Properties

Label 197.3.c.a.14.8
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 14.8
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.84369 + 1.84369i) q^{2} +(-1.89732 + 1.89732i) q^{3} -2.79835i q^{4} +(6.24444 - 6.24444i) q^{5} -6.99613i q^{6} +9.93768i q^{7} +(-2.21546 - 2.21546i) q^{8} +1.80035i q^{9} +O(q^{10})\) \(q+(-1.84369 + 1.84369i) q^{2} +(-1.89732 + 1.89732i) q^{3} -2.79835i q^{4} +(6.24444 - 6.24444i) q^{5} -6.99613i q^{6} +9.93768i q^{7} +(-2.21546 - 2.21546i) q^{8} +1.80035i q^{9} +23.0256i q^{10} +(-8.38589 + 8.38589i) q^{11} +(5.30937 + 5.30937i) q^{12} +(-3.75764 + 3.75764i) q^{13} +(-18.3220 - 18.3220i) q^{14} +23.6954i q^{15} +19.3626 q^{16} +(-9.45941 - 9.45941i) q^{17} +(-3.31927 - 3.31927i) q^{18} +14.2722i q^{19} +(-17.4741 - 17.4741i) q^{20} +(-18.8550 - 18.8550i) q^{21} -30.9219i q^{22} -13.7509 q^{23} +8.40688 q^{24} -52.9860i q^{25} -13.8558i q^{26} +(-20.4917 - 20.4917i) q^{27} +27.8091 q^{28} +24.6517 q^{29} +(-43.6869 - 43.6869i) q^{30} +(-15.2126 + 15.2126i) q^{31} +(-26.8368 + 26.8368i) q^{32} -31.8215i q^{33} +34.8804 q^{34} +(62.0552 + 62.0552i) q^{35} +5.03800 q^{36} -73.8706 q^{37} +(-26.3134 - 26.3134i) q^{38} -14.2589i q^{39} -27.6686 q^{40} +61.6384i q^{41} +69.5252 q^{42} +35.7306i q^{43} +(23.4667 + 23.4667i) q^{44} +(11.2422 + 11.2422i) q^{45} +(25.3523 - 25.3523i) q^{46} -76.9664i q^{47} +(-36.7371 + 36.7371i) q^{48} -49.7574 q^{49} +(97.6895 + 97.6895i) q^{50} +35.8951 q^{51} +(10.5152 + 10.5152i) q^{52} +32.3548 q^{53} +75.5606 q^{54} +104.730i q^{55} +(22.0165 - 22.0165i) q^{56} +(-27.0789 - 27.0789i) q^{57} +(-45.4500 + 45.4500i) q^{58} -54.4486 q^{59} +66.3081 q^{60} -17.1333 q^{61} -56.0946i q^{62} -17.8913 q^{63} -21.5066i q^{64} +46.9286i q^{65} +(58.6688 + 58.6688i) q^{66} +(1.09112 - 1.09112i) q^{67} +(-26.4708 + 26.4708i) q^{68} +(26.0898 - 26.0898i) q^{69} -228.820 q^{70} +(26.4633 + 26.4633i) q^{71} +(3.98860 - 3.98860i) q^{72} +(46.8996 - 46.8996i) q^{73} +(136.194 - 136.194i) q^{74} +(100.531 + 100.531i) q^{75} +39.9386 q^{76} +(-83.3363 - 83.3363i) q^{77} +(26.2889 + 26.2889i) q^{78} +(110.202 + 110.202i) q^{79} +(120.909 - 120.909i) q^{80} +61.5556 q^{81} +(-113.642 - 113.642i) q^{82} +37.3833i q^{83} +(-52.7628 + 52.7628i) q^{84} -118.137 q^{85} +(-65.8760 - 65.8760i) q^{86} +(-46.7722 + 46.7722i) q^{87} +37.1572 q^{88} +(16.9595 + 16.9595i) q^{89} -41.4540 q^{90} +(-37.3422 - 37.3422i) q^{91} +38.4798i q^{92} -57.7265i q^{93} +(141.902 + 141.902i) q^{94} +(89.1218 + 89.1218i) q^{95} -101.836i q^{96} +149.988i q^{97} +(91.7370 - 91.7370i) q^{98} +(-15.0975 - 15.0975i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84369 + 1.84369i −0.921843 + 0.921843i −0.997160 0.0753169i \(-0.976003\pi\)
0.0753169 + 0.997160i \(0.476003\pi\)
\(3\) −1.89732 + 1.89732i −0.632440 + 0.632440i −0.948679 0.316239i \(-0.897580\pi\)
0.316239 + 0.948679i \(0.397580\pi\)
\(4\) 2.79835i 0.699588i
\(5\) 6.24444 6.24444i 1.24889 1.24889i 0.292675 0.956212i \(-0.405454\pi\)
0.956212 0.292675i \(-0.0945455\pi\)
\(6\) 6.99613i 1.16602i
\(7\) 9.93768i 1.41967i 0.704369 + 0.709834i \(0.251230\pi\)
−0.704369 + 0.709834i \(0.748770\pi\)
\(8\) −2.21546 2.21546i −0.276933 0.276933i
\(9\) 1.80035i 0.200039i
\(10\) 23.0256i 2.30256i
\(11\) −8.38589 + 8.38589i −0.762354 + 0.762354i −0.976747 0.214394i \(-0.931222\pi\)
0.214394 + 0.976747i \(0.431222\pi\)
\(12\) 5.30937 + 5.30937i 0.442448 + 0.442448i
\(13\) −3.75764 + 3.75764i −0.289049 + 0.289049i −0.836704 0.547655i \(-0.815521\pi\)
0.547655 + 0.836704i \(0.315521\pi\)
\(14\) −18.3220 18.3220i −1.30871 1.30871i
\(15\) 23.6954i 1.57969i
\(16\) 19.3626 1.21016
\(17\) −9.45941 9.45941i −0.556436 0.556436i 0.371855 0.928291i \(-0.378722\pi\)
−0.928291 + 0.371855i \(0.878722\pi\)
\(18\) −3.31927 3.31927i −0.184404 0.184404i
\(19\) 14.2722i 0.751168i 0.926788 + 0.375584i \(0.122558\pi\)
−0.926788 + 0.375584i \(0.877442\pi\)
\(20\) −17.4741 17.4741i −0.873707 0.873707i
\(21\) −18.8550 18.8550i −0.897855 0.897855i
\(22\) 30.9219i 1.40554i
\(23\) −13.7509 −0.597864 −0.298932 0.954274i \(-0.596630\pi\)
−0.298932 + 0.954274i \(0.596630\pi\)
\(24\) 8.40688 0.350287
\(25\) 52.9860i 2.11944i
\(26\) 13.8558i 0.532915i
\(27\) −20.4917 20.4917i −0.758953 0.758953i
\(28\) 27.8091 0.993183
\(29\) 24.6517 0.850059 0.425030 0.905179i \(-0.360264\pi\)
0.425030 + 0.905179i \(0.360264\pi\)
\(30\) −43.6869 43.6869i −1.45623 1.45623i
\(31\) −15.2126 + 15.2126i −0.490730 + 0.490730i −0.908536 0.417806i \(-0.862799\pi\)
0.417806 + 0.908536i \(0.362799\pi\)
\(32\) −26.8368 + 26.8368i −0.838649 + 0.838649i
\(33\) 31.8215i 0.964287i
\(34\) 34.8804 1.02589
\(35\) 62.0552 + 62.0552i 1.77301 + 1.77301i
\(36\) 5.03800 0.139945
\(37\) −73.8706 −1.99650 −0.998252 0.0591081i \(-0.981174\pi\)
−0.998252 + 0.0591081i \(0.981174\pi\)
\(38\) −26.3134 26.3134i −0.692459 0.692459i
\(39\) 14.2589i 0.365612i
\(40\) −27.6686 −0.691715
\(41\) 61.6384i 1.50338i 0.659519 + 0.751688i \(0.270760\pi\)
−0.659519 + 0.751688i \(0.729240\pi\)
\(42\) 69.5252 1.65536
\(43\) 35.7306i 0.830944i 0.909606 + 0.415472i \(0.136384\pi\)
−0.909606 + 0.415472i \(0.863616\pi\)
\(44\) 23.4667 + 23.4667i 0.533334 + 0.533334i
\(45\) 11.2422 + 11.2422i 0.249826 + 0.249826i
\(46\) 25.3523 25.3523i 0.551136 0.551136i
\(47\) 76.9664i 1.63758i −0.574091 0.818791i \(-0.694645\pi\)
0.574091 0.818791i \(-0.305355\pi\)
\(48\) −36.7371 + 36.7371i −0.765357 + 0.765357i
\(49\) −49.7574 −1.01546
\(50\) 97.6895 + 97.6895i 1.95379 + 1.95379i
\(51\) 35.8951 0.703825
\(52\) 10.5152 + 10.5152i 0.202215 + 0.202215i
\(53\) 32.3548 0.610468 0.305234 0.952277i \(-0.401265\pi\)
0.305234 + 0.952277i \(0.401265\pi\)
\(54\) 75.5606 1.39927
\(55\) 104.730i 1.90419i
\(56\) 22.0165 22.0165i 0.393152 0.393152i
\(57\) −27.0789 27.0789i −0.475069 0.475069i
\(58\) −45.4500 + 45.4500i −0.783621 + 0.783621i
\(59\) −54.4486 −0.922857 −0.461429 0.887177i \(-0.652663\pi\)
−0.461429 + 0.887177i \(0.652663\pi\)
\(60\) 66.3081 1.10513
\(61\) −17.1333 −0.280874 −0.140437 0.990090i \(-0.544851\pi\)
−0.140437 + 0.990090i \(0.544851\pi\)
\(62\) 56.0946i 0.904751i
\(63\) −17.8913 −0.283988
\(64\) 21.5066i 0.336040i
\(65\) 46.9286i 0.721979i
\(66\) 58.6688 + 58.6688i 0.888921 + 0.888921i
\(67\) 1.09112 1.09112i 0.0162853 0.0162853i −0.698917 0.715203i \(-0.746334\pi\)
0.715203 + 0.698917i \(0.246334\pi\)
\(68\) −26.4708 + 26.4708i −0.389276 + 0.389276i
\(69\) 26.0898 26.0898i 0.378113 0.378113i
\(70\) −228.820 −3.26886
\(71\) 26.4633 + 26.4633i 0.372722 + 0.372722i 0.868468 0.495746i \(-0.165105\pi\)
−0.495746 + 0.868468i \(0.665105\pi\)
\(72\) 3.98860 3.98860i 0.0553972 0.0553972i
\(73\) 46.8996 46.8996i 0.642460 0.642460i −0.308699 0.951160i \(-0.599894\pi\)
0.951160 + 0.308699i \(0.0998937\pi\)
\(74\) 136.194 136.194i 1.84046 1.84046i
\(75\) 100.531 + 100.531i 1.34042 + 1.34042i
\(76\) 39.9386 0.525508
\(77\) −83.3363 83.3363i −1.08229 1.08229i
\(78\) 26.2889 + 26.2889i 0.337037 + 0.337037i
\(79\) 110.202 + 110.202i 1.39497 + 1.39497i 0.813744 + 0.581224i \(0.197426\pi\)
0.581224 + 0.813744i \(0.302574\pi\)
\(80\) 120.909 120.909i 1.51136 1.51136i
\(81\) 61.5556 0.759946
\(82\) −113.642 113.642i −1.38588 1.38588i
\(83\) 37.3833i 0.450401i 0.974312 + 0.225201i \(0.0723037\pi\)
−0.974312 + 0.225201i \(0.927696\pi\)
\(84\) −52.7628 + 52.7628i −0.628129 + 0.628129i
\(85\) −118.137 −1.38985
\(86\) −65.8760 65.8760i −0.766000 0.766000i
\(87\) −46.7722 + 46.7722i −0.537612 + 0.537612i
\(88\) 37.1572 0.422241
\(89\) 16.9595 + 16.9595i 0.190557 + 0.190557i 0.795937 0.605380i \(-0.206979\pi\)
−0.605380 + 0.795937i \(0.706979\pi\)
\(90\) −41.4540 −0.460600
\(91\) −37.3422 37.3422i −0.410354 0.410354i
\(92\) 38.4798i 0.418258i
\(93\) 57.7265i 0.620715i
\(94\) 141.902 + 141.902i 1.50959 + 1.50959i
\(95\) 89.1218 + 89.1218i 0.938125 + 0.938125i
\(96\) 101.836i 1.06079i
\(97\) 149.988i 1.54627i 0.634241 + 0.773136i \(0.281313\pi\)
−0.634241 + 0.773136i \(0.718687\pi\)
\(98\) 91.7370 91.7370i 0.936092 0.936092i
\(99\) −15.0975 15.0975i −0.152500 0.152500i
\(100\) −148.273 −1.48273
\(101\) 73.8825 0.731509 0.365755 0.930711i \(-0.380811\pi\)
0.365755 + 0.930711i \(0.380811\pi\)
\(102\) −66.1792 + 66.1792i −0.648816 + 0.648816i
\(103\) −9.44382 + 9.44382i −0.0916875 + 0.0916875i −0.751463 0.659775i \(-0.770651\pi\)
0.659775 + 0.751463i \(0.270651\pi\)
\(104\) 16.6498 0.160094
\(105\) −235.477 −2.24264
\(106\) −59.6520 + 59.6520i −0.562755 + 0.562755i
\(107\) 66.4183i 0.620732i 0.950617 + 0.310366i \(0.100452\pi\)
−0.950617 + 0.310366i \(0.899548\pi\)
\(108\) −57.3431 + 57.3431i −0.530954 + 0.530954i
\(109\) 172.012i 1.57809i −0.614332 0.789047i \(-0.710575\pi\)
0.614332 0.789047i \(-0.289425\pi\)
\(110\) −193.090 193.090i −1.75536 1.75536i
\(111\) 140.156 140.156i 1.26267 1.26267i
\(112\) 192.420i 1.71803i
\(113\) 150.739 + 150.739i 1.33397 + 1.33397i 0.901783 + 0.432188i \(0.142258\pi\)
0.432188 + 0.901783i \(0.357742\pi\)
\(114\) 99.8501 0.875878
\(115\) −85.8664 + 85.8664i −0.746665 + 0.746665i
\(116\) 68.9842i 0.594691i
\(117\) −6.76505 6.76505i −0.0578209 0.0578209i
\(118\) 100.386 100.386i 0.850729 0.850729i
\(119\) 94.0046 94.0046i 0.789955 0.789955i
\(120\) 52.4962 52.4962i 0.437469 0.437469i
\(121\) 19.6464i 0.162367i
\(122\) 31.5884 31.5884i 0.258922 0.258922i
\(123\) −116.948 116.948i −0.950796 0.950796i
\(124\) 42.5703 + 42.5703i 0.343309 + 0.343309i
\(125\) −174.757 174.757i −1.39805 1.39805i
\(126\) 32.9859 32.9859i 0.261793 0.261793i
\(127\) 7.94707i 0.0625754i −0.999510 0.0312877i \(-0.990039\pi\)
0.999510 0.0312877i \(-0.00996081\pi\)
\(128\) −67.6957 67.6957i −0.528873 0.528873i
\(129\) −67.7924 67.7924i −0.525523 0.525523i
\(130\) −86.5217 86.5217i −0.665551 0.665551i
\(131\) 19.7271 19.7271i 0.150588 0.150588i −0.627792 0.778381i \(-0.716041\pi\)
0.778381 + 0.627792i \(0.216041\pi\)
\(132\) −89.0476 −0.674603
\(133\) −141.833 −1.06641
\(134\) 4.02335i 0.0300250i
\(135\) −255.919 −1.89569
\(136\) 41.9139i 0.308191i
\(137\) 87.1116i 0.635851i 0.948116 + 0.317925i \(0.102986\pi\)
−0.948116 + 0.317925i \(0.897014\pi\)
\(138\) 96.2028i 0.697122i
\(139\) −169.421 169.421i −1.21886 1.21886i −0.968032 0.250825i \(-0.919298\pi\)
−0.250825 0.968032i \(-0.580702\pi\)
\(140\) 173.652 173.652i 1.24037 1.24037i
\(141\) 146.030 + 146.030i 1.03567 + 1.03567i
\(142\) −97.5798 −0.687182
\(143\) 63.0223i 0.440715i
\(144\) 34.8595i 0.242080i
\(145\) 153.936 153.936i 1.06163 1.06163i
\(146\) 172.936i 1.18449i
\(147\) 94.4058 94.4058i 0.642216 0.642216i
\(148\) 206.716i 1.39673i
\(149\) 107.539 + 107.539i 0.721735 + 0.721735i 0.968958 0.247223i \(-0.0795182\pi\)
−0.247223 + 0.968958i \(0.579518\pi\)
\(150\) −370.696 −2.47131
\(151\) 9.51203 + 9.51203i 0.0629936 + 0.0629936i 0.737902 0.674908i \(-0.235817\pi\)
−0.674908 + 0.737902i \(0.735817\pi\)
\(152\) 31.6195 31.6195i 0.208023 0.208023i
\(153\) 17.0302 17.0302i 0.111309 0.111309i
\(154\) 307.292 1.99540
\(155\) 189.989i 1.22573i
\(156\) −39.9014 −0.255778
\(157\) 212.101i 1.35096i 0.737376 + 0.675482i \(0.236065\pi\)
−0.737376 + 0.675482i \(0.763935\pi\)
\(158\) −406.357 −2.57188
\(159\) −61.3874 + 61.3874i −0.386084 + 0.386084i
\(160\) 335.161i 2.09476i
\(161\) 136.652i 0.848768i
\(162\) −113.489 + 113.489i −0.700551 + 0.700551i
\(163\) 28.6411i 0.175712i 0.996133 + 0.0878560i \(0.0280015\pi\)
−0.996133 + 0.0878560i \(0.971998\pi\)
\(164\) 172.486 1.05174
\(165\) −198.707 198.707i −1.20429 1.20429i
\(166\) −68.9230 68.9230i −0.415199 0.415199i
\(167\) 137.557 137.557i 0.823696 0.823696i −0.162940 0.986636i \(-0.552098\pi\)
0.986636 + 0.162940i \(0.0520978\pi\)
\(168\) 83.5449i 0.497291i
\(169\) 140.760i 0.832901i
\(170\) 217.808 217.808i 1.28122 1.28122i
\(171\) −25.6949 −0.150263
\(172\) 99.9868 0.581319
\(173\) 121.271i 0.700986i −0.936565 0.350493i \(-0.886014\pi\)
0.936565 0.350493i \(-0.113986\pi\)
\(174\) 172.467i 0.991187i
\(175\) 526.557 3.00890
\(176\) −162.373 + 162.373i −0.922574 + 0.922574i
\(177\) 103.306 103.306i 0.583652 0.583652i
\(178\) −62.5361 −0.351326
\(179\) 76.9802 76.9802i 0.430057 0.430057i −0.458591 0.888648i \(-0.651646\pi\)
0.888648 + 0.458591i \(0.151646\pi\)
\(180\) 31.4595 31.4595i 0.174775 0.174775i
\(181\) 94.7437i 0.523446i −0.965143 0.261723i \(-0.915709\pi\)
0.965143 0.261723i \(-0.0842907\pi\)
\(182\) 137.694 0.756563
\(183\) 32.5074 32.5074i 0.177636 0.177636i
\(184\) 30.4645 + 30.4645i 0.165568 + 0.165568i
\(185\) −461.280 + 461.280i −2.49341 + 2.49341i
\(186\) 106.429 + 106.429i 0.572201 + 0.572201i
\(187\) 158.651 0.848402
\(188\) −215.379 −1.14563
\(189\) 203.640 203.640i 1.07746 1.07746i
\(190\) −328.625 −1.72961
\(191\) 213.364 1.11709 0.558545 0.829474i \(-0.311360\pi\)
0.558545 + 0.829474i \(0.311360\pi\)
\(192\) 40.8048 + 40.8048i 0.212525 + 0.212525i
\(193\) 103.019 0.533780 0.266890 0.963727i \(-0.414004\pi\)
0.266890 + 0.963727i \(0.414004\pi\)
\(194\) −276.531 276.531i −1.42542 1.42542i
\(195\) −89.0387 89.0387i −0.456609 0.456609i
\(196\) 139.239i 0.710402i
\(197\) 186.398 + 63.7558i 0.946182 + 0.323634i
\(198\) 55.6701 0.281162
\(199\) 120.592 120.592i 0.605992 0.605992i −0.335904 0.941896i \(-0.609042\pi\)
0.941896 + 0.335904i \(0.109042\pi\)
\(200\) −117.388 + 117.388i −0.586942 + 0.586942i
\(201\) 4.14040i 0.0205990i
\(202\) −136.216 + 136.216i −0.674337 + 0.674337i
\(203\) 244.981i 1.20680i
\(204\) 100.447i 0.492388i
\(205\) 384.897 + 384.897i 1.87755 + 1.87755i
\(206\) 34.8229i 0.169043i
\(207\) 24.7563i 0.119596i
\(208\) −72.7577 + 72.7577i −0.349797 + 0.349797i
\(209\) −119.685 119.685i −0.572656 0.572656i
\(210\) 434.146 434.146i 2.06736 2.06736i
\(211\) 202.083 + 202.083i 0.957741 + 0.957741i 0.999143 0.0414018i \(-0.0131824\pi\)
−0.0414018 + 0.999143i \(0.513182\pi\)
\(212\) 90.5401i 0.427076i
\(213\) −100.419 −0.471449
\(214\) −122.455 122.455i −0.572217 0.572217i
\(215\) 223.117 + 223.117i 1.03776 + 1.03776i
\(216\) 90.7972i 0.420358i
\(217\) −151.178 151.178i −0.696673 0.696673i
\(218\) 317.137 + 317.137i 1.45476 + 1.45476i
\(219\) 177.967i 0.812635i
\(220\) 293.072 1.33215
\(221\) 71.0901 0.321675
\(222\) 516.808i 2.32796i
\(223\) 31.3570i 0.140614i −0.997525 0.0703072i \(-0.977602\pi\)
0.997525 0.0703072i \(-0.0223980\pi\)
\(224\) −266.695 266.695i −1.19060 1.19060i
\(225\) 95.3931 0.423969
\(226\) −555.830 −2.45942
\(227\) −214.583 214.583i −0.945299 0.945299i 0.0532805 0.998580i \(-0.483032\pi\)
−0.998580 + 0.0532805i \(0.983032\pi\)
\(228\) −75.7764 + 75.7764i −0.332353 + 0.332353i
\(229\) −37.5633 + 37.5633i −0.164032 + 0.164032i −0.784350 0.620318i \(-0.787003\pi\)
0.620318 + 0.784350i \(0.287003\pi\)
\(230\) 316.621i 1.37661i
\(231\) 316.231 1.36897
\(232\) −54.6149 54.6149i −0.235409 0.235409i
\(233\) −151.782 −0.651424 −0.325712 0.945469i \(-0.605604\pi\)
−0.325712 + 0.945469i \(0.605604\pi\)
\(234\) 24.9452 0.106604
\(235\) −480.612 480.612i −2.04516 2.04516i
\(236\) 152.366i 0.645620i
\(237\) −418.179 −1.76447
\(238\) 346.630i 1.45643i
\(239\) 136.734 0.572108 0.286054 0.958213i \(-0.407656\pi\)
0.286054 + 0.958213i \(0.407656\pi\)
\(240\) 458.805i 1.91169i
\(241\) −37.4491 37.4491i −0.155391 0.155391i 0.625130 0.780521i \(-0.285046\pi\)
−0.780521 + 0.625130i \(0.785046\pi\)
\(242\) 36.2217 + 36.2217i 0.149677 + 0.149677i
\(243\) 67.6347 67.6347i 0.278332 0.278332i
\(244\) 47.9450i 0.196496i
\(245\) −310.707 + 310.707i −1.26819 + 1.26819i
\(246\) 431.230 1.75297
\(247\) −53.6297 53.6297i −0.217124 0.217124i
\(248\) 67.4059 0.271798
\(249\) −70.9281 70.9281i −0.284852 0.284852i
\(250\) 644.392 2.57757
\(251\) −86.6180 −0.345092 −0.172546 0.985002i \(-0.555199\pi\)
−0.172546 + 0.985002i \(0.555199\pi\)
\(252\) 50.0661i 0.198675i
\(253\) 115.313 115.313i 0.455784 0.455784i
\(254\) 14.6519 + 14.6519i 0.0576846 + 0.0576846i
\(255\) 224.145 224.145i 0.878998 0.878998i
\(256\) 335.645 1.31112
\(257\) −289.139 −1.12505 −0.562527 0.826779i \(-0.690171\pi\)
−0.562527 + 0.826779i \(0.690171\pi\)
\(258\) 249.976 0.968898
\(259\) 734.102i 2.83437i
\(260\) 131.323 0.505088
\(261\) 44.3816i 0.170045i
\(262\) 72.7410i 0.277638i
\(263\) −207.276 207.276i −0.788121 0.788121i 0.193065 0.981186i \(-0.438157\pi\)
−0.981186 + 0.193065i \(0.938157\pi\)
\(264\) −70.4992 + 70.4992i −0.267042 + 0.267042i
\(265\) 202.037 202.037i 0.762405 0.762405i
\(266\) 261.495 261.495i 0.983062 0.983062i
\(267\) −64.3554 −0.241031
\(268\) −3.05333 3.05333i −0.0113930 0.0113930i
\(269\) 196.877 196.877i 0.731884 0.731884i −0.239109 0.970993i \(-0.576855\pi\)
0.970993 + 0.239109i \(0.0768553\pi\)
\(270\) 471.833 471.833i 1.74753 1.74753i
\(271\) −260.930 + 260.930i −0.962840 + 0.962840i −0.999334 0.0364937i \(-0.988381\pi\)
0.0364937 + 0.999334i \(0.488381\pi\)
\(272\) −183.159 183.159i −0.673379 0.673379i
\(273\) 141.700 0.519048
\(274\) −160.606 160.606i −0.586155 0.586155i
\(275\) 444.335 + 444.335i 1.61576 + 1.61576i
\(276\) −73.0085 73.0085i −0.264523 0.264523i
\(277\) 301.993 301.993i 1.09023 1.09023i 0.0947220 0.995504i \(-0.469804\pi\)
0.995504 0.0947220i \(-0.0301962\pi\)
\(278\) 624.719 2.24719
\(279\) −27.3880 27.3880i −0.0981649 0.0981649i
\(280\) 274.962i 0.982006i
\(281\) −317.794 + 317.794i −1.13094 + 1.13094i −0.140920 + 0.990021i \(0.545006\pi\)
−0.990021 + 0.140920i \(0.954994\pi\)
\(282\) −538.466 −1.90946
\(283\) 85.6167 + 85.6167i 0.302533 + 0.302533i 0.842004 0.539471i \(-0.181376\pi\)
−0.539471 + 0.842004i \(0.681376\pi\)
\(284\) 74.0535 74.0535i 0.260752 0.260752i
\(285\) −338.185 −1.18662
\(286\) 116.193 + 116.193i 0.406270 + 0.406270i
\(287\) −612.543 −2.13430
\(288\) −48.3155 48.3155i −0.167762 0.167762i
\(289\) 110.039i 0.380758i
\(290\) 567.619i 1.95731i
\(291\) −284.576 284.576i −0.977924 0.977924i
\(292\) −131.242 131.242i −0.449457 0.449457i
\(293\) 234.258i 0.799517i 0.916621 + 0.399758i \(0.130906\pi\)
−0.916621 + 0.399758i \(0.869094\pi\)
\(294\) 348.109i 1.18404i
\(295\) −340.001 + 340.001i −1.15254 + 1.15254i
\(296\) 163.657 + 163.657i 0.552897 + 0.552897i
\(297\) 343.683 1.15718
\(298\) −396.534 −1.33065
\(299\) 51.6708 51.6708i 0.172812 0.172812i
\(300\) 281.322 281.322i 0.937741 0.937741i
\(301\) −355.079 −1.17966
\(302\) −35.0744 −0.116140
\(303\) −140.179 + 140.179i −0.462636 + 0.462636i
\(304\) 276.347i 0.909038i
\(305\) −106.988 + 106.988i −0.350780 + 0.350780i
\(306\) 62.7968i 0.205218i
\(307\) 307.631 + 307.631i 1.00206 + 1.00206i 0.999998 + 0.00205834i \(0.000655189\pi\)
0.00205834 + 0.999998i \(0.499345\pi\)
\(308\) −233.204 + 233.204i −0.757157 + 0.757157i
\(309\) 35.8359i 0.115974i
\(310\) −350.279 350.279i −1.12993 1.12993i
\(311\) −518.247 −1.66639 −0.833195 0.552979i \(-0.813491\pi\)
−0.833195 + 0.552979i \(0.813491\pi\)
\(312\) −31.5900 + 31.5900i −0.101250 + 0.101250i
\(313\) 238.017i 0.760438i −0.924897 0.380219i \(-0.875849\pi\)
0.924897 0.380219i \(-0.124151\pi\)
\(314\) −391.048 391.048i −1.24538 1.24538i
\(315\) −111.721 + 111.721i −0.354669 + 0.354669i
\(316\) 308.385 308.385i 0.975903 0.975903i
\(317\) −88.0090 + 88.0090i −0.277631 + 0.277631i −0.832163 0.554532i \(-0.812897\pi\)
0.554532 + 0.832163i \(0.312897\pi\)
\(318\) 226.358i 0.711818i
\(319\) −206.727 + 206.727i −0.648046 + 0.648046i
\(320\) −134.296 134.296i −0.419676 0.419676i
\(321\) −126.017 126.017i −0.392576 0.392576i
\(322\) 251.943 + 251.943i 0.782431 + 0.782431i
\(323\) 135.007 135.007i 0.417977 0.417977i
\(324\) 172.254i 0.531649i
\(325\) 199.102 + 199.102i 0.612622 + 0.612622i
\(326\) −52.8051 52.8051i −0.161979 0.161979i
\(327\) 326.363 + 326.363i 0.998051 + 0.998051i
\(328\) 136.558 136.558i 0.416334 0.416334i
\(329\) 764.867 2.32482
\(330\) 732.707 2.22032
\(331\) 461.949i 1.39562i 0.716285 + 0.697808i \(0.245841\pi\)
−0.716285 + 0.697808i \(0.754159\pi\)
\(332\) 104.612 0.315095
\(333\) 132.993i 0.399378i
\(334\) 507.224i 1.51864i
\(335\) 13.6268i 0.0406770i
\(336\) −365.082 365.082i −1.08655 1.08655i
\(337\) −273.821 + 273.821i −0.812525 + 0.812525i −0.985012 0.172487i \(-0.944820\pi\)
0.172487 + 0.985012i \(0.444820\pi\)
\(338\) −259.518 259.518i −0.767804 0.767804i
\(339\) −572.000 −1.68731
\(340\) 330.590i 0.972324i
\(341\) 255.143i 0.748219i
\(342\) 47.3733 47.3733i 0.138519 0.138519i
\(343\) 7.52704i 0.0219447i
\(344\) 79.1597 79.1597i 0.230116 0.230116i
\(345\) 325.832i 0.944441i
\(346\) 223.585 + 223.585i 0.646199 + 0.646199i
\(347\) −226.557 −0.652901 −0.326451 0.945214i \(-0.605853\pi\)
−0.326451 + 0.945214i \(0.605853\pi\)
\(348\) 130.885 + 130.885i 0.376107 + 0.376107i
\(349\) 235.104 235.104i 0.673651 0.673651i −0.284905 0.958556i \(-0.591962\pi\)
0.958556 + 0.284905i \(0.0919620\pi\)
\(350\) −970.806 + 970.806i −2.77373 + 2.77373i
\(351\) 154.001 0.438749
\(352\) 450.100i 1.27869i
\(353\) −249.426 −0.706589 −0.353295 0.935512i \(-0.614939\pi\)
−0.353295 + 0.935512i \(0.614939\pi\)
\(354\) 380.929i 1.07607i
\(355\) 330.496 0.930975
\(356\) 47.4588 47.4588i 0.133311 0.133311i
\(357\) 356.714i 0.999198i
\(358\) 283.855i 0.792890i
\(359\) 329.605 329.605i 0.918119 0.918119i −0.0787734 0.996893i \(-0.525100\pi\)
0.996893 + 0.0787734i \(0.0251004\pi\)
\(360\) 49.8131i 0.138370i
\(361\) 157.304 0.435746
\(362\) 174.678 + 174.678i 0.482535 + 0.482535i
\(363\) 37.2755 + 37.2755i 0.102687 + 0.102687i
\(364\) −104.497 + 104.497i −0.287078 + 0.287078i
\(365\) 585.723i 1.60472i
\(366\) 119.867i 0.327505i
\(367\) 284.071 284.071i 0.774035 0.774035i −0.204774 0.978809i \(-0.565646\pi\)
0.978809 + 0.204774i \(0.0656460\pi\)
\(368\) −266.253 −0.723514
\(369\) −110.971 −0.300733
\(370\) 1700.91i 4.59706i
\(371\) 321.531i 0.866661i
\(372\) −161.539 −0.434244
\(373\) −391.998 + 391.998i −1.05093 + 1.05093i −0.0523003 + 0.998631i \(0.516655\pi\)
−0.998631 + 0.0523003i \(0.983345\pi\)
\(374\) −292.503 + 292.503i −0.782093 + 0.782093i
\(375\) 663.139 1.76837
\(376\) −170.516 + 170.516i −0.453500 + 0.453500i
\(377\) −92.6322 + 92.6322i −0.245709 + 0.245709i
\(378\) 750.897i 1.98650i
\(379\) −399.075 −1.05297 −0.526485 0.850185i \(-0.676490\pi\)
−0.526485 + 0.850185i \(0.676490\pi\)
\(380\) 249.394 249.394i 0.656301 0.656301i
\(381\) 15.0781 + 15.0781i 0.0395752 + 0.0395752i
\(382\) −393.376 + 393.376i −1.02978 + 1.02978i
\(383\) 38.7143 + 38.7143i 0.101082 + 0.101082i 0.755839 0.654757i \(-0.227229\pi\)
−0.654757 + 0.755839i \(0.727229\pi\)
\(384\) 256.881 0.668961
\(385\) −1040.78 −2.70331
\(386\) −189.936 + 189.936i −0.492061 + 0.492061i
\(387\) −64.3275 −0.166221
\(388\) 419.720 1.08175
\(389\) 64.2373 + 64.2373i 0.165134 + 0.165134i 0.784837 0.619702i \(-0.212747\pi\)
−0.619702 + 0.784837i \(0.712747\pi\)
\(390\) 328.319 0.841843
\(391\) 130.075 + 130.075i 0.332673 + 0.332673i
\(392\) 110.236 + 110.236i 0.281213 + 0.281213i
\(393\) 74.8572i 0.190476i
\(394\) −461.205 + 226.114i −1.17057 + 0.573892i
\(395\) 1376.30 3.48431
\(396\) −42.2482 + 42.2482i −0.106687 + 0.106687i
\(397\) 70.4690 70.4690i 0.177504 0.177504i −0.612763 0.790267i \(-0.709942\pi\)
0.790267 + 0.612763i \(0.209942\pi\)
\(398\) 444.669i 1.11726i
\(399\) 269.102 269.102i 0.674441 0.674441i
\(400\) 1025.95i 2.56487i
\(401\) 38.7530i 0.0966408i −0.998832 0.0483204i \(-0.984613\pi\)
0.998832 0.0483204i \(-0.0153869\pi\)
\(402\) −7.63359 7.63359i −0.0189890 0.0189890i
\(403\) 114.327i 0.283690i
\(404\) 206.749i 0.511755i
\(405\) 384.380 384.380i 0.949087 0.949087i
\(406\) −451.668 451.668i −1.11248 1.11248i
\(407\) 619.471 619.471i 1.52204 1.52204i
\(408\) −79.5242 79.5242i −0.194912 0.194912i
\(409\) 64.5540i 0.157834i 0.996881 + 0.0789168i \(0.0251462\pi\)
−0.996881 + 0.0789168i \(0.974854\pi\)
\(410\) −1419.26 −3.46161
\(411\) −165.279 165.279i −0.402138 0.402138i
\(412\) 26.4271 + 26.4271i 0.0641435 + 0.0641435i
\(413\) 541.092i 1.31015i
\(414\) 45.6429 + 45.6429i 0.110249 + 0.110249i
\(415\) 233.438 + 233.438i 0.562500 + 0.562500i
\(416\) 201.686i 0.484821i
\(417\) 642.893 1.54171
\(418\) 441.323 1.05580
\(419\) 175.706i 0.419345i −0.977772 0.209673i \(-0.932760\pi\)
0.977772 0.209673i \(-0.0672398\pi\)
\(420\) 658.948i 1.56892i
\(421\) −522.439 522.439i −1.24095 1.24095i −0.959609 0.281338i \(-0.909222\pi\)
−0.281338 0.959609i \(-0.590778\pi\)
\(422\) −745.156 −1.76577
\(423\) 138.566 0.327580
\(424\) −71.6808 71.6808i −0.169058 0.169058i
\(425\) −501.216 + 501.216i −1.17933 + 1.17933i
\(426\) 185.140 185.140i 0.434602 0.434602i
\(427\) 170.265i 0.398748i
\(428\) 185.862 0.434257
\(429\) 119.573 + 119.573i 0.278726 + 0.278726i
\(430\) −822.717 −1.91329
\(431\) −530.606 −1.23110 −0.615552 0.788096i \(-0.711067\pi\)
−0.615552 + 0.788096i \(0.711067\pi\)
\(432\) −396.774 396.774i −0.918458 0.918458i
\(433\) 371.625i 0.858256i 0.903244 + 0.429128i \(0.141179\pi\)
−0.903244 + 0.429128i \(0.858821\pi\)
\(434\) 557.450 1.28445
\(435\) 584.132i 1.34283i
\(436\) −481.351 −1.10402
\(437\) 196.255i 0.449096i
\(438\) −328.115 328.115i −0.749122 0.749122i
\(439\) 448.128 + 448.128i 1.02079 + 1.02079i 0.999779 + 0.0210143i \(0.00668955\pi\)
0.0210143 + 0.999779i \(0.493310\pi\)
\(440\) 232.026 232.026i 0.527332 0.527332i
\(441\) 89.5806i 0.203131i
\(442\) −131.068 + 131.068i −0.296533 + 0.296533i
\(443\) 376.076 0.848929 0.424465 0.905445i \(-0.360462\pi\)
0.424465 + 0.905445i \(0.360462\pi\)
\(444\) −392.207 392.207i −0.883348 0.883348i
\(445\) 211.806 0.475967
\(446\) 57.8125 + 57.8125i 0.129624 + 0.129624i
\(447\) −408.070 −0.912909
\(448\) 213.725 0.477065
\(449\) 578.241i 1.28784i −0.765092 0.643921i \(-0.777306\pi\)
0.765092 0.643921i \(-0.222694\pi\)
\(450\) −175.875 + 175.875i −0.390833 + 0.390833i
\(451\) −516.893 516.893i −1.14610 1.14610i
\(452\) 421.820 421.820i 0.933231 0.933231i
\(453\) −36.0948 −0.0796794
\(454\) 791.247 1.74283
\(455\) −466.362 −1.02497
\(456\) 119.985i 0.263124i
\(457\) 850.225 1.86045 0.930224 0.366991i \(-0.119612\pi\)
0.930224 + 0.366991i \(0.119612\pi\)
\(458\) 138.510i 0.302423i
\(459\) 387.679i 0.844617i
\(460\) 240.284 + 240.284i 0.522358 + 0.522358i
\(461\) −28.8812 + 28.8812i −0.0626489 + 0.0626489i −0.737737 0.675088i \(-0.764106\pi\)
0.675088 + 0.737737i \(0.264106\pi\)
\(462\) −583.031 + 583.031i −1.26197 + 1.26197i
\(463\) −367.989 + 367.989i −0.794793 + 0.794793i −0.982269 0.187476i \(-0.939969\pi\)
0.187476 + 0.982269i \(0.439969\pi\)
\(464\) 477.322 1.02871
\(465\) −360.469 360.469i −0.775203 0.775203i
\(466\) 279.838 279.838i 0.600511 0.600511i
\(467\) −395.347 + 395.347i −0.846567 + 0.846567i −0.989703 0.143136i \(-0.954281\pi\)
0.143136 + 0.989703i \(0.454281\pi\)
\(468\) −18.9310 + 18.9310i −0.0404508 + 0.0404508i
\(469\) 10.8432 + 10.8432i 0.0231197 + 0.0231197i
\(470\) 1772.19 3.77062
\(471\) −402.425 402.425i −0.854405 0.854405i
\(472\) 120.629 + 120.629i 0.255569 + 0.255569i
\(473\) −299.633 299.633i −0.633473 0.633473i
\(474\) 770.990 770.990i 1.62656 1.62656i
\(475\) 756.226 1.59206
\(476\) −263.058 263.058i −0.552643 0.552643i
\(477\) 58.2498i 0.122117i
\(478\) −252.094 + 252.094i −0.527394 + 0.527394i
\(479\) −272.868 −0.569662 −0.284831 0.958578i \(-0.591938\pi\)
−0.284831 + 0.958578i \(0.591938\pi\)
\(480\) −635.908 635.908i −1.32481 1.32481i
\(481\) 277.579 277.579i 0.577087 0.577087i
\(482\) 138.089 0.286491
\(483\) 259.272 + 259.272i 0.536795 + 0.536795i
\(484\) −54.9775 −0.113590
\(485\) 936.592 + 936.592i 1.93112 + 1.93112i
\(486\) 249.394i 0.513157i
\(487\) 689.852i 1.41653i 0.705945 + 0.708267i \(0.250523\pi\)
−0.705945 + 0.708267i \(0.749477\pi\)
\(488\) 37.9582 + 37.9582i 0.0777831 + 0.0777831i
\(489\) −54.3413 54.3413i −0.111127 0.111127i
\(490\) 1145.69i 2.33815i
\(491\) 194.268i 0.395657i −0.980237 0.197829i \(-0.936611\pi\)
0.980237 0.197829i \(-0.0633890\pi\)
\(492\) −327.261 + 327.261i −0.665165 + 0.665165i
\(493\) −233.191 233.191i −0.473004 0.473004i
\(494\) 197.753 0.400309
\(495\) −188.551 −0.380911
\(496\) −294.556 + 294.556i −0.593864 + 0.593864i
\(497\) −262.983 + 262.983i −0.529141 + 0.529141i
\(498\) 261.538 0.525177
\(499\) 629.825 1.26218 0.631088 0.775712i \(-0.282609\pi\)
0.631088 + 0.775712i \(0.282609\pi\)
\(500\) −489.030 + 489.030i −0.978061 + 0.978061i
\(501\) 521.980i 1.04188i
\(502\) 159.696 159.696i 0.318120 0.318120i
\(503\) 267.879i 0.532562i −0.963895 0.266281i \(-0.914205\pi\)
0.963895 0.266281i \(-0.0857949\pi\)
\(504\) 39.6374 + 39.6374i 0.0786456 + 0.0786456i
\(505\) 461.354 461.354i 0.913573 0.913573i
\(506\) 425.203i 0.840322i
\(507\) −267.068 267.068i −0.526760 0.526760i
\(508\) −22.2387 −0.0437770
\(509\) 93.2973 93.2973i 0.183295 0.183295i −0.609495 0.792790i \(-0.708628\pi\)
0.792790 + 0.609495i \(0.208628\pi\)
\(510\) 826.504i 1.62060i
\(511\) 466.073 + 466.073i 0.912080 + 0.912080i
\(512\) −348.042 + 348.042i −0.679769 + 0.679769i
\(513\) 292.462 292.462i 0.570101 0.570101i
\(514\) 533.082 533.082i 1.03712 1.03712i
\(515\) 117.943i 0.229015i
\(516\) −189.707 + 189.707i −0.367649 + 0.367649i
\(517\) 645.432 + 645.432i 1.24842 + 1.24842i
\(518\) 1353.45 + 1353.45i 2.61285 + 2.61285i
\(519\) 230.089 + 230.089i 0.443332 + 0.443332i
\(520\) 103.969 103.969i 0.199940 0.199940i
\(521\) 1028.38i 1.97387i 0.161133 + 0.986933i \(0.448485\pi\)
−0.161133 + 0.986933i \(0.551515\pi\)
\(522\) −81.8258 81.8258i −0.156754 0.156754i
\(523\) 31.6141 + 31.6141i 0.0604475 + 0.0604475i 0.736684 0.676237i \(-0.236390\pi\)
−0.676237 + 0.736684i \(0.736390\pi\)
\(524\) −55.2033 55.2033i −0.105350 0.105350i
\(525\) −999.048 + 999.048i −1.90295 + 1.90295i
\(526\) 764.303 1.45305
\(527\) 287.805 0.546119
\(528\) 616.147i 1.16695i
\(529\) −339.914 −0.642559
\(530\) 744.987i 1.40564i
\(531\) 98.0263i 0.184607i
\(532\) 396.897i 0.746048i
\(533\) −231.615 231.615i −0.434549 0.434549i
\(534\) 118.651 118.651i 0.222193 0.222193i
\(535\) 414.745 + 414.745i 0.775225 + 0.775225i
\(536\) −4.83465 −0.00901987
\(537\) 292.112i 0.543971i
\(538\) 725.958i 1.34936i
\(539\) 417.260 417.260i 0.774138 0.774138i
\(540\) 716.150i 1.32620i
\(541\) 201.666 201.666i 0.372764 0.372764i −0.495719 0.868483i \(-0.665095\pi\)
0.868483 + 0.495719i \(0.165095\pi\)
\(542\) 962.145i 1.77517i
\(543\) 179.759 + 179.759i 0.331048 + 0.331048i
\(544\) 507.720 0.933309
\(545\) −1074.12 1074.12i −1.97086 1.97086i
\(546\) −261.251 + 261.251i −0.478481 + 0.478481i
\(547\) −684.763 + 684.763i −1.25185 + 1.25185i −0.296964 + 0.954889i \(0.595974\pi\)
−0.954889 + 0.296964i \(0.904026\pi\)
\(548\) 243.769 0.444834
\(549\) 30.8459i 0.0561856i
\(550\) −1638.43 −2.97896
\(551\) 351.834i 0.638538i
\(552\) −115.602 −0.209424
\(553\) −1095.16 + 1095.16i −1.98039 + 1.98039i
\(554\) 1113.56i 2.01003i
\(555\) 1750.39i 3.15386i
\(556\) −474.100 + 474.100i −0.852698 + 0.852698i
\(557\) 856.244i 1.53724i −0.639704 0.768621i \(-0.720943\pi\)
0.639704 0.768621i \(-0.279057\pi\)
\(558\) 100.990 0.180985
\(559\) −134.263 134.263i −0.240184 0.240184i
\(560\) 1201.55 + 1201.55i 2.14563 + 2.14563i
\(561\) −301.012 + 301.012i −0.536564 + 0.536564i
\(562\) 1171.83i 2.08510i
\(563\) 504.957i 0.896905i −0.893807 0.448452i \(-0.851975\pi\)
0.893807 0.448452i \(-0.148025\pi\)
\(564\) 408.643 408.643i 0.724544 0.724544i
\(565\) 1882.56 3.33196
\(566\) −315.701 −0.557775
\(567\) 611.720i 1.07887i
\(568\) 117.257i 0.206438i
\(569\) −315.908 −0.555198 −0.277599 0.960697i \(-0.589539\pi\)
−0.277599 + 0.960697i \(0.589539\pi\)
\(570\) 623.508 623.508i 1.09387 1.09387i
\(571\) 652.110 652.110i 1.14205 1.14205i 0.153975 0.988075i \(-0.450793\pi\)
0.988075 0.153975i \(-0.0492074\pi\)
\(572\) −176.358 −0.308319
\(573\) −404.820 + 404.820i −0.706493 + 0.706493i
\(574\) 1129.34 1129.34i 1.96748 1.96748i
\(575\) 728.603i 1.26714i
\(576\) 38.7193 0.0672210
\(577\) 88.6003 88.6003i 0.153553 0.153553i −0.626150 0.779703i \(-0.715370\pi\)
0.779703 + 0.626150i \(0.215370\pi\)
\(578\) 202.877 + 202.877i 0.350999 + 0.350999i
\(579\) −195.461 + 195.461i −0.337584 + 0.337584i
\(580\) −430.767 430.767i −0.742702 0.742702i
\(581\) −371.503 −0.639420
\(582\) 1049.34 1.80298
\(583\) −271.324 + 271.324i −0.465392 + 0.465392i
\(584\) −207.808 −0.355836
\(585\) −84.4878 −0.144424
\(586\) −431.899 431.899i −0.737029 0.737029i
\(587\) −310.466 −0.528903 −0.264451 0.964399i \(-0.585191\pi\)
−0.264451 + 0.964399i \(0.585191\pi\)
\(588\) −264.181 264.181i −0.449287 0.449287i
\(589\) −217.118 217.118i −0.368621 0.368621i
\(590\) 1253.71i 2.12493i
\(591\) −474.622 + 232.691i −0.803083 + 0.393725i
\(592\) −1430.33 −2.41610
\(593\) 434.760 434.760i 0.733153 0.733153i −0.238090 0.971243i \(-0.576521\pi\)
0.971243 + 0.238090i \(0.0765213\pi\)
\(594\) −633.643 + 633.643i −1.06674 + 1.06674i
\(595\) 1174.01i 1.97313i
\(596\) 300.931 300.931i 0.504917 0.504917i
\(597\) 457.605i 0.766507i
\(598\) 190.529i 0.318611i
\(599\) 600.005 + 600.005i 1.00168 + 1.00168i 0.999999 + 0.00167862i \(0.000534321\pi\)
0.00167862 + 0.999999i \(0.499466\pi\)
\(600\) 445.447i 0.742411i
\(601\) 810.285i 1.34823i 0.738628 + 0.674114i \(0.235474\pi\)
−0.738628 + 0.674114i \(0.764526\pi\)
\(602\) 654.654 654.654i 1.08747 1.08747i
\(603\) 1.96439 + 1.96439i 0.00325769 + 0.00325769i
\(604\) 26.6180 26.6180i 0.0440696 0.0440696i
\(605\) −122.680 122.680i −0.202778 0.202778i
\(606\) 516.891i 0.852955i
\(607\) 94.1168 0.155052 0.0775262 0.996990i \(-0.475298\pi\)
0.0775262 + 0.996990i \(0.475298\pi\)
\(608\) −383.020 383.020i −0.629967 0.629967i
\(609\) −464.807 464.807i −0.763230 0.763230i
\(610\) 394.504i 0.646728i
\(611\) 289.212 + 289.212i 0.473341 + 0.473341i
\(612\) −47.6566 47.6566i −0.0778702 0.0778702i
\(613\) 264.174i 0.430953i −0.976509 0.215476i \(-0.930870\pi\)
0.976509 0.215476i \(-0.0691304\pi\)
\(614\) −1134.35 −1.84748
\(615\) −1460.55 −2.37487
\(616\) 369.257i 0.599442i
\(617\) 189.539i 0.307195i −0.988133 0.153598i \(-0.950914\pi\)
0.988133 0.153598i \(-0.0490859\pi\)
\(618\) 66.0701 + 66.0701i 0.106910 + 0.106910i
\(619\) 432.171 0.698176 0.349088 0.937090i \(-0.386491\pi\)
0.349088 + 0.937090i \(0.386491\pi\)
\(620\) 531.655 0.857508
\(621\) 281.779 + 281.779i 0.453750 + 0.453750i
\(622\) 955.485 955.485i 1.53615 1.53615i
\(623\) −168.538 + 168.538i −0.270527 + 0.270527i
\(624\) 276.090i 0.442451i
\(625\) −857.863 −1.37258
\(626\) 438.828 + 438.828i 0.701004 + 0.701004i
\(627\) 454.162 0.724342
\(628\) 593.535 0.945119
\(629\) 698.773 + 698.773i 1.11093 + 1.11093i
\(630\) 411.956i 0.653899i
\(631\) −169.613 −0.268800 −0.134400 0.990927i \(-0.542911\pi\)
−0.134400 + 0.990927i \(0.542911\pi\)
\(632\) 488.298i 0.772624i
\(633\) −766.834 −1.21143
\(634\) 324.522i 0.511864i
\(635\) −49.6250 49.6250i −0.0781496 0.0781496i
\(636\) 171.784 + 171.784i 0.270100 + 0.270100i
\(637\) 186.970 186.970i 0.293517 0.293517i
\(638\) 762.278i 1.19479i
\(639\) −47.6430 + 47.6430i −0.0745588 + 0.0745588i
\(640\) −845.443 −1.32100
\(641\) −178.904 178.904i −0.279101 0.279101i 0.553649 0.832750i \(-0.313235\pi\)
−0.832750 + 0.553649i \(0.813235\pi\)
\(642\) 464.671 0.723787
\(643\) 102.965 + 102.965i 0.160132 + 0.160132i 0.782625 0.622493i \(-0.213880\pi\)
−0.622493 + 0.782625i \(0.713880\pi\)
\(644\) −382.400 −0.593788
\(645\) −846.651 −1.31264
\(646\) 497.820i 0.770618i
\(647\) 499.726 499.726i 0.772374 0.772374i −0.206147 0.978521i \(-0.566093\pi\)
0.978521 + 0.206147i \(0.0660926\pi\)
\(648\) −136.374 136.374i −0.210454 0.210454i
\(649\) 456.600 456.600i 0.703544 0.703544i
\(650\) −734.163 −1.12948
\(651\) 573.667 0.881209
\(652\) 80.1478 0.122926
\(653\) 199.775i 0.305934i −0.988231 0.152967i \(-0.951117\pi\)
0.988231 0.152967i \(-0.0488827\pi\)
\(654\) −1203.42 −1.84009
\(655\) 246.369i 0.376136i
\(656\) 1193.48i 1.81933i
\(657\) 84.4356 + 84.4356i 0.128517 + 0.128517i
\(658\) −1410.17 + 1410.17i −2.14312 + 2.14312i
\(659\) 22.8023 22.8023i 0.0346013 0.0346013i −0.689594 0.724196i \(-0.742211\pi\)
0.724196 + 0.689594i \(0.242211\pi\)
\(660\) −556.052 + 556.052i −0.842503 + 0.842503i
\(661\) −398.088 −0.602251 −0.301126 0.953584i \(-0.597362\pi\)
−0.301126 + 0.953584i \(0.597362\pi\)
\(662\) −851.688 851.688i −1.28654 1.28654i
\(663\) −134.881 + 134.881i −0.203440 + 0.203440i
\(664\) 82.8212 82.8212i 0.124731 0.124731i
\(665\) −885.664 + 885.664i −1.33183 + 1.33183i
\(666\) 245.197 + 245.197i 0.368163 + 0.368163i
\(667\) −338.983 −0.508220
\(668\) −384.933 384.933i −0.576248 0.576248i
\(669\) 59.4943 + 59.4943i 0.0889302 + 0.0889302i
\(670\) 25.1236 + 25.1236i 0.0374978 + 0.0374978i
\(671\) 143.678 143.678i 0.214125 0.214125i
\(672\) 1012.01 1.50597
\(673\) −556.213 556.213i −0.826468 0.826468i 0.160558 0.987026i \(-0.448671\pi\)
−0.987026 + 0.160558i \(0.948671\pi\)
\(674\) 1009.68i 1.49804i
\(675\) −1085.77 + 1085.77i −1.60855 + 1.60855i
\(676\) 393.897 0.582688
\(677\) 406.198 + 406.198i 0.599997 + 0.599997i 0.940312 0.340315i \(-0.110534\pi\)
−0.340315 + 0.940312i \(0.610534\pi\)
\(678\) 1054.59 1054.59i 1.55544 1.55544i
\(679\) −1490.54 −2.19519
\(680\) 261.729 + 261.729i 0.384895 + 0.384895i
\(681\) 814.265 1.19569
\(682\) 470.403 + 470.403i 0.689741 + 0.689741i
\(683\) 428.119i 0.626821i −0.949618 0.313411i \(-0.898528\pi\)
0.949618 0.313411i \(-0.101472\pi\)
\(684\) 71.9034i 0.105122i
\(685\) 543.963 + 543.963i 0.794106 + 0.794106i
\(686\) 13.8775 + 13.8775i 0.0202296 + 0.0202296i
\(687\) 142.539i 0.207481i
\(688\) 691.838i 1.00558i
\(689\) −121.578 + 121.578i −0.176455 + 0.176455i
\(690\) 600.732 + 600.732i 0.870627 + 0.870627i
\(691\) −590.323 −0.854302 −0.427151 0.904180i \(-0.640483\pi\)
−0.427151 + 0.904180i \(0.640483\pi\)
\(692\) −339.358 −0.490401
\(693\) 150.034 150.034i 0.216500 0.216500i
\(694\) 417.699 417.699i 0.601872 0.601872i
\(695\) −2115.88 −3.04443
\(696\) 207.244 0.297764
\(697\) 583.063 583.063i 0.836533 0.836533i
\(698\) 866.917i 1.24200i
\(699\) 287.979 287.979i 0.411987 0.411987i
\(700\) 1473.49i 2.10499i
\(701\) −137.703 137.703i −0.196438 0.196438i 0.602033 0.798471i \(-0.294358\pi\)
−0.798471 + 0.602033i \(0.794358\pi\)
\(702\) −283.929 + 283.929i −0.404458 + 0.404458i
\(703\) 1054.30i 1.49971i
\(704\) 180.352 + 180.352i 0.256181 + 0.256181i
\(705\) 1823.75 2.58688
\(706\) 459.863 459.863i 0.651364 0.651364i
\(707\) 734.220i 1.03850i
\(708\) −289.088 289.088i −0.408316 0.408316i
\(709\) 185.755 185.755i 0.261995 0.261995i −0.563869 0.825864i \(-0.690688\pi\)
0.825864 + 0.563869i \(0.190688\pi\)
\(710\) −609.331 + 609.331i −0.858213 + 0.858213i
\(711\) −198.403 + 198.403i −0.279047 + 0.279047i
\(712\) 75.1464i 0.105543i
\(713\) 209.187 209.187i 0.293390 0.293390i
\(714\) −657.668 657.668i −0.921104 0.921104i
\(715\) −393.539 393.539i −0.550404 0.550404i
\(716\) −215.418 215.418i −0.300863 0.300863i
\(717\) −259.428 + 259.428i −0.361824 + 0.361824i
\(718\) 1215.38i 1.69272i
\(719\) 155.950 + 155.950i 0.216899 + 0.216899i 0.807190 0.590291i \(-0.200987\pi\)
−0.590291 + 0.807190i \(0.700987\pi\)
\(720\) 217.678 + 217.678i 0.302330 + 0.302330i
\(721\) −93.8496 93.8496i −0.130166 0.130166i
\(722\) −290.020 + 290.020i −0.401689 + 0.401689i
\(723\) 142.106 0.196551
\(724\) −265.126 −0.366196
\(725\) 1306.19i 1.80165i
\(726\) −137.448 −0.189323
\(727\) 927.410i 1.27567i −0.770174 0.637834i \(-0.779831\pi\)
0.770174 0.637834i \(-0.220169\pi\)
\(728\) 165.460i 0.227281i
\(729\) 810.650i 1.11200i
\(730\) 1079.89 + 1079.89i 1.47930 + 1.47930i
\(731\) 337.990 337.990i 0.462367 0.462367i
\(732\) −90.9671 90.9671i −0.124272 0.124272i
\(733\) −464.411 −0.633576 −0.316788 0.948496i \(-0.602604\pi\)
−0.316788 + 0.948496i \(0.602604\pi\)
\(734\) 1047.47i 1.42708i
\(735\) 1179.02i 1.60411i
\(736\) 369.029 369.029i 0.501398 0.501398i
\(737\) 18.3000i 0.0248303i
\(738\) 204.595 204.595i 0.277229 0.277229i
\(739\) 13.9757i 0.0189116i −0.999955 0.00945580i \(-0.996990\pi\)
0.999955 0.00945580i \(-0.00300992\pi\)
\(740\) 1290.82 + 1290.82i 1.74436 + 1.74436i
\(741\) 203.506 0.274637
\(742\) −592.803 592.803i −0.798926 0.798926i
\(743\) −808.587 + 808.587i −1.08827 + 1.08827i −0.0925672 + 0.995706i \(0.529507\pi\)
−0.995706 + 0.0925672i \(0.970493\pi\)
\(744\) −127.891 + 127.891i −0.171896 + 0.171896i
\(745\) 1343.03 1.80273
\(746\) 1445.44i 1.93759i
\(747\) −67.3029 −0.0900976
\(748\) 443.962i 0.593532i
\(749\) −660.044 −0.881234
\(750\) −1222.62 + 1222.62i −1.63016 + 1.63016i
\(751\) 274.540i 0.365566i −0.983153 0.182783i \(-0.941489\pi\)
0.983153 0.182783i \(-0.0585107\pi\)
\(752\) 1490.27i 1.98174i
\(753\) 164.342 164.342i 0.218250 0.218250i
\(754\) 341.569i 0.453010i
\(755\) 118.795 0.157344
\(756\) −569.857 569.857i −0.753779 0.753779i
\(757\) 63.8356 + 63.8356i 0.0843271 + 0.0843271i 0.748012 0.663685i \(-0.231008\pi\)
−0.663685 + 0.748012i \(0.731008\pi\)
\(758\) 735.770 735.770i 0.970672 0.970672i
\(759\) 437.573i 0.576512i
\(760\) 394.892i 0.519595i
\(761\) 304.764 304.764i 0.400478 0.400478i −0.477923 0.878402i \(-0.658610\pi\)
0.878402 + 0.477923i \(0.158610\pi\)
\(762\) −55.5987 −0.0729642
\(763\) 1709.40 2.24037
\(764\) 597.068i 0.781503i
\(765\) 212.688i 0.278024i
\(766\) −142.754 −0.186363
\(767\) 204.598 204.598i 0.266751 0.266751i
\(768\) −636.827 + 636.827i −0.829202 + 0.829202i
\(769\) −807.891 −1.05057 −0.525286 0.850925i \(-0.676042\pi\)
−0.525286 + 0.850925i \(0.676042\pi\)
\(770\) 1918.86 1918.86i 2.49203 2.49203i
\(771\) 548.590 548.590i 0.711530 0.711530i
\(772\) 288.285i 0.373426i
\(773\) 293.474 0.379656 0.189828 0.981817i \(-0.439207\pi\)
0.189828 + 0.981817i \(0.439207\pi\)
\(774\) 118.600 118.600i 0.153229 0.153229i
\(775\) 806.056 + 806.056i 1.04007 + 1.04007i