 236 q^{74} + 64 q^{75} - 260 q^{76} - 388 q^{77} - 782 q^{78} + 202 q^{79} + 796 q^{80} - 516 q^{81} + 72 q^{82} - 294 q^{84} - 696 q^{85} + 618 q^{86} + 464 q^{87} - 244 q^{88} - 536 q^{89} + 1484 q^{90} + 212 q^{91} + 132 q^{94} + 370 q^{95} - 530 q^{98} - 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/197\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.667408 0.667408i 0.333704 0.333704i −0.520287 0.853991i \(-0.674175\pi\)
0.853991 + 0.520287i \(0.174175\pi\)
\(3\) 2.53367 2.53367i 0.844555 0.844555i −0.144892 0.989447i \(-0.546283\pi\)
0.989447 + 0.144892i \(0.0462835\pi\)
\(4\) 3.10913i 0.777283i
\(5\) −6.79914 + 6.79914i −1.35983 + 1.35983i −0.485704 + 0.874123i \(0.661437\pi\)
−0.874123 + 0.485704i \(0.838563\pi\)
\(6\) 3.38198i 0.563663i
\(7\) 5.78196i 0.825994i 0.910732 + 0.412997i \(0.135518\pi\)
−0.910732 + 0.412997i \(0.864482\pi\)
\(8\) 4.74469 + 4.74469i 0.593086 + 0.593086i
\(9\) 3.83893i 0.426548i
\(10\) 9.07559i 0.907559i
\(11\) 1.00971 1.00971i 0.0917922 0.0917922i −0.659720 0.751512i \(-0.729325\pi\)
0.751512 + 0.659720i \(0.229325\pi\)
\(12\) 7.87751 + 7.87751i 0.656459 + 0.656459i
\(13\) −3.79947 + 3.79947i −0.292267 + 0.292267i −0.837975 0.545708i \(-0.816261\pi\)
0.545708 + 0.837975i \(0.316261\pi\)
\(14\) 3.85893 + 3.85893i 0.275638 + 0.275638i
\(15\) 34.4535i 2.29690i
\(16\) −6.10325 −0.381453
\(17\) 2.05428 + 2.05428i 0.120840 + 0.120840i 0.764941 0.644101i \(-0.222768\pi\)
−0.644101 + 0.764941i \(0.722768\pi\)
\(18\) −2.56213 2.56213i −0.142341 0.142341i
\(19\) 21.0491i 1.10785i −0.832567 0.553924i \(-0.813130\pi\)
0.832567 0.553924i \(-0.186870\pi\)
\(20\) −21.1394 21.1394i −1.05697 1.05697i
\(21\) 14.6496 + 14.6496i 0.697598 + 0.697598i
\(22\) 1.34778i 0.0612629i
\(23\) 30.3445 1.31932 0.659662 0.751562i \(-0.270699\pi\)
0.659662 + 0.751562i \(0.270699\pi\)
\(24\) 24.0429 1.00179
\(25\) 67.4565i 2.69826i
\(26\) 5.07159i 0.195061i
\(27\) 13.0764 + 13.0764i 0.484312 + 0.484312i
\(28\) −17.9769 −0.642032
\(29\) −22.3251 −0.769831 −0.384915 0.922952i \(-0.625769\pi\)
−0.384915 + 0.922952i \(0.625769\pi\)
\(30\) 22.9945 + 22.9945i 0.766484 + 0.766484i
\(31\) 18.3286 18.3286i 0.591245 0.591245i −0.346723 0.937968i \(-0.612706\pi\)
0.937968 + 0.346723i \(0.112706\pi\)
\(32\) −23.0521 + 23.0521i −0.720379 + 0.720379i
\(33\) 5.11656i 0.155047i
\(34\) 2.74208 0.0806494
\(35\) −39.3123 39.3123i −1.12321 1.12321i
\(36\) 11.9357 0.331549
\(37\) 58.7681 1.58833 0.794164 0.607703i \(-0.207909\pi\)
0.794164 + 0.607703i \(0.207909\pi\)
\(38\) −14.0483 14.0483i −0.369693 0.369693i
\(39\) 19.2532i 0.493671i
\(40\) −64.5196 −1.61299
\(41\) 3.61067i 0.0880652i 0.999030 + 0.0440326i \(0.0140206\pi\)
−0.999030 + 0.0440326i \(0.985979\pi\)
\(42\) 19.5545 0.465582
\(43\) 58.1181i 1.35158i 0.737092 + 0.675792i \(0.236198\pi\)
−0.737092 + 0.675792i \(0.763802\pi\)
\(44\) 3.13934 + 3.13934i 0.0713486 + 0.0713486i
\(45\) 26.1014 + 26.1014i 0.580031 + 0.580031i
\(46\) 20.2521 20.2521i 0.440264 0.440264i
\(47\) 54.1791i 1.15275i 0.817187 + 0.576373i \(0.195532\pi\)
−0.817187 + 0.576373i \(0.804468\pi\)
\(48\) −15.4636 + 15.4636i −0.322158 + 0.322158i
\(49\) 15.5689 0.317733
\(50\) −45.0210 45.0210i −0.900420 0.900420i
\(51\) 10.4097 0.204112
\(52\) −11.8131 11.8131i −0.227174 0.227174i
\(53\) 0.486855 0.00918594 0.00459297 0.999989i \(-0.498538\pi\)
0.00459297 + 0.999989i \(0.498538\pi\)
\(54\) 17.4546 0.323234
\(55\) 13.7304i 0.249643i
\(56\) −27.4336 + 27.4336i −0.489886 + 0.489886i
\(57\) −53.3315 53.3315i −0.935640 0.935640i
\(58\) −14.8999 + 14.8999i −0.256896 + 0.256896i
\(59\) −41.0327 −0.695469 −0.347735 0.937593i \(-0.613049\pi\)
−0.347735 + 0.937593i \(0.613049\pi\)
\(60\) −107.121 −1.78534
\(61\) −22.5942 −0.370396 −0.185198 0.982701i \(-0.559293\pi\)
−0.185198 + 0.982701i \(0.559293\pi\)
\(62\) 24.4653i 0.394601i
\(63\) 22.1965 0.352326
\(64\) 6.35733i 0.0993333i
\(65\) 51.6663i 0.794866i
\(66\) −3.41483 3.41483i −0.0517399 0.0517399i
\(67\) 36.7245 36.7245i 0.548127 0.548127i −0.377771 0.925899i \(-0.623310\pi\)
0.925899 + 0.377771i \(0.123310\pi\)
\(68\) −6.38702 + 6.38702i −0.0939267 + 0.0939267i
\(69\) 76.8827 76.8827i 1.11424 1.11424i
\(70\) −52.4747 −0.749639
\(71\) 61.5039 + 61.5039i 0.866252 + 0.866252i 0.992055 0.125803i \(-0.0401507\pi\)
−0.125803 + 0.992055i \(0.540151\pi\)
\(72\) 18.2145 18.2145i 0.252980 0.252980i
\(73\) 55.0929 55.0929i 0.754697 0.754697i −0.220655 0.975352i \(-0.570819\pi\)
0.975352 + 0.220655i \(0.0708193\pi\)
\(74\) 39.2223 39.2223i 0.530031 0.530031i
\(75\) −170.912 170.912i −2.27883 2.27883i
\(76\) 65.4445 0.861112
\(77\) 5.83813 + 5.83813i 0.0758199 + 0.0758199i
\(78\) 12.8497 + 12.8497i 0.164740 + 0.164740i
\(79\) −80.3629 80.3629i −1.01725 1.01725i −0.999849 0.0174029i \(-0.994460\pi\)
−0.0174029 0.999849i \(-0.505540\pi\)
\(80\) 41.4968 41.4968i 0.518710 0.518710i
\(81\) 100.813 1.24460
\(82\) 2.40979 + 2.40979i 0.0293877 + 0.0293877i
\(83\) 82.9292i 0.999147i 0.866271 + 0.499574i \(0.166510\pi\)
−0.866271 + 0.499574i \(0.833490\pi\)
\(84\) −45.5474 + 45.5474i −0.542231 + 0.542231i
\(85\) −27.9346 −0.328642
\(86\) 38.7885 + 38.7885i 0.451029 + 0.451029i
\(87\) −56.5643 + 56.5643i −0.650165 + 0.650165i
\(88\) 9.58157 0.108881
\(89\) −104.173 104.173i −1.17048 1.17048i −0.982095 0.188389i \(-0.939674\pi\)
−0.188389 0.982095i \(-0.560326\pi\)
\(90\) 34.8406 0.387117
\(91\) −21.9684 21.9684i −0.241411 0.241411i
\(92\) 94.3450i 1.02549i
\(93\) 92.8771i 0.998678i
\(94\) 36.1595 + 36.1595i 0.384676 + 0.384676i
\(95\) 143.116 + 143.116i 1.50648 + 1.50648i
\(96\) 116.813i 1.21680i
\(97\) 94.0182i 0.969260i −0.874719 0.484630i \(-0.838954\pi\)
0.874719 0.484630i \(-0.161046\pi\)
\(98\) 10.3908 10.3908i 0.106029 0.106029i
\(99\) −3.87622 3.87622i −0.0391538 0.0391538i
\(100\) 209.731 2.09731
\(101\) 38.7897 0.384057 0.192028 0.981389i \(-0.438493\pi\)
0.192028 + 0.981389i \(0.438493\pi\)
\(102\) 6.94751 6.94751i 0.0681129 0.0681129i
\(103\) 7.99967 7.99967i 0.0776667 0.0776667i −0.667206 0.744873i \(-0.732510\pi\)
0.744873 + 0.667206i \(0.232510\pi\)
\(104\) −36.0546 −0.346679
\(105\) −199.209 −1.89723
\(106\) 0.324931 0.324931i 0.00306538 0.00306538i
\(107\) 105.683i 0.987689i 0.869550 + 0.493845i \(0.164409\pi\)
−0.869550 + 0.493845i \(0.835591\pi\)
\(108\) −40.6564 + 40.6564i −0.376448 + 0.376448i
\(109\) 112.675i 1.03372i 0.856071 + 0.516858i \(0.172899\pi\)
−0.856071 + 0.516858i \(0.827101\pi\)
\(110\) 9.16376 + 9.16376i 0.0833069 + 0.0833069i
\(111\) 148.899 148.899i 1.34143 1.34143i
\(112\) 35.2887i 0.315078i
\(113\) −113.119 113.119i −1.00106 1.00106i −0.999999 0.00105786i \(-0.999663\pi\)
−0.00105786 0.999999i \(-0.500337\pi\)
\(114\) −71.1877 −0.624453
\(115\) −206.316 + 206.316i −1.79405 + 1.79405i
\(116\) 69.4117i 0.598377i
\(117\) 14.5859 + 14.5859i 0.124666 + 0.124666i
\(118\) −27.3855 + 27.3855i −0.232081 + 0.232081i
\(119\) −11.8777 + 11.8777i −0.0998130 + 0.0998130i
\(120\) −163.471 + 163.471i −1.36226 + 1.36226i
\(121\) 118.961i 0.983148i
\(122\) −15.0795 + 15.0795i −0.123603 + 0.123603i
\(123\) 9.14825 + 9.14825i 0.0743760 + 0.0743760i
\(124\) 56.9860 + 56.9860i 0.459565 + 0.459565i
\(125\) 288.668 + 288.668i 2.30934 + 2.30934i
\(126\) 14.8141 14.8141i 0.117573 0.117573i
\(127\) 220.144i 1.73341i −0.498818 0.866707i \(-0.666232\pi\)
0.498818 0.866707i \(-0.333768\pi\)
\(128\) −87.9655 87.9655i −0.687231 0.687231i
\(129\) 147.252 + 147.252i 1.14149 + 1.14149i
\(130\) −34.4825 34.4825i −0.265250 0.265250i
\(131\) 36.6896 36.6896i 0.280073 0.280073i −0.553065 0.833138i \(-0.686542\pi\)
0.833138 + 0.553065i \(0.186542\pi\)
\(132\) 15.9081 0.120516
\(133\) 121.705 0.915077
\(134\) 49.0205i 0.365824i
\(135\) −177.817 −1.31716
\(136\) 19.4938i 0.143337i
\(137\) 81.8815i 0.597675i −0.954304 0.298838i \(-0.903401\pi\)
0.954304 0.298838i \(-0.0965989\pi\)
\(138\) 102.624i 0.743654i
\(139\) −100.787 100.787i −0.725087 0.725087i 0.244549 0.969637i \(-0.421360\pi\)
−0.969637 + 0.244549i \(0.921360\pi\)
\(140\) 122.227 122.227i 0.873053 0.873053i
\(141\) 137.272 + 137.272i 0.973558 + 0.973558i
\(142\) 82.0964 0.578144
\(143\) 7.67276i 0.0536557i
\(144\) 23.4299i 0.162708i
\(145\) 151.791 151.791i 1.04684 1.04684i
\(146\) 73.5389i 0.503691i
\(147\) 39.4465 39.4465i 0.268343 0.268343i
\(148\) 182.718i 1.23458i
\(149\) 78.6215 + 78.6215i 0.527661 + 0.527661i 0.919874 0.392213i \(-0.128291\pi\)
−0.392213 + 0.919874i \(0.628291\pi\)
\(150\) −228.137 −1.52091
\(151\) 132.841 + 132.841i 0.879742 + 0.879742i 0.993508 0.113765i \(-0.0362912\pi\)
−0.113765 + 0.993508i \(0.536291\pi\)
\(152\) 99.8716 99.8716i 0.657050 0.657050i
\(153\) 7.88622 7.88622i 0.0515439 0.0515439i
\(154\) 7.79283 0.0506028
\(155\) 249.237i 1.60798i
\(156\) −59.8607 −0.383723
\(157\) 35.4535i 0.225818i 0.993605 + 0.112909i \(0.0360169\pi\)
−0.993605 + 0.112909i \(0.963983\pi\)
\(158\) −107.270 −0.678921
\(159\) 1.23353 1.23353i 0.00775804 0.00775804i
\(160\) 313.469i 1.95918i
\(161\) 175.450i 1.08975i
\(162\) 67.2834 67.2834i 0.415329 0.415329i
\(163\) 264.682i 1.62382i −0.583786 0.811908i \(-0.698429\pi\)
0.583786 0.811908i \(-0.301571\pi\)
\(164\) −11.2261 −0.0684517
\(165\) 34.7882 + 34.7882i 0.210838 + 0.210838i
\(166\) 55.3476 + 55.3476i 0.333419 + 0.333419i
\(167\) 50.4707 50.4707i 0.302219 0.302219i −0.539662 0.841882i \(-0.681448\pi\)
0.841882 + 0.539662i \(0.181448\pi\)
\(168\) 139.015i 0.827472i
\(169\) 140.128i 0.829160i
\(170\) −18.6438 + 18.6438i −0.109669 + 0.109669i
\(171\) −80.8061 −0.472550
\(172\) −180.697 −1.05056
\(173\) 130.406i 0.753794i −0.926255 0.376897i \(-0.876991\pi\)
0.926255 0.376897i \(-0.123009\pi\)
\(174\) 75.5030i 0.433925i
\(175\) 390.031 2.22875
\(176\) −6.16254 + 6.16254i −0.0350144 + 0.0350144i
\(177\) −103.963 + 103.963i −0.587362 + 0.587362i
\(178\) −139.052 −0.781190
\(179\) 8.57108 8.57108i 0.0478831 0.0478831i −0.682760 0.730643i \(-0.739220\pi\)
0.730643 + 0.682760i \(0.239220\pi\)
\(180\) −81.1528 + 81.1528i −0.450849 + 0.450849i
\(181\) 307.341i 1.69802i −0.528379 0.849008i \(-0.677200\pi\)
0.528379 0.849008i \(-0.322800\pi\)
\(182\) −29.3238 −0.161120
\(183\) −57.2461 + 57.2461i −0.312820 + 0.312820i
\(184\) 143.975 + 143.975i 0.782473 + 0.782473i
\(185\) −399.573 + 399.573i −2.15985 + 2.15985i
\(186\) −61.9869 61.9869i −0.333263 0.333263i
\(187\) 4.14846 0.0221843
\(188\) −168.450 −0.896010
\(189\) −75.6074 + 75.6074i −0.400039 + 0.400039i
\(190\) 191.033 1.00544
\(191\) 59.2313 0.310112 0.155056 0.987906i \(-0.450444\pi\)
0.155056 + 0.987906i \(0.450444\pi\)
\(192\) 16.1074 + 16.1074i 0.0838925 + 0.0838925i
\(193\) 224.589 1.16367 0.581836 0.813306i \(-0.302335\pi\)
0.581836 + 0.813306i \(0.302335\pi\)
\(194\) −62.7485 62.7485i −0.323446 0.323446i
\(195\) −130.905 130.905i −0.671308 0.671308i
\(196\) 48.4059i 0.246969i
\(197\) −188.779 + 56.3155i −0.958270 + 0.285865i
\(198\) −5.17404 −0.0261315
\(199\) −104.061 + 104.061i −0.522922 + 0.522922i −0.918453 0.395531i \(-0.870561\pi\)
0.395531 + 0.918453i \(0.370561\pi\)
\(200\) 320.060 320.060i 1.60030 1.60030i
\(201\) 186.095i 0.925848i
\(202\) 25.8886 25.8886i 0.128161 0.128161i
\(203\) 129.083i 0.635876i
\(204\) 32.3651i 0.158653i
\(205\) −24.5495 24.5495i −0.119754 0.119754i
\(206\) 10.6781i 0.0518353i
\(207\) 116.490i 0.562755i
\(208\) 23.1891 23.1891i 0.111486 0.111486i
\(209\) −21.2536 21.2536i −0.101692 0.101692i
\(210\) −132.953 + 132.953i −0.633112 + 0.633112i
\(211\) 242.031 + 242.031i 1.14707 + 1.14707i 0.987127 + 0.159941i \(0.0511304\pi\)
0.159941 + 0.987127i \(0.448870\pi\)
\(212\) 1.51370i 0.00714008i
\(213\) 311.661 1.46320
\(214\) 70.5335 + 70.5335i 0.329596 + 0.329596i
\(215\) −395.153 395.153i −1.83792 1.83792i
\(216\) 124.087i 0.574478i
\(217\) 105.975 + 105.975i 0.488365 + 0.488365i
\(218\) 75.2003 + 75.2003i 0.344955 + 0.344955i
\(219\) 279.174i 1.27477i
\(220\) −42.6896 −0.194044
\(221\) −15.6103 −0.0706350
\(222\) 198.753i 0.895282i
\(223\) 208.663i 0.935709i −0.883806 0.467854i \(-0.845027\pi\)
0.883806 0.467854i \(-0.154973\pi\)
\(224\) −133.286 133.286i −0.595029 0.595029i
\(225\) −258.961 −1.15094
\(226\) −150.994 −0.668113
\(227\) 86.3883 + 86.3883i 0.380565 + 0.380565i 0.871306 0.490741i \(-0.163274\pi\)
−0.490741 + 0.871306i \(0.663274\pi\)
\(228\) 165.815 165.815i 0.727257 0.727257i
\(229\) −111.819 + 111.819i −0.488295 + 0.488295i −0.907768 0.419473i \(-0.862215\pi\)
0.419473 + 0.907768i \(0.362215\pi\)
\(230\) 275.394i 1.19737i
\(231\) 29.5838 0.128068
\(232\) −105.926 105.926i −0.456576 0.456576i
\(233\) −220.073 −0.944518 −0.472259 0.881460i \(-0.656561\pi\)
−0.472259 + 0.881460i \(0.656561\pi\)
\(234\) 19.4695 0.0832030
\(235\) −368.371 368.371i −1.56754 1.56754i
\(236\) 127.576i 0.540577i
\(237\) −407.225 −1.71825
\(238\) 15.8546i 0.0666159i
\(239\) 362.452 1.51654 0.758268 0.651943i \(-0.226046\pi\)
0.758268 + 0.651943i \(0.226046\pi\)
\(240\) 210.278i 0.876159i
\(241\) 197.780 + 197.780i 0.820666 + 0.820666i 0.986203 0.165538i \(-0.0529360\pi\)
−0.165538 + 0.986203i \(0.552936\pi\)
\(242\) 79.3955 + 79.3955i 0.328080 + 0.328080i
\(243\) 137.739 137.739i 0.566826 0.566826i
\(244\) 70.2483i 0.287903i
\(245\) −105.855 + 105.855i −0.432062 + 0.432062i
\(246\) 12.2112 0.0496391
\(247\) 79.9755 + 79.9755i 0.323788 + 0.323788i
\(248\) 173.927 0.701319
\(249\) 210.115 + 210.115i 0.843835 + 0.843835i
\(250\) 385.318 1.54127
\(251\) −248.445 −0.989820 −0.494910 0.868944i \(-0.664799\pi\)
−0.494910 + 0.868944i \(0.664799\pi\)
\(252\) 69.0120i 0.273857i
\(253\) 30.6392 30.6392i 0.121104 0.121104i
\(254\) −146.925 146.925i −0.578447 0.578447i
\(255\) −70.7770 + 70.7770i −0.277557 + 0.277557i
\(256\) −142.847 −0.557996
\(257\) −181.630 −0.706732 −0.353366 0.935485i \(-0.614963\pi\)
−0.353366 + 0.935485i \(0.614963\pi\)
\(258\) 196.554 0.761838
\(259\) 339.795i 1.31195i
\(260\) 160.637 0.617836
\(261\) 85.7045i 0.328370i
\(262\) 48.9738i 0.186923i
\(263\) −235.897 235.897i −0.896948 0.896948i 0.0982168 0.995165i \(-0.468686\pi\)
−0.995165 + 0.0982168i \(0.968686\pi\)
\(264\) 24.2765 24.2765i 0.0919564 0.0919564i
\(265\) −3.31019 + 3.31019i −0.0124913 + 0.0124913i
\(266\) 81.2270 81.2270i 0.305365 0.305365i
\(267\) −527.879 −1.97708
\(268\) 114.181 + 114.181i 0.426050 + 0.426050i
\(269\) −186.106 + 186.106i −0.691844 + 0.691844i −0.962637 0.270794i \(-0.912714\pi\)
0.270794 + 0.962637i \(0.412714\pi\)
\(270\) −118.676 + 118.676i −0.439542 + 0.439542i
\(271\) 285.987 285.987i 1.05530 1.05530i 0.0569245 0.998378i \(-0.481871\pi\)
0.998378 0.0569245i \(-0.0181294\pi\)
\(272\) −12.5378 12.5378i −0.0460947 0.0460947i
\(273\) −111.321 −0.407770
\(274\) −54.6484 54.6484i −0.199447 0.199447i
\(275\) −68.1119 68.1119i −0.247680 0.247680i
\(276\) 239.039 + 239.039i 0.866082 + 0.866082i
\(277\) 8.19494 8.19494i 0.0295846 0.0295846i −0.692160 0.721744i \(-0.743341\pi\)
0.721744 + 0.692160i \(0.243341\pi\)
\(278\) −134.532 −0.483929
\(279\) −70.3622 70.3622i −0.252194 0.252194i
\(280\) 373.050i 1.33232i
\(281\) −154.239 + 154.239i −0.548894 + 0.548894i −0.926121 0.377227i \(-0.876878\pi\)
0.377227 + 0.926121i \(0.376878\pi\)
\(282\) 183.232 0.649760
\(283\) −179.606 179.606i −0.634649 0.634649i 0.314581 0.949230i \(-0.398136\pi\)
−0.949230 + 0.314581i \(0.898136\pi\)
\(284\) −191.224 + 191.224i −0.673324 + 0.673324i
\(285\) 725.216 2.54462
\(286\) 5.12086 + 5.12086i 0.0179051 + 0.0179051i
\(287\) −20.8768 −0.0727414
\(288\) 88.4955 + 88.4955i 0.307276 + 0.307276i
\(289\) 280.560i 0.970796i
\(290\) 202.614i 0.698667i
\(291\) −238.211 238.211i −0.818594 0.818594i
\(292\) 171.291 + 171.291i 0.586614 + 0.586614i
\(293\) 373.796i 1.27575i 0.770139 + 0.637876i \(0.220187\pi\)
−0.770139 + 0.637876i \(0.779813\pi\)
\(294\) 52.6538i 0.179094i
\(295\) 278.987 278.987i 0.945718 0.945718i
\(296\) 278.837 + 278.837i 0.942016 + 0.942016i
\(297\) 26.4069 0.0889122
\(298\) 104.945 0.352165
\(299\) −115.293 + 115.293i −0.385595 + 0.385595i
\(300\) 531.389 531.389i 1.77130 1.77130i
\(301\) −336.037 −1.11640
\(302\) 177.318 0.587147
\(303\) 98.2802 98.2802i 0.324357 0.324357i
\(304\) 128.468i 0.422592i
\(305\) 153.621 153.621i 0.503675 0.503675i
\(306\) 10.5267i 0.0344008i
\(307\) −330.389 330.389i −1.07618 1.07618i −0.996848 0.0793370i \(-0.974720\pi\)
−0.0793370 0.996848i \(-0.525280\pi\)
\(308\) −18.1515 + 18.1515i −0.0589335 + 0.0589335i
\(309\) 40.5370i 0.131188i
\(310\) 166.343 + 166.343i 0.536590 + 0.536590i
\(311\) −381.189 −1.22569 −0.612844 0.790204i \(-0.709975\pi\)
−0.612844 + 0.790204i \(0.709975\pi\)
\(312\) −91.3504 + 91.3504i −0.292790 + 0.292790i
\(313\) 7.71024i 0.0246334i −0.999924 0.0123167i \(-0.996079\pi\)
0.999924 0.0123167i \(-0.00392062\pi\)
\(314\) 23.6619 + 23.6619i 0.0753565 + 0.0753565i
\(315\) −150.917 + 150.917i −0.479103 + 0.479103i
\(316\) 249.859 249.859i 0.790693 0.790693i
\(317\) 240.853 240.853i 0.759790 0.759790i −0.216494 0.976284i \(-0.569462\pi\)
0.976284 + 0.216494i \(0.0694621\pi\)
\(318\) 1.64653i 0.00517777i
\(319\) −22.5420 + 22.5420i −0.0706645 + 0.0706645i
\(320\) −43.2244 43.2244i −0.135076 0.135076i
\(321\) 267.765 + 267.765i 0.834158 + 0.834158i
\(322\) 117.097 + 117.097i 0.363655 + 0.363655i
\(323\) 43.2407 43.2407i 0.133872 0.133872i
\(324\) 313.441i 0.967411i
\(325\) 256.299 + 256.299i 0.788613 + 0.788613i
\(326\) −176.651 176.651i −0.541874 0.541874i
\(327\) 285.481 + 285.481i 0.873031 + 0.873031i
\(328\) −17.1315 + 17.1315i −0.0522303 + 0.0522303i
\(329\) −313.261 −0.952162
\(330\) 46.4358 0.140715
\(331\) 223.284i 0.674575i −0.941402 0.337288i \(-0.890491\pi\)
0.941402 0.337288i \(-0.109509\pi\)
\(332\) −257.838 −0.776621
\(333\) 225.607i 0.677498i
\(334\) 67.3690i 0.201704i
\(335\) 499.390i 1.49072i
\(336\) −89.4099 89.4099i −0.266101 0.266101i
\(337\) −435.784 + 435.784i −1.29313 + 1.29313i −0.360285 + 0.932842i \(0.617321\pi\)
−0.932842 + 0.360285i \(0.882679\pi\)
\(338\) 93.5225 + 93.5225i 0.276694 + 0.276694i
\(339\) −573.214 −1.69090
\(340\) 86.8524i 0.255448i
\(341\) 37.0133i 0.108543i
\(342\) −53.9306 + 53.9306i −0.157692 + 0.157692i
\(343\) 373.335i 1.08844i
\(344\) −275.753 + 275.753i −0.801606 + 0.801606i
\(345\) 1045.47i 3.03036i
\(346\) −87.0342 87.0342i −0.251544 0.251544i
\(347\) 456.987 1.31696 0.658482 0.752596i \(-0.271199\pi\)
0.658482 + 0.752596i \(0.271199\pi\)
\(348\) −175.866 175.866i −0.505362 0.505362i
\(349\) −151.008 + 151.008i −0.432688 + 0.432688i −0.889542 0.456854i \(-0.848976\pi\)
0.456854 + 0.889542i \(0.348976\pi\)
\(350\) 260.310 260.310i 0.743742 0.743742i
\(351\) −99.3670 −0.283097
\(352\) 46.5521i 0.132250i
\(353\) 679.336 1.92446 0.962232 0.272231i \(-0.0877614\pi\)
0.962232 + 0.272231i \(0.0877614\pi\)
\(354\) 138.772i 0.392010i
\(355\) −836.347 −2.35591
\(356\) 323.888 323.888i 0.909797 0.909797i
\(357\) 60.1885i 0.168595i
\(358\) 11.4408i 0.0319576i
\(359\) 40.7213 40.7213i 0.113430 0.113430i −0.648114 0.761544i \(-0.724442\pi\)
0.761544 + 0.648114i \(0.224442\pi\)
\(360\) 247.686i 0.688018i
\(361\) −82.0656 −0.227328
\(362\) −205.122 205.122i −0.566635 0.566635i
\(363\) 301.407 + 301.407i 0.830323 + 0.830323i
\(364\) 68.3027 68.3027i 0.187645 0.187645i
\(365\) 749.169i 2.05252i
\(366\) 76.4130i 0.208779i
\(367\) −227.877 + 227.877i −0.620919 + 0.620919i −0.945767 0.324847i \(-0.894687\pi\)
0.324847 + 0.945767i \(0.394687\pi\)
\(368\) −185.200 −0.503260
\(369\) 13.8611 0.0375640
\(370\) 533.356i 1.44150i
\(371\) 2.81498i 0.00758754i
\(372\) 288.767 0.776256
\(373\) 31.0197 31.0197i 0.0831626 0.0831626i −0.664302 0.747464i \(-0.731271\pi\)
0.747464 + 0.664302i \(0.231271\pi\)
\(374\) 2.76872 2.76872i 0.00740299 0.00740299i
\(375\) 1462.78 3.90074
\(376\) −257.063 + 257.063i −0.683678 + 0.683678i
\(377\) 84.8236 84.8236i 0.224996 0.224996i
\(378\) 100.922i 0.266989i
\(379\) 530.439 1.39958 0.699788 0.714351i \(-0.253278\pi\)
0.699788 + 0.714351i \(0.253278\pi\)
\(380\) −444.966 + 444.966i −1.17096 + 1.17096i
\(381\) −557.770 557.770i −1.46396 1.46396i
\(382\) 39.5314 39.5314i 0.103485 0.103485i
\(383\) −109.961 109.961i −0.287105 0.287105i 0.548829 0.835935i \(-0.315074\pi\)
−0.835935 + 0.548829i \(0.815074\pi\)
\(384\) −445.751 −1.16081
\(385\) −79.3885 −0.206204
\(386\) 149.892 149.892i 0.388322 0.388322i
\(387\) 223.111 0.576515
\(388\) 292.315 0.753390
\(389\) 23.4246 + 23.4246i 0.0602174 + 0.0602174i 0.736574 0.676357i \(-0.236442\pi\)
−0.676357 + 0.736574i \(0.736442\pi\)
\(390\) −174.734 −0.448036
\(391\) 62.3359 + 62.3359i 0.159427 + 0.159427i
\(392\) 73.8697 + 73.8697i 0.188443 + 0.188443i
\(393\) 185.918i 0.473075i
\(394\) −88.4073 + 163.578i −0.224384 + 0.415173i
\(395\) 1092.80 2.76657
\(396\) 12.0517 12.0517i 0.0304336 0.0304336i
\(397\) 28.8064 28.8064i 0.0725603 0.0725603i −0.669895 0.742456i \(-0.733661\pi\)
0.742456 + 0.669895i \(0.233661\pi\)
\(398\) 138.903i 0.349002i
\(399\) 308.360 308.360i 0.772833 0.772833i
\(400\) 411.704i 1.02926i
\(401\) 523.412i 1.30527i −0.757674 0.652633i \(-0.773664\pi\)
0.757674 0.652633i \(-0.226336\pi\)
\(402\) −124.202 124.202i −0.308959 0.308959i
\(403\) 139.278i 0.345603i
\(404\) 120.602i 0.298521i
\(405\) −685.441 + 685.441i −1.69245 + 1.69245i
\(406\) −86.1509 86.1509i −0.212194 0.212194i
\(407\) 59.3391 59.3391i 0.145796 0.145796i
\(408\) 49.3908 + 49.3908i 0.121056 + 0.121056i
\(409\) 128.343i 0.313797i 0.987615 + 0.156898i \(0.0501495\pi\)
−0.987615 + 0.156898i \(0.949851\pi\)
\(410\) −32.7690 −0.0799244
\(411\) −207.460 207.460i −0.504770 0.504770i
\(412\) 24.8720 + 24.8720i 0.0603690 + 0.0603690i
\(413\) 237.249i 0.574454i
\(414\) −77.7465 77.7465i −0.187793 0.187793i
\(415\) −563.847 563.847i −1.35867 1.35867i
\(416\) 175.172i 0.421086i
\(417\) −510.722 −1.22475
\(418\) −28.3696 −0.0678700
\(419\) 79.7564i 0.190350i 0.995461 + 0.0951748i \(0.0303410\pi\)
−0.995461 + 0.0951748i \(0.969659\pi\)
\(420\) 619.367i 1.47468i
\(421\) 33.4622 + 33.4622i 0.0794827 + 0.0794827i 0.745730 0.666248i \(-0.232101\pi\)
−0.666248 + 0.745730i \(0.732101\pi\)
\(422\) 323.067 0.765562
\(423\) 207.990 0.491701
\(424\) 2.30998 + 2.30998i 0.00544806 + 0.00544806i
\(425\) 138.574 138.574i 0.326057 0.326057i
\(426\) 208.005 208.005i 0.488274 0.488274i
\(427\) 130.639i 0.305945i
\(428\) −328.582 −0.767714
\(429\) 19.4402 + 19.4402i 0.0453152 + 0.0453152i
\(430\) −527.456 −1.22664
\(431\) 354.778 0.823151 0.411575 0.911376i \(-0.364979\pi\)
0.411575 + 0.911376i \(0.364979\pi\)
\(432\) −79.8087 79.8087i −0.184742 0.184742i
\(433\) 797.239i 1.84120i −0.390509 0.920599i \(-0.627701\pi\)
0.390509 0.920599i \(-0.372299\pi\)
\(434\) 141.457 0.325939
\(435\) 769.178i 1.76822i
\(436\) −350.322 −0.803491
\(437\) 638.724i 1.46161i
\(438\) −186.323 186.323i −0.425395 0.425395i
\(439\) −266.871 266.871i −0.607906 0.607906i 0.334492 0.942399i \(-0.391435\pi\)
−0.942399 + 0.334492i \(0.891435\pi\)
\(440\) −65.1464 + 65.1464i −0.148060 + 0.148060i
\(441\) 59.7680i 0.135528i
\(442\) −10.4185 + 10.4185i −0.0235712 + 0.0235712i
\(443\) −51.6516 −0.116595 −0.0582976 0.998299i \(-0.518567\pi\)
−0.0582976 + 0.998299i \(0.518567\pi\)
\(444\) 462.947 + 462.947i 1.04267 + 1.04267i
\(445\) 1416.57 3.18331
\(446\) −139.263 139.263i −0.312250 0.312250i
\(447\) 398.401 0.891278
\(448\) −36.7578 −0.0820488
\(449\) 335.846i 0.747987i −0.927431 0.373994i \(-0.877988\pi\)
0.927431 0.373994i \(-0.122012\pi\)
\(450\) −172.833 + 172.833i −0.384072 + 0.384072i
\(451\) 3.64575 + 3.64575i 0.00808371 + 0.00808371i
\(452\) 351.704 351.704i 0.778105 0.778105i
\(453\) 673.150 1.48598
\(454\) 115.312 0.253992
\(455\) 298.732 0.656555
\(456\) 506.083i 1.10983i
\(457\) −199.958 −0.437544 −0.218772 0.975776i \(-0.570205\pi\)
−0.218772 + 0.975776i \(0.570205\pi\)
\(458\) 149.258i 0.325892i
\(459\) 53.7252i 0.117048i
\(460\) −641.464 641.464i −1.39449 1.39449i
\(461\) 516.007 516.007i 1.11932 1.11932i 0.127481 0.991841i \(-0.459311\pi\)
0.991841 0.127481i \(-0.0406892\pi\)
\(462\) 19.7444 19.7444i 0.0427369 0.0427369i
\(463\) −84.4878 + 84.4878i −0.182479 + 0.182479i −0.792435 0.609956i \(-0.791187\pi\)
0.609956 + 0.792435i \(0.291187\pi\)
\(464\) 136.256 0.293654
\(465\) 631.484 + 631.484i 1.35803 + 1.35803i
\(466\) −146.878 + 146.878i −0.315189 + 0.315189i
\(467\) −325.185 + 325.185i −0.696328 + 0.696328i −0.963617 0.267288i \(-0.913872\pi\)
0.267288 + 0.963617i \(0.413872\pi\)
\(468\) −45.3495 + 45.3495i −0.0969007 + 0.0969007i
\(469\) 212.340 + 212.340i 0.452750 + 0.452750i
\(470\) −491.707 −1.04619
\(471\) 89.8273 + 89.8273i 0.190716 + 0.190716i
\(472\) −194.687 194.687i −0.412473 0.412473i
\(473\) 58.6827 + 58.6827i 0.124065 + 0.124065i
\(474\) −271.785 + 271.785i −0.573387 + 0.573387i
\(475\) −1419.90 −2.98927
\(476\) −36.9295 36.9295i −0.0775830 0.0775830i
\(477\) 1.86900i 0.00391824i
\(478\) 241.903 241.903i 0.506074 0.506074i
\(479\) −855.393 −1.78579 −0.892894 0.450266i \(-0.851329\pi\)
−0.892894 + 0.450266i \(0.851329\pi\)
\(480\) −794.226 794.226i −1.65464 1.65464i
\(481\) −223.288 + 223.288i −0.464216 + 0.464216i
\(482\) 264.000 0.547719
\(483\) 444.533 + 444.533i 0.920358 + 0.920358i
\(484\) −369.866 −0.764185
\(485\) 639.243 + 639.243i 1.31803 + 1.31803i
\(486\) 183.856i 0.378304i
\(487\) 506.767i 1.04059i 0.853987 + 0.520295i \(0.174178\pi\)
−0.853987 + 0.520295i \(0.825822\pi\)
\(488\) −107.202 107.202i −0.219677 0.219677i
\(489\) −670.616 670.616i −1.37140 1.37140i
\(490\) 141.297i 0.288362i
\(491\) 423.405i 0.862332i −0.902273 0.431166i \(-0.858102\pi\)
0.902273 0.431166i \(-0.141898\pi\)
\(492\) −28.4431 + 28.4431i −0.0578112 + 0.0578112i
\(493\) −45.8619 45.8619i −0.0930262 0.0930262i
\(494\) 106.753 0.216098
\(495\) 52.7100 0.106485
\(496\) −111.864 + 111.864i −0.225532 + 0.225532i
\(497\) −355.613 + 355.613i −0.715520 + 0.715520i
\(498\) 280.465 0.563182
\(499\) −816.198 −1.63567 −0.817833 0.575455i \(-0.804825\pi\)
−0.817833 + 0.575455i \(0.804825\pi\)
\(500\) −897.507 + 897.507i −1.79501 + 1.79501i
\(501\) 255.752i 0.510482i
\(502\) −165.814 + 165.814i −0.330307 + 0.330307i
\(503\) 393.199i 0.781708i 0.920453 + 0.390854i \(0.127820\pi\)
−0.920453 + 0.390854i \(0.872180\pi\)
\(504\) 105.316 + 105.316i 0.208960 + 0.208960i
\(505\) −263.737 + 263.737i −0.522251 + 0.522251i
\(506\) 40.8977i 0.0808256i
\(507\) 355.038 + 355.038i 0.700272 + 0.700272i
\(508\) 684.456 1.34735
\(509\) −414.170 + 414.170i −0.813693 + 0.813693i −0.985185 0.171493i \(-0.945141\pi\)
0.171493 + 0.985185i \(0.445141\pi\)
\(510\) 94.4742i 0.185244i
\(511\) 318.545 + 318.545i 0.623376 + 0.623376i
\(512\) 256.525 256.525i 0.501025 0.501025i
\(513\) 275.247 275.247i 0.536545 0.536545i
\(514\) −121.221 + 121.221i −0.235839 + 0.235839i
\(515\) 108.782i 0.211227i
\(516\) −457.826 + 457.826i −0.887260 + 0.887260i
\(517\) 54.7054 + 54.7054i 0.105813 + 0.105813i
\(518\) 226.782 + 226.782i 0.437803 + 0.437803i
\(519\) −330.406 330.406i −0.636621 0.636621i
\(520\) 245.140 245.140i 0.471424 0.471424i
\(521\) 442.868i 0.850035i −0.905185 0.425017i \(-0.860268\pi\)
0.905185 0.425017i \(-0.139732\pi\)
\(522\) 57.1998 + 57.1998i 0.109578 + 0.109578i
\(523\) 132.896 + 132.896i 0.254104 + 0.254104i 0.822651 0.568547i \(-0.192494\pi\)
−0.568547 + 0.822651i \(0.692494\pi\)
\(524\) 114.073 + 114.073i 0.217696 + 0.217696i
\(525\) 988.209 988.209i 1.88230 1.88230i
\(526\) −314.879 −0.598630
\(527\) 75.3040 0.142892
\(528\) 31.2276i 0.0591433i
\(529\) 391.786 0.740616
\(530\) 4.41850i 0.00833679i
\(531\) 157.522i 0.296651i
\(532\) 378.398i 0.711274i
\(533\) −13.7187 13.7187i −0.0257386 0.0257386i
\(534\) −352.311 + 352.311i −0.659758 + 0.659758i
\(535\) −718.551 718.551i −1.34309 1.34309i
\(536\) 348.493 0.650174
\(537\) 43.4325i 0.0808799i
\(538\) 248.417i 0.461742i
\(539\) 15.7202 15.7202i 0.0291654 0.0291654i
\(540\) 552.856i 1.02381i
\(541\) −217.985 + 217.985i −0.402929 + 0.402929i −0.879264 0.476335i \(-0.841965\pi\)
0.476335 + 0.879264i \(0.341965\pi\)
\(542\) 381.740i 0.704317i
\(543\) −778.700 778.700i −1.43407 1.43407i
\(544\) −94.7108 −0.174101
\(545\) −766.094 766.094i −1.40568 1.40568i
\(546\) −74.2966 + 74.2966i −0.136074 + 0.136074i
\(547\) 27.2395 27.2395i 0.0497980 0.0497980i −0.681769 0.731567i \(-0.738789\pi\)
0.731567 + 0.681769i \(0.238789\pi\)
\(548\) 254.581 0.464563
\(549\) 86.7375i 0.157992i
\(550\) −90.9168 −0.165303
\(551\) 469.924i 0.852856i
\(552\) 729.570 1.32168
\(553\) 464.655 464.655i 0.840244 0.840244i
\(554\) 10.9387i 0.0197450i
\(555\) 2024.77i 3.64823i
\(556\) 313.361 313.361i 0.563598 0.563598i
\(557\) 85.8619i 0.154151i −0.997025 0.0770754i \(-0.975442\pi\)
0.997025 0.0770754i \(-0.0245582\pi\)
\(558\) −93.9205 −0.168316
\(559\) −220.818 220.818i −0.395023 0.395023i
\(560\) 239.933 + 239.933i 0.428452 + 0.428452i
\(561\) 10.5108 10.5108i 0.0187359 0.0187359i
\(562\) 205.881i 0.366336i
\(563\) 675.575i 1.19996i 0.800017 + 0.599978i \(0.204824\pi\)
−0.800017 + 0.599978i \(0.795176\pi\)
\(564\) −426.796 + 426.796i −0.756731 + 0.756731i
\(565\) 1538.23 2.72253
\(566\) −239.740 −0.423570
\(567\) 582.897i 1.02804i
\(568\) 583.634i 1.02753i
\(569\) 442.696 0.778025 0.389013 0.921232i \(-0.372816\pi\)
0.389013 + 0.921232i \(0.372816\pi\)
\(570\) 484.015 484.015i 0.849149 0.849149i
\(571\) −163.321 + 163.321i −0.286026 + 0.286026i −0.835507 0.549480i \(-0.814826\pi\)
0.549480 + 0.835507i \(0.314826\pi\)
\(572\) −23.8557 −0.0417057
\(573\) 150.072 150.072i 0.261906 0.261906i
\(574\) −13.9333 + 13.9333i −0.0242741 + 0.0242741i
\(575\) 2046.93i 3.55988i
\(576\) 24.4054 0.0423704
\(577\) 712.767 712.767i 1.23530 1.23530i 0.273397 0.961901i \(-0.411853\pi\)
0.961901 0.273397i \(-0.0881473\pi\)
\(578\) −187.248 187.248i −0.323958 0.323958i
\(579\) 569.033 569.033i 0.982786 0.982786i
\(580\) 471.940 + 471.940i 0.813689 + 0.813689i
\(581\) −479.494 −0.825290
\(582\) −317.967 −0.546336
\(583\) 0.491585 0.491585i 0.000843198 0.000843198i
\(584\) 522.798 0.895202
\(585\) −198.343 −0.339048
\(586\) 249.474 + 249.474i 0.425724 + 0.425724i
\(587\) 92.7714 0.158043 0.0790217 0.996873i \(-0.474820\pi\)
0.0790217 + 0.996873i \(0.474820\pi\)
\(588\) 122.644 + 122.644i 0.208579 + 0.208579i
\(589\) −385.801 385.801i −0.655010 0.655010i
\(590\) 372.396i 0.631180i
\(591\) −335.619 + 620.988i −0.567883 + 1.05074i
\(592\) −358.677 −0.605873
\(593\) 742.567 742.567i 1.25222 1.25222i 0.297498 0.954722i \(-0.403848\pi\)
0.954722 0.297498i \(-0.0961523\pi\)
\(594\) 17.6242 17.6242i 0.0296703 0.0296703i
\(595\) 161.517i 0.271457i
\(596\) −244.445 + 244.445i −0.410142 + 0.410142i
\(597\) 527.314i 0.883273i
\(598\) 153.895i 0.257349i
\(599\) 73.7717 + 73.7717i 0.123158 + 0.123158i 0.765999 0.642841i \(-0.222245\pi\)
−0.642841 + 0.765999i \(0.722245\pi\)
\(600\) 1621.85i 2.70309i
\(601\) 287.726i 0.478745i 0.970928 + 0.239372i \(0.0769416\pi\)
−0.970928 + 0.239372i \(0.923058\pi\)
\(602\) −224.273 + 224.273i −0.372547 + 0.372547i
\(603\) −140.983 140.983i −0.233803 0.233803i
\(604\) −413.021 + 413.021i −0.683809 + 0.683809i
\(605\) −808.832 808.832i −1.33691 1.33691i
\(606\) 131.186i 0.216478i
\(607\) −355.159 −0.585105 −0.292553 0.956249i \(-0.594505\pi\)
−0.292553 + 0.956249i \(0.594505\pi\)
\(608\) 485.227 + 485.227i 0.798071 + 0.798071i
\(609\) −327.053 327.053i −0.537033 0.537033i
\(610\) 205.056i 0.336157i
\(611\) −205.852 205.852i −0.336910 0.336910i
\(612\) 24.5193 + 24.5193i 0.0400642 + 0.0400642i
\(613\) 1057.66i 1.72538i 0.505731 + 0.862691i \(0.331223\pi\)
−0.505731 + 0.862691i \(0.668777\pi\)
\(614\) −441.008 −0.718254
\(615\) −124.400 −0.202277
\(616\) 55.4003i 0.0899355i
\(617\) 788.170i 1.27742i 0.769447 + 0.638711i \(0.220532\pi\)
−0.769447 + 0.638711i \(0.779468\pi\)
\(618\) −27.0547 27.0547i −0.0437778 0.0437778i
\(619\) 17.0969 0.0276202 0.0138101 0.999905i \(-0.495604\pi\)
0.0138101 + 0.999905i \(0.495604\pi\)
\(620\) −774.912 −1.24986
\(621\) 396.797 + 396.797i 0.638965 + 0.638965i
\(622\) −254.409 + 254.409i −0.409017 + 0.409017i
\(623\) 602.324 602.324i 0.966813 0.966813i
\(624\) 117.507i 0.188312i
\(625\) −2238.97 −3.58236
\(626\) −5.14587 5.14587i −0.00822025 0.00822025i
\(627\) −107.699 −0.171769
\(628\) −110.230 −0.175525
\(629\) 120.726 + 120.726i 0.191933 + 0.191933i
\(630\) 201.447i 0.319757i
\(631\) 33.6668 0.0533547 0.0266774 0.999644i \(-0.491507\pi\)
0.0266774 + 0.999644i \(0.491507\pi\)
\(632\) 762.594i 1.20664i
\(633\) 1226.45 1.93752
\(634\) 321.495i 0.507090i
\(635\) 1496.79 + 1496.79i 2.35714 + 2.35714i
\(636\) 3.83520 + 3.83520i 0.00603019 + 0.00603019i
\(637\) −59.1537 + 59.1537i −0.0928629 + 0.0928629i
\(638\) 30.0894i 0.0471620i
\(639\) 236.109 236.109i 0.369498 0.369498i
\(640\) 1196.18 1.86903
\(641\) 423.988 + 423.988i 0.661447 + 0.661447i 0.955721 0.294274i \(-0.0950777\pi\)
−0.294274 + 0.955721i \(0.595078\pi\)
\(642\) 357.417 0.556724
\(643\) −58.3662 58.3662i −0.0907717 0.0907717i 0.660263 0.751035i \(-0.270445\pi\)
−0.751035 + 0.660263i \(0.770445\pi\)
\(644\) −545.499 −0.847048
\(645\) −2002.37 −3.10445
\(646\) 57.7184i 0.0893473i
\(647\) 189.680 189.680i 0.293168 0.293168i −0.545162 0.838331i \(-0.683532\pi\)
0.838331 + 0.545162i \(0.183532\pi\)
\(648\) 478.326 + 478.326i 0.738158 + 0.738158i
\(649\) −41.4313 + 41.4313i −0.0638387 + 0.0638387i
\(650\) 342.112 0.526326
\(651\) 537.012 0.824903
\(652\) 822.932 1.26217
\(653\) 512.285i 0.784510i 0.919856 + 0.392255i \(0.128305\pi\)
−0.919856 + 0.392255i \(0.871695\pi\)
\(654\) 381.065 0.582668
\(655\) 498.915i 0.761703i
\(656\) 22.0368i 0.0335928i
\(657\) −211.498 211.498i −0.321915 0.321915i
\(658\) −209.073 + 209.073i −0.317740 + 0.317740i
\(659\) 552.326 552.326i 0.838128 0.838128i −0.150485 0.988612i \(-0.548083\pi\)
0.988612 + 0.150485i \(0.0480834\pi\)
\(660\) −108.161 + 108.161i −0.163881 + 0.163881i
\(661\) 564.855 0.854547 0.427273 0.904122i \(-0.359474\pi\)
0.427273 + 0.904122i \(0.359474\pi\)
\(662\) −149.022 149.022i −0.225108 0.225108i
\(663\) −39.5514 + 39.5514i −0.0596551 + 0.0596551i
\(664\) −393.474 + 393.474i −0.592581 + 0.592581i
\(665\) −827.490 + 827.490i −1.24435 + 1.24435i
\(666\) −150.572 150.572i −0.226084 0.226084i
\(667\) −677.443 −1.01566
\(668\) 156.920 + 156.920i 0.234910 + 0.234910i
\(669\) −528.683 528.683i −0.790258 0.790258i
\(670\) 333.297 + 333.297i 0.497458 + 0.497458i
\(671\) −22.8137 + 22.8137i −0.0339995 + 0.0339995i
\(672\) −675.407 −1.00507
\(673\) 284.508 + 284.508i 0.422746 + 0.422746i 0.886148 0.463402i \(-0.153371\pi\)
−0.463402 + 0.886148i \(0.653371\pi\)
\(674\) 581.691i 0.863043i
\(675\) 882.091 882.091i 1.30680 1.30680i
\(676\) −435.677 −0.644492
\(677\) −343.841 343.841i −0.507889 0.507889i 0.405989 0.913878i \(-0.366927\pi\)
−0.913878 + 0.405989i \(0.866927\pi\)
\(678\) −382.567 + 382.567i −0.564259 + 0.564259i
\(679\) 543.610 0.800603
\(680\) −132.541 132.541i −0.194913 0.194913i
\(681\) 437.758 0.642817
\(682\) −24.7030 24.7030i −0.0362214 0.0362214i
\(683\) 747.941i 1.09508i −0.836779 0.547541i \(-0.815564\pi\)
0.836779 0.547541i \(-0.184436\pi\)
\(684\) 251.237i 0.367306i
\(685\) 556.724 + 556.724i 0.812735 + 0.812735i
\(686\) 249.167 + 249.167i 0.363217 + 0.363217i
\(687\) 566.626i 0.824784i
\(688\) 354.709i 0.515566i
\(689\) −1.84979 + 1.84979i −0.00268475 + 0.00268475i
\(690\) 697.756 + 697.756i 1.01124 + 1.01124i
\(691\) 652.256 0.943930 0.471965 0.881617i \(-0.343545\pi\)
0.471965 + 0.881617i \(0.343545\pi\)
\(692\) 405.451 0.585911
\(693\) 22.4122 22.4122i 0.0323408 0.0323408i
\(694\) 304.996 304.996i 0.439476 0.439476i
\(695\) 1370.53 1.97199
\(696\) −536.761 −0.771208
\(697\) −7.41732 + 7.41732i −0.0106418 + 0.0106418i
\(698\) 201.568i 0.288779i
\(699\) −557.590 + 557.590i −0.797697 + 0.797697i
\(700\) 1212.66i 1.73237i
\(701\) 329.174 + 329.174i 0.469577 + 0.469577i 0.901778 0.432200i \(-0.142263\pi\)
−0.432200 + 0.901778i \(0.642263\pi\)
\(702\) −66.3183 + 66.3183i −0.0944706 + 0.0944706i
\(703\) 1237.02i 1.75963i
\(704\) 6.41909 + 6.41909i 0.00911803 + 0.00911803i
\(705\) −1866.66 −2.64774
\(706\) 453.394 453.394i 0.642201 0.642201i
\(707\) 224.281i 0.317229i
\(708\) −323.235 323.235i −0.456547 0.456547i
\(709\) 104.752 104.752i 0.147746 0.147746i −0.629364 0.777110i \(-0.716685\pi\)
0.777110 + 0.629364i \(0.216685\pi\)
\(710\) −558.185 + 558.185i −0.786176 + 0.786176i
\(711\) −308.507 + 308.507i −0.433906 + 0.433906i
\(712\) 988.537i 1.38840i
\(713\) 556.171 556.171i 0.780044 0.780044i
\(714\) 40.1703 + 40.1703i 0.0562609 + 0.0562609i
\(715\) −52.1682 52.1682i −0.0729625 0.0729625i
\(716\) 26.6486 + 26.6486i 0.0372188 + 0.0372188i
\(717\) 918.333 918.333i 1.28080 1.28080i
\(718\) 54.3555i 0.0757040i
\(719\) 342.186 + 342.186i 0.475920 + 0.475920i 0.903824 0.427904i \(-0.140748\pi\)
−0.427904 + 0.903824i \(0.640748\pi\)
\(720\) −159.303 159.303i −0.221255 0.221255i
\(721\) 46.2538 + 46.2538i 0.0641522 + 0.0641522i
\(722\) −54.7712 + 54.7712i −0.0758604 + 0.0758604i
\(723\) 1002.22 1.38620
\(724\) 955.564 1.31984
\(725\) 1505.97i 2.07721i
\(726\) 402.323 0.554164
\(727\) 1161.83i 1.59811i −0.601257 0.799056i \(-0.705333\pi\)
0.601257 0.799056i \(-0.294667\pi\)
\(728\) 208.467i 0.286355i
\(729\) 209.349i 0.287174i
\(730\) 500.001 + 500.001i 0.684933 + 0.684933i
\(731\) −119.391 + 119.391i −0.163325 + 0.163325i
\(732\) −177.986 177.986i −0.243150 0.243150i
\(733\) −986.866 −1.34634 −0.673169 0.739489i \(-0.735067\pi\)
−0.673169 + 0.739489i \(0.735067\pi\)
\(734\) 304.174i 0.414406i
\(735\) 536.404i 0.729801i
\(736\) −699.504 + 699.504i −0.950413 + 0.950413i
\(737\) 74.1626i 0.100628i
\(738\) 9.25103 9.25103i 0.0125353 0.0125353i
\(739\) 1236.09i 1.67265i 0.548231 + 0.836327i \(0.315302\pi\)
−0.548231 + 0.836327i \(0.684698\pi\)
\(740\) −1242.33 1242.33i −1.67882 1.67882i
\(741\) 405.263 0.546913
\(742\) 1.87874 + 1.87874i 0.00253199 + 0.00253199i
\(743\) 354.588 354.588i 0.477239 0.477239i −0.427009 0.904247i \(-0.640433\pi\)
0.904247 + 0.427009i \(0.140433\pi\)
\(744\) 440.673 440.673i 0.592302 0.592302i
\(745\) −1069.12 −1.43506
\(746\) 41.4055i 0.0555034i
\(747\) 318.360 0.426184
\(748\) 12.8981i 0.0172435i
\(749\) −611.053 −0.815826
\(750\) 976.268 976.268i 1.30169 1.30169i
\(751\) 638.554i 0.850272i 0.905130 + 0.425136i \(0.139774\pi\)
−0.905130 + 0.425136i \(0.860226\pi\)
\(752\) 330.668i 0.439718i
\(753\) −629.476 + 629.476i −0.835958 + 0.835958i
\(754\) 113.224i 0.150164i
\(755\) −1806.41 −2.39260
\(756\) −235.074 235.074i −0.310944 0.310944i
\(757\) 336.326 + 336.326i 0.444288 + 0.444288i 0.893450 0.449162i \(-0.148277\pi\)
−0.449162 + 0.893450i \(0.648277\pi\)
\(758\) 354.019 354.019i 0.467044 0.467044i
\(759\) 155.259i 0.204558i
\(760\) 1358.08i 1.78695i
\(761\) −215.247 + 215.247i −0.282847 + 0.282847i −0.834244 0.551396i \(-0.814095\pi\)
0.551396 + 0.834244i \(0.314095\pi\)
\(762\) −744.520 −0.977061
\(763\) −651.483 −0.853844
\(764\) 184.158i 0.241045i
\(765\) 107.239i 0.140182i
\(766\) −146.778 −0.191616
\(767\) 155.903 155.903i 0.203263 0.203263i
\(768\) −361.927 + 361.927i −0.471259 + 0.471259i
\(769\) 905.056 1.17693 0.588463 0.808524i \(-0.299733\pi\)
0.588463 + 0.808524i \(0.299733\pi\)
\(770\) −52.9845 + 52.9845i −0.0688111 + 0.0688111i
\(771\) −460.190 + 460.190i −0.596875 + 0.596875i
\(772\) 698.276i 0.904503i
\(773\) 419.708 0.542959 0.271480 0.962444i \(-0.412487\pi\)
0.271480 + 0.962444i \(0.412487\pi\)
\(774\) 148.906 148.906i 0.192385 0.192385i
\(775\) −1236.38 1236.38i −1.59533 1.59533i