Properties

Label 197.3.c.a.14.16
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 14.16
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.0624262 + 0.0624262i) q^{2} +(1.58284 - 1.58284i) q^{3} +3.99221i q^{4} +(3.24675 - 3.24675i) q^{5} +0.197621i q^{6} +10.7744i q^{7} +(-0.498923 - 0.498923i) q^{8} +3.98923i q^{9} +O(q^{10})\) \(q+(-0.0624262 + 0.0624262i) q^{2} +(1.58284 - 1.58284i) q^{3} +3.99221i q^{4} +(3.24675 - 3.24675i) q^{5} +0.197621i q^{6} +10.7744i q^{7} +(-0.498923 - 0.498923i) q^{8} +3.98923i q^{9} +0.405365i q^{10} +(-3.93817 + 3.93817i) q^{11} +(6.31903 + 6.31903i) q^{12} +(9.78974 - 9.78974i) q^{13} +(-0.672603 - 0.672603i) q^{14} -10.2782i q^{15} -15.9065 q^{16} +(19.0991 + 19.0991i) q^{17} +(-0.249033 - 0.249033i) q^{18} -31.7760i q^{19} +(12.9617 + 12.9617i) q^{20} +(17.0541 + 17.0541i) q^{21} -0.491690i q^{22} -18.4961 q^{23} -1.57943 q^{24} +3.91721i q^{25} +1.22227i q^{26} +(20.5599 + 20.5599i) q^{27} -43.0135 q^{28} +31.7061 q^{29} +(0.641628 + 0.641628i) q^{30} +(21.5701 - 21.5701i) q^{31} +(2.98868 - 2.98868i) q^{32} +12.4670i q^{33} -2.38457 q^{34} +(34.9817 + 34.9817i) q^{35} -15.9258 q^{36} -38.7864 q^{37} +(1.98366 + 1.98366i) q^{38} -30.9912i q^{39} -3.23976 q^{40} +5.21153i q^{41} -2.12925 q^{42} -77.7784i q^{43} +(-15.7220 - 15.7220i) q^{44} +(12.9520 + 12.9520i) q^{45} +(1.15464 - 1.15464i) q^{46} -4.20836i q^{47} +(-25.1775 + 25.1775i) q^{48} -67.0870 q^{49} +(-0.244537 - 0.244537i) q^{50} +60.4617 q^{51} +(39.0827 + 39.0827i) q^{52} -24.7423 q^{53} -2.56695 q^{54} +25.5725i q^{55} +(5.37558 - 5.37558i) q^{56} +(-50.2964 - 50.2964i) q^{57} +(-1.97929 + 1.97929i) q^{58} -34.2105 q^{59} +41.0326 q^{60} -12.0497 q^{61} +2.69308i q^{62} -42.9815 q^{63} -63.2530i q^{64} -63.5697i q^{65} +(-0.778267 - 0.778267i) q^{66} +(-2.95553 + 2.95553i) q^{67} +(-76.2476 + 76.2476i) q^{68} +(-29.2764 + 29.2764i) q^{69} -4.36755 q^{70} +(-43.7088 - 43.7088i) q^{71} +(1.99032 - 1.99032i) q^{72} +(-37.0895 + 37.0895i) q^{73} +(2.42129 - 2.42129i) q^{74} +(6.20032 + 6.20032i) q^{75} +126.856 q^{76} +(-42.4313 - 42.4313i) q^{77} +(1.93466 + 1.93466i) q^{78} +(-44.5612 - 44.5612i) q^{79} +(-51.6446 + 51.6446i) q^{80} +29.1829 q^{81} +(-0.325336 - 0.325336i) q^{82} -128.962i q^{83} +(-68.0835 + 68.0835i) q^{84} +124.020 q^{85} +(4.85541 + 4.85541i) q^{86} +(50.1857 - 50.1857i) q^{87} +3.92969 q^{88} +(22.1462 + 22.1462i) q^{89} -1.61709 q^{90} +(105.478 + 105.478i) q^{91} -73.8403i q^{92} -68.2840i q^{93} +(0.262712 + 0.262712i) q^{94} +(-103.169 - 103.169i) q^{95} -9.46120i q^{96} -129.468i q^{97} +(4.18799 - 4.18799i) q^{98} +(-15.7103 - 15.7103i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0624262 + 0.0624262i −0.0312131 + 0.0312131i −0.722541 0.691328i \(-0.757026\pi\)
0.691328 + 0.722541i \(0.257026\pi\)
\(3\) 1.58284 1.58284i 0.527613 0.527613i −0.392247 0.919860i \(-0.628302\pi\)
0.919860 + 0.392247i \(0.128302\pi\)
\(4\) 3.99221i 0.998051i
\(5\) 3.24675 3.24675i 0.649350 0.649350i −0.303486 0.952836i \(-0.598150\pi\)
0.952836 + 0.303486i \(0.0981505\pi\)
\(6\) 0.197621i 0.0329369i
\(7\) 10.7744i 1.53920i 0.638529 + 0.769598i \(0.279543\pi\)
−0.638529 + 0.769598i \(0.720457\pi\)
\(8\) −0.498923 0.498923i −0.0623654 0.0623654i
\(9\) 3.98923i 0.443248i
\(10\) 0.405365i 0.0405365i
\(11\) −3.93817 + 3.93817i −0.358015 + 0.358015i −0.863081 0.505066i \(-0.831468\pi\)
0.505066 + 0.863081i \(0.331468\pi\)
\(12\) 6.31903 + 6.31903i 0.526585 + 0.526585i
\(13\) 9.78974 9.78974i 0.753057 0.753057i −0.221992 0.975049i \(-0.571256\pi\)
0.975049 + 0.221992i \(0.0712558\pi\)
\(14\) −0.672603 0.672603i −0.0480431 0.0480431i
\(15\) 10.2782i 0.685212i
\(16\) −15.9065 −0.994158
\(17\) 19.0991 + 19.0991i 1.12348 + 1.12348i 0.991215 + 0.132262i \(0.0422240\pi\)
0.132262 + 0.991215i \(0.457776\pi\)
\(18\) −0.249033 0.249033i −0.0138351 0.0138351i
\(19\) 31.7760i 1.67242i −0.548407 0.836212i \(-0.684766\pi\)
0.548407 0.836212i \(-0.315234\pi\)
\(20\) 12.9617 + 12.9617i 0.648085 + 0.648085i
\(21\) 17.0541 + 17.0541i 0.812100 + 0.812100i
\(22\) 0.491690i 0.0223495i
\(23\) −18.4961 −0.804179 −0.402090 0.915600i \(-0.631716\pi\)
−0.402090 + 0.915600i \(0.631716\pi\)
\(24\) −1.57943 −0.0658096
\(25\) 3.91721i 0.156689i
\(26\) 1.22227i 0.0470105i
\(27\) 20.5599 + 20.5599i 0.761477 + 0.761477i
\(28\) −43.0135 −1.53620
\(29\) 31.7061 1.09331 0.546656 0.837357i \(-0.315900\pi\)
0.546656 + 0.837357i \(0.315900\pi\)
\(30\) 0.641628 + 0.641628i 0.0213876 + 0.0213876i
\(31\) 21.5701 21.5701i 0.695809 0.695809i −0.267695 0.963504i \(-0.586262\pi\)
0.963504 + 0.267695i \(0.0862619\pi\)
\(32\) 2.98868 2.98868i 0.0933961 0.0933961i
\(33\) 12.4670i 0.377787i
\(34\) −2.38457 −0.0701344
\(35\) 34.9817 + 34.9817i 0.999477 + 0.999477i
\(36\) −15.9258 −0.442384
\(37\) −38.7864 −1.04828 −0.524140 0.851632i \(-0.675613\pi\)
−0.524140 + 0.851632i \(0.675613\pi\)
\(38\) 1.98366 + 1.98366i 0.0522015 + 0.0522015i
\(39\) 30.9912i 0.794646i
\(40\) −3.23976 −0.0809939
\(41\) 5.21153i 0.127110i 0.997978 + 0.0635552i \(0.0202439\pi\)
−0.997978 + 0.0635552i \(0.979756\pi\)
\(42\) −2.12925 −0.0506963
\(43\) 77.7784i 1.80880i −0.426687 0.904399i \(-0.640319\pi\)
0.426687 0.904399i \(-0.359681\pi\)
\(44\) −15.7220 15.7220i −0.357318 0.357318i
\(45\) 12.9520 + 12.9520i 0.287823 + 0.287823i
\(46\) 1.15464 1.15464i 0.0251009 0.0251009i
\(47\) 4.20836i 0.0895395i −0.998997 0.0447697i \(-0.985745\pi\)
0.998997 0.0447697i \(-0.0142554\pi\)
\(48\) −25.1775 + 25.1775i −0.524531 + 0.524531i
\(49\) −67.0870 −1.36912
\(50\) −0.244537 0.244537i −0.00489073 0.00489073i
\(51\) 60.4617 1.18552
\(52\) 39.0827 + 39.0827i 0.751589 + 0.751589i
\(53\) −24.7423 −0.466835 −0.233418 0.972377i \(-0.574991\pi\)
−0.233418 + 0.972377i \(0.574991\pi\)
\(54\) −2.56695 −0.0475361
\(55\) 25.5725i 0.464955i
\(56\) 5.37558 5.37558i 0.0959925 0.0959925i
\(57\) −50.2964 50.2964i −0.882393 0.882393i
\(58\) −1.97929 + 1.97929i −0.0341257 + 0.0341257i
\(59\) −34.2105 −0.579839 −0.289919 0.957051i \(-0.593628\pi\)
−0.289919 + 0.957051i \(0.593628\pi\)
\(60\) 41.0326 0.683877
\(61\) −12.0497 −0.197537 −0.0987684 0.995110i \(-0.531490\pi\)
−0.0987684 + 0.995110i \(0.531490\pi\)
\(62\) 2.69308i 0.0434367i
\(63\) −42.9815 −0.682245
\(64\) 63.2530i 0.988328i
\(65\) 63.5697i 0.977995i
\(66\) −0.778267 0.778267i −0.0117919 0.0117919i
\(67\) −2.95553 + 2.95553i −0.0441124 + 0.0441124i −0.728819 0.684706i \(-0.759930\pi\)
0.684706 + 0.728819i \(0.259930\pi\)
\(68\) −76.2476 + 76.2476i −1.12129 + 1.12129i
\(69\) −29.2764 + 29.2764i −0.424296 + 0.424296i
\(70\) −4.36755 −0.0623935
\(71\) −43.7088 43.7088i −0.615617 0.615617i 0.328787 0.944404i \(-0.393360\pi\)
−0.944404 + 0.328787i \(0.893360\pi\)
\(72\) 1.99032 1.99032i 0.0276433 0.0276433i
\(73\) −37.0895 + 37.0895i −0.508075 + 0.508075i −0.913935 0.405860i \(-0.866972\pi\)
0.405860 + 0.913935i \(0.366972\pi\)
\(74\) 2.42129 2.42129i 0.0327201 0.0327201i
\(75\) 6.20032 + 6.20032i 0.0826710 + 0.0826710i
\(76\) 126.856 1.66916
\(77\) −42.4313 42.4313i −0.551056 0.551056i
\(78\) 1.93466 + 1.93466i 0.0248034 + 0.0248034i
\(79\) −44.5612 44.5612i −0.564065 0.564065i 0.366394 0.930460i \(-0.380592\pi\)
−0.930460 + 0.366394i \(0.880592\pi\)
\(80\) −51.6446 + 51.6446i −0.645557 + 0.645557i
\(81\) 29.1829 0.360283
\(82\) −0.325336 0.325336i −0.00396751 0.00396751i
\(83\) 128.962i 1.55375i −0.629653 0.776877i \(-0.716803\pi\)
0.629653 0.776877i \(-0.283197\pi\)
\(84\) −68.0835 + 68.0835i −0.810518 + 0.810518i
\(85\) 124.020 1.45906
\(86\) 4.85541 + 4.85541i 0.0564582 + 0.0564582i
\(87\) 50.1857 50.1857i 0.576847 0.576847i
\(88\) 3.92969 0.0446555
\(89\) 22.1462 + 22.1462i 0.248834 + 0.248834i 0.820492 0.571658i \(-0.193700\pi\)
−0.571658 + 0.820492i \(0.693700\pi\)
\(90\) −1.61709 −0.0179677
\(91\) 105.478 + 105.478i 1.15910 + 1.15910i
\(92\) 73.8403i 0.802612i
\(93\) 68.2840i 0.734236i
\(94\) 0.262712 + 0.262712i 0.00279480 + 0.00279480i
\(95\) −103.169 103.169i −1.08599 1.08599i
\(96\) 9.46120i 0.0985541i
\(97\) 129.468i 1.33472i −0.744734 0.667361i \(-0.767424\pi\)
0.744734 0.667361i \(-0.232576\pi\)
\(98\) 4.18799 4.18799i 0.0427346 0.0427346i
\(99\) −15.7103 15.7103i −0.158690 0.158690i
\(100\) −15.6383 −0.156383
\(101\) 28.6192 0.283359 0.141679 0.989913i \(-0.454750\pi\)
0.141679 + 0.989913i \(0.454750\pi\)
\(102\) −3.77439 + 3.77439i −0.0370038 + 0.0370038i
\(103\) 92.9620 92.9620i 0.902544 0.902544i −0.0931119 0.995656i \(-0.529681\pi\)
0.995656 + 0.0931119i \(0.0296814\pi\)
\(104\) −9.76865 −0.0939293
\(105\) 110.741 1.05468
\(106\) 1.54457 1.54457i 0.0145714 0.0145714i
\(107\) 202.394i 1.89153i 0.324853 + 0.945765i \(0.394685\pi\)
−0.324853 + 0.945765i \(0.605315\pi\)
\(108\) −82.0793 + 82.0793i −0.759993 + 0.759993i
\(109\) 23.1520i 0.212403i 0.994345 + 0.106202i \(0.0338689\pi\)
−0.994345 + 0.106202i \(0.966131\pi\)
\(110\) −1.59639 1.59639i −0.0145127 0.0145127i
\(111\) −61.3927 + 61.3927i −0.553087 + 0.553087i
\(112\) 171.383i 1.53020i
\(113\) 100.066 + 100.066i 0.885540 + 0.885540i 0.994091 0.108551i \(-0.0346210\pi\)
−0.108551 + 0.994091i \(0.534621\pi\)
\(114\) 6.27963 0.0550844
\(115\) −60.0523 + 60.0523i −0.522194 + 0.522194i
\(116\) 126.577i 1.09118i
\(117\) 39.0535 + 39.0535i 0.333791 + 0.333791i
\(118\) 2.13563 2.13563i 0.0180986 0.0180986i
\(119\) −205.781 + 205.781i −1.72925 + 1.72925i
\(120\) −5.12802 + 5.12802i −0.0427335 + 0.0427335i
\(121\) 89.9817i 0.743650i
\(122\) 0.752220 0.752220i 0.00616574 0.00616574i
\(123\) 8.24902 + 8.24902i 0.0670652 + 0.0670652i
\(124\) 86.1122 + 86.1122i 0.694453 + 0.694453i
\(125\) 93.8870 + 93.8870i 0.751096 + 0.751096i
\(126\) 2.68317 2.68317i 0.0212950 0.0212950i
\(127\) 131.466i 1.03517i 0.855633 + 0.517583i \(0.173168\pi\)
−0.855633 + 0.517583i \(0.826832\pi\)
\(128\) 15.9033 + 15.9033i 0.124245 + 0.124245i
\(129\) −123.111 123.111i −0.954347 0.954347i
\(130\) 3.96841 + 3.96841i 0.0305263 + 0.0305263i
\(131\) −36.0804 + 36.0804i −0.275423 + 0.275423i −0.831279 0.555856i \(-0.812391\pi\)
0.555856 + 0.831279i \(0.312391\pi\)
\(132\) −49.7708 −0.377051
\(133\) 342.367 2.57419
\(134\) 0.369006i 0.00275377i
\(135\) 133.506 0.988931
\(136\) 19.0580i 0.140132i
\(137\) 215.945i 1.57624i −0.615519 0.788122i \(-0.711053\pi\)
0.615519 0.788122i \(-0.288947\pi\)
\(138\) 3.65523i 0.0264872i
\(139\) 61.1637 + 61.1637i 0.440027 + 0.440027i 0.892021 0.451994i \(-0.149287\pi\)
−0.451994 + 0.892021i \(0.649287\pi\)
\(140\) −139.654 + 139.654i −0.997530 + 0.997530i
\(141\) −6.66116 6.66116i −0.0472422 0.0472422i
\(142\) 5.45715 0.0384307
\(143\) 77.1073i 0.539212i
\(144\) 63.4548i 0.440659i
\(145\) 102.942 102.942i 0.709943 0.709943i
\(146\) 4.63071i 0.0317172i
\(147\) −106.188 + 106.188i −0.722368 + 0.722368i
\(148\) 154.843i 1.04624i
\(149\) 162.520 + 162.520i 1.09074 + 1.09074i 0.995450 + 0.0952856i \(0.0303764\pi\)
0.0952856 + 0.995450i \(0.469624\pi\)
\(150\) −0.774125 −0.00516084
\(151\) −112.272 112.272i −0.743524 0.743524i 0.229730 0.973254i \(-0.426216\pi\)
−0.973254 + 0.229730i \(0.926216\pi\)
\(152\) −15.8538 + 15.8538i −0.104301 + 0.104301i
\(153\) −76.1908 + 76.1908i −0.497979 + 0.497979i
\(154\) 5.29765 0.0344003
\(155\) 140.065i 0.903647i
\(156\) 123.723 0.793097
\(157\) 101.987i 0.649602i 0.945782 + 0.324801i \(0.105297\pi\)
−0.945782 + 0.324801i \(0.894703\pi\)
\(158\) 5.56357 0.0352125
\(159\) −39.1631 + 39.1631i −0.246309 + 0.246309i
\(160\) 19.4070i 0.121294i
\(161\) 199.284i 1.23779i
\(162\) −1.82178 + 1.82178i −0.0112456 + 0.0112456i
\(163\) 245.743i 1.50762i −0.657091 0.753812i \(-0.728213\pi\)
0.657091 0.753812i \(-0.271787\pi\)
\(164\) −20.8055 −0.126863
\(165\) 40.4772 + 40.4772i 0.245316 + 0.245316i
\(166\) 8.05058 + 8.05058i 0.0484975 + 0.0484975i
\(167\) 46.4281 46.4281i 0.278012 0.278012i −0.554303 0.832315i \(-0.687015\pi\)
0.832315 + 0.554303i \(0.187015\pi\)
\(168\) 17.0174i 0.101294i
\(169\) 22.6780i 0.134189i
\(170\) −7.74210 + 7.74210i −0.0455418 + 0.0455418i
\(171\) 126.762 0.741298
\(172\) 310.507 1.80527
\(173\) 284.894i 1.64679i −0.567471 0.823394i \(-0.692078\pi\)
0.567471 0.823394i \(-0.307922\pi\)
\(174\) 6.26580i 0.0360103i
\(175\) −42.2055 −0.241174
\(176\) 62.6426 62.6426i 0.355924 0.355924i
\(177\) −54.1497 + 54.1497i −0.305931 + 0.305931i
\(178\) −2.76501 −0.0155337
\(179\) 155.483 155.483i 0.868622 0.868622i −0.123698 0.992320i \(-0.539476\pi\)
0.992320 + 0.123698i \(0.0394755\pi\)
\(180\) −51.7072 + 51.7072i −0.287262 + 0.287262i
\(181\) 114.889i 0.634744i 0.948301 + 0.317372i \(0.102800\pi\)
−0.948301 + 0.317372i \(0.897200\pi\)
\(182\) −13.1692 −0.0723583
\(183\) −19.0728 + 19.0728i −0.104223 + 0.104223i
\(184\) 9.22814 + 9.22814i 0.0501529 + 0.0501529i
\(185\) −125.930 + 125.930i −0.680701 + 0.680701i
\(186\) 4.26271 + 4.26271i 0.0229178 + 0.0229178i
\(187\) −150.431 −0.804444
\(188\) 16.8006 0.0893650
\(189\) −221.520 + 221.520i −1.17206 + 1.17206i
\(190\) 12.8809 0.0677941
\(191\) 152.068 0.796168 0.398084 0.917349i \(-0.369675\pi\)
0.398084 + 0.917349i \(0.369675\pi\)
\(192\) −100.119 100.119i −0.521455 0.521455i
\(193\) −292.686 −1.51651 −0.758254 0.651959i \(-0.773948\pi\)
−0.758254 + 0.651959i \(0.773948\pi\)
\(194\) 8.08220 + 8.08220i 0.0416608 + 0.0416608i
\(195\) −100.621 100.621i −0.516003 0.516003i
\(196\) 267.825i 1.36646i
\(197\) −196.641 11.8956i −0.998175 0.0603839i
\(198\) 1.96146 0.00990639
\(199\) 0.181286 0.181286i 0.000910983 0.000910983i −0.706651 0.707562i \(-0.749795\pi\)
0.707562 + 0.706651i \(0.249795\pi\)
\(200\) 1.95439 1.95439i 0.00977194 0.00977194i
\(201\) 9.35628i 0.0465486i
\(202\) −1.78659 + 1.78659i −0.00884450 + 0.00884450i
\(203\) 341.613i 1.68282i
\(204\) 241.375i 1.18321i
\(205\) 16.9205 + 16.9205i 0.0825392 + 0.0825392i
\(206\) 11.6065i 0.0563424i
\(207\) 73.7853i 0.356451i
\(208\) −155.721 + 155.721i −0.748658 + 0.748658i
\(209\) 125.139 + 125.139i 0.598753 + 0.598753i
\(210\) −6.91313 + 6.91313i −0.0329197 + 0.0329197i
\(211\) −134.216 134.216i −0.636092 0.636092i 0.313497 0.949589i \(-0.398500\pi\)
−0.949589 + 0.313497i \(0.898500\pi\)
\(212\) 98.7763i 0.465926i
\(213\) −138.368 −0.649616
\(214\) −12.6347 12.6347i −0.0590405 0.0590405i
\(215\) −252.527 252.527i −1.17454 1.17454i
\(216\) 20.5156i 0.0949796i
\(217\) 232.404 + 232.404i 1.07099 + 1.07099i
\(218\) −1.44529 1.44529i −0.00662976 0.00662976i
\(219\) 117.414i 0.536135i
\(220\) −102.091 −0.464049
\(221\) 373.950 1.69208
\(222\) 7.66502i 0.0345271i
\(223\) 4.20298i 0.0188474i 0.999956 + 0.00942371i \(0.00299970\pi\)
−0.999956 + 0.00942371i \(0.997000\pi\)
\(224\) 32.2011 + 32.2011i 0.143755 + 0.143755i
\(225\) −15.6267 −0.0694519
\(226\) −12.4935 −0.0552809
\(227\) 259.198 + 259.198i 1.14184 + 1.14184i 0.988113 + 0.153729i \(0.0491283\pi\)
0.153729 + 0.988113i \(0.450872\pi\)
\(228\) 200.794 200.794i 0.880674 0.880674i
\(229\) 207.713 207.713i 0.907045 0.907045i −0.0889878 0.996033i \(-0.528363\pi\)
0.996033 + 0.0889878i \(0.0283632\pi\)
\(230\) 7.49767i 0.0325986i
\(231\) −134.324 −0.581489
\(232\) −15.8189 15.8189i −0.0681849 0.0681849i
\(233\) −195.509 −0.839093 −0.419546 0.907734i \(-0.637811\pi\)
−0.419546 + 0.907734i \(0.637811\pi\)
\(234\) −4.87593 −0.0208373
\(235\) −13.6635 13.6635i −0.0581425 0.0581425i
\(236\) 136.575i 0.578709i
\(237\) −141.066 −0.595217
\(238\) 25.6922i 0.107951i
\(239\) −196.185 −0.820857 −0.410428 0.911893i \(-0.634621\pi\)
−0.410428 + 0.911893i \(0.634621\pi\)
\(240\) 163.490i 0.681209i
\(241\) −22.4349 22.4349i −0.0930909 0.0930909i 0.659028 0.752119i \(-0.270968\pi\)
−0.752119 + 0.659028i \(0.770968\pi\)
\(242\) −5.61721 5.61721i −0.0232116 0.0232116i
\(243\) −138.847 + 138.847i −0.571387 + 0.571387i
\(244\) 48.1051i 0.197152i
\(245\) −217.815 + 217.815i −0.889040 + 0.889040i
\(246\) −1.02991 −0.00418662
\(247\) −311.079 311.079i −1.25943 1.25943i
\(248\) −21.5236 −0.0867888
\(249\) −204.126 204.126i −0.819781 0.819781i
\(250\) −11.7220 −0.0468881
\(251\) −318.964 −1.27077 −0.635386 0.772194i \(-0.719159\pi\)
−0.635386 + 0.772194i \(0.719159\pi\)
\(252\) 171.591i 0.680916i
\(253\) 72.8408 72.8408i 0.287908 0.287908i
\(254\) −8.20692 8.20692i −0.0323107 0.0323107i
\(255\) 196.304 196.304i 0.769820 0.769820i
\(256\) 251.026 0.980572
\(257\) 234.621 0.912924 0.456462 0.889743i \(-0.349116\pi\)
0.456462 + 0.889743i \(0.349116\pi\)
\(258\) 15.3707 0.0595762
\(259\) 417.899i 1.61351i
\(260\) 253.783 0.976090
\(261\) 126.483i 0.484609i
\(262\) 4.50473i 0.0171936i
\(263\) 228.738 + 228.738i 0.869725 + 0.869725i 0.992442 0.122717i \(-0.0391607\pi\)
−0.122717 + 0.992442i \(0.539161\pi\)
\(264\) 6.22007 6.22007i 0.0235609 0.0235609i
\(265\) −80.3320 + 80.3320i −0.303140 + 0.303140i
\(266\) −21.3727 + 21.3727i −0.0803483 + 0.0803483i
\(267\) 70.1078 0.262576
\(268\) −11.7991 11.7991i −0.0440265 0.0440265i
\(269\) −43.2513 + 43.2513i −0.160786 + 0.160786i −0.782915 0.622129i \(-0.786268\pi\)
0.622129 + 0.782915i \(0.286268\pi\)
\(270\) −8.33425 + 8.33425i −0.0308676 + 0.0308676i
\(271\) −96.0163 + 96.0163i −0.354304 + 0.354304i −0.861708 0.507404i \(-0.830605\pi\)
0.507404 + 0.861708i \(0.330605\pi\)
\(272\) −303.800 303.800i −1.11691 1.11691i
\(273\) 333.911 1.22312
\(274\) 13.4807 + 13.4807i 0.0491995 + 0.0491995i
\(275\) −15.4266 15.4266i −0.0560969 0.0560969i
\(276\) −116.877 116.877i −0.423469 0.423469i
\(277\) 315.357 315.357i 1.13847 1.13847i 0.149747 0.988724i \(-0.452154\pi\)
0.988724 0.149747i \(-0.0478459\pi\)
\(278\) −7.63643 −0.0274692
\(279\) 86.0480 + 86.0480i 0.308416 + 0.308416i
\(280\) 34.9063i 0.124666i
\(281\) −115.671 + 115.671i −0.411640 + 0.411640i −0.882310 0.470670i \(-0.844012\pi\)
0.470670 + 0.882310i \(0.344012\pi\)
\(282\) 0.831661 0.00294915
\(283\) −232.391 232.391i −0.821170 0.821170i 0.165106 0.986276i \(-0.447203\pi\)
−0.986276 + 0.165106i \(0.947203\pi\)
\(284\) 174.495 174.495i 0.614418 0.614418i
\(285\) −326.600 −1.14596
\(286\) −4.81351 4.81351i −0.0168305 0.0168305i
\(287\) −56.1509 −0.195648
\(288\) 11.9225 + 11.9225i 0.0413977 + 0.0413977i
\(289\) 440.551i 1.52440i
\(290\) 12.8525i 0.0443190i
\(291\) −204.927 204.927i −0.704218 0.704218i
\(292\) −148.069 148.069i −0.507085 0.507085i
\(293\) 145.015i 0.494931i 0.968897 + 0.247466i \(0.0795977\pi\)
−0.968897 + 0.247466i \(0.920402\pi\)
\(294\) 13.2578i 0.0450947i
\(295\) −111.073 + 111.073i −0.376518 + 0.376518i
\(296\) 19.3514 + 19.3514i 0.0653764 + 0.0653764i
\(297\) −161.937 −0.545241
\(298\) −20.2910 −0.0680905
\(299\) −181.072 + 181.072i −0.605593 + 0.605593i
\(300\) −24.7530 + 24.7530i −0.0825099 + 0.0825099i
\(301\) 838.013 2.78410
\(302\) 14.0174 0.0464154
\(303\) 45.2997 45.2997i 0.149504 0.149504i
\(304\) 505.447i 1.66265i
\(305\) −39.1225 + 39.1225i −0.128271 + 0.128271i
\(306\) 9.51260i 0.0310869i
\(307\) 303.855 + 303.855i 0.989754 + 0.989754i 0.999948 0.0101938i \(-0.00324484\pi\)
−0.0101938 + 0.999948i \(0.503245\pi\)
\(308\) 169.394 169.394i 0.549982 0.549982i
\(309\) 294.288i 0.952389i
\(310\) 8.74375 + 8.74375i 0.0282056 + 0.0282056i
\(311\) 158.554 0.509821 0.254911 0.966965i \(-0.417954\pi\)
0.254911 + 0.966965i \(0.417954\pi\)
\(312\) −15.4622 + 15.4622i −0.0495584 + 0.0495584i
\(313\) 84.0443i 0.268512i −0.990947 0.134256i \(-0.957136\pi\)
0.990947 0.134256i \(-0.0428645\pi\)
\(314\) −6.36669 6.36669i −0.0202761 0.0202761i
\(315\) −139.550 + 139.550i −0.443016 + 0.443016i
\(316\) 177.897 177.897i 0.562966 0.562966i
\(317\) −255.281 + 255.281i −0.805303 + 0.805303i −0.983919 0.178616i \(-0.942838\pi\)
0.178616 + 0.983919i \(0.442838\pi\)
\(318\) 4.88960i 0.0153761i
\(319\) −124.864 + 124.864i −0.391423 + 0.391423i
\(320\) −205.367 205.367i −0.641771 0.641771i
\(321\) 320.357 + 320.357i 0.997996 + 0.997996i
\(322\) 12.4405 + 12.4405i 0.0386352 + 0.0386352i
\(323\) 606.894 606.894i 1.87893 1.87893i
\(324\) 116.504i 0.359581i
\(325\) 38.3485 + 38.3485i 0.117995 + 0.117995i
\(326\) 15.3408 + 15.3408i 0.0470576 + 0.0470576i
\(327\) 36.6458 + 36.6458i 0.112067 + 0.112067i
\(328\) 2.60015 2.60015i 0.00792729 0.00792729i
\(329\) 45.3424 0.137819
\(330\) −5.05368 −0.0153142
\(331\) 322.111i 0.973144i 0.873640 + 0.486572i \(0.161753\pi\)
−0.873640 + 0.486572i \(0.838247\pi\)
\(332\) 514.841 1.55073
\(333\) 154.728i 0.464648i
\(334\) 5.79666i 0.0173553i
\(335\) 19.1918i 0.0572889i
\(336\) −271.272 271.272i −0.807356 0.807356i
\(337\) −117.987 + 117.987i −0.350109 + 0.350109i −0.860150 0.510041i \(-0.829630\pi\)
0.510041 + 0.860150i \(0.329630\pi\)
\(338\) 1.41570 + 1.41570i 0.00418846 + 0.00418846i
\(339\) 316.777 0.934446
\(340\) 495.114i 1.45622i
\(341\) 169.893i 0.498221i
\(342\) −7.91327 + 7.91327i −0.0231382 + 0.0231382i
\(343\) 194.876i 0.568153i
\(344\) −38.8054 + 38.8054i −0.112806 + 0.112806i
\(345\) 190.106i 0.551033i
\(346\) 17.7849 + 17.7849i 0.0514013 + 0.0514013i
\(347\) −606.002 −1.74640 −0.873201 0.487360i \(-0.837960\pi\)
−0.873201 + 0.487360i \(0.837960\pi\)
\(348\) 200.351 + 200.351i 0.575723 + 0.575723i
\(349\) −66.9633 + 66.9633i −0.191872 + 0.191872i −0.796505 0.604633i \(-0.793320\pi\)
0.604633 + 0.796505i \(0.293320\pi\)
\(350\) 2.63473 2.63473i 0.00752780 0.00752780i
\(351\) 402.552 1.14687
\(352\) 23.5398i 0.0668745i
\(353\) −56.6785 −0.160562 −0.0802812 0.996772i \(-0.525582\pi\)
−0.0802812 + 0.996772i \(0.525582\pi\)
\(354\) 6.76072i 0.0190981i
\(355\) −283.823 −0.799503
\(356\) −88.4122 + 88.4122i −0.248349 + 0.248349i
\(357\) 651.436i 1.82475i
\(358\) 19.4125i 0.0542247i
\(359\) −396.230 + 396.230i −1.10371 + 1.10371i −0.109745 + 0.993960i \(0.535004\pi\)
−0.993960 + 0.109745i \(0.964996\pi\)
\(360\) 12.9241i 0.0359004i
\(361\) −648.717 −1.79700
\(362\) −7.17206 7.17206i −0.0198123 0.0198123i
\(363\) 142.427 + 142.427i 0.392360 + 0.392360i
\(364\) −421.091 + 421.091i −1.15684 + 1.15684i
\(365\) 240.841i 0.659838i
\(366\) 2.38129i 0.00650625i
\(367\) 110.641 110.641i 0.301474 0.301474i −0.540117 0.841590i \(-0.681620\pi\)
0.841590 + 0.540117i \(0.181620\pi\)
\(368\) 294.209 0.799481
\(369\) −20.7900 −0.0563415
\(370\) 15.7226i 0.0424936i
\(371\) 266.582i 0.718551i
\(372\) 272.604 0.732806
\(373\) 269.116 269.116i 0.721490 0.721490i −0.247419 0.968909i \(-0.579582\pi\)
0.968909 + 0.247419i \(0.0795824\pi\)
\(374\) 9.39083 9.39083i 0.0251092 0.0251092i
\(375\) 297.216 0.792577
\(376\) −2.09965 + 2.09965i −0.00558416 + 0.00558416i
\(377\) 310.394 310.394i 0.823327 0.823327i
\(378\) 27.6573i 0.0731674i
\(379\) −509.824 −1.34518 −0.672592 0.740014i \(-0.734819\pi\)
−0.672592 + 0.740014i \(0.734819\pi\)
\(380\) 411.871 411.871i 1.08387 1.08387i
\(381\) 208.090 + 208.090i 0.546167 + 0.546167i
\(382\) −9.49304 + 9.49304i −0.0248509 + 0.0248509i
\(383\) −10.9212 10.9212i −0.0285148 0.0285148i 0.692706 0.721220i \(-0.256419\pi\)
−0.721220 + 0.692706i \(0.756419\pi\)
\(384\) 50.3449 0.131107
\(385\) −275.528 −0.715656
\(386\) 18.2713 18.2713i 0.0473349 0.0473349i
\(387\) 310.276 0.801747
\(388\) 516.863 1.33212
\(389\) 458.741 + 458.741i 1.17928 + 1.17928i 0.979927 + 0.199356i \(0.0638851\pi\)
0.199356 + 0.979927i \(0.436115\pi\)
\(390\) 12.5627 0.0322121
\(391\) −353.259 353.259i −0.903477 0.903477i
\(392\) 33.4713 + 33.4713i 0.0853859 + 0.0853859i
\(393\) 114.219i 0.290634i
\(394\) 13.0181 11.5329i 0.0330409 0.0292714i
\(395\) −289.358 −0.732552
\(396\) 62.7186 62.7186i 0.158380 0.158380i
\(397\) 187.230 187.230i 0.471612 0.471612i −0.430824 0.902436i \(-0.641777\pi\)
0.902436 + 0.430824i \(0.141777\pi\)
\(398\) 0.0226339i 5.68692e-5i
\(399\) 541.912 541.912i 1.35818 1.35818i
\(400\) 62.3093i 0.155773i
\(401\) 38.3304i 0.0955869i −0.998857 0.0477935i \(-0.984781\pi\)
0.998857 0.0477935i \(-0.0152189\pi\)
\(402\) −0.584077 0.584077i −0.00145293 0.00145293i
\(403\) 422.331i 1.04797i
\(404\) 114.254i 0.282807i
\(405\) 94.7497 94.7497i 0.233950 0.233950i
\(406\) −21.3256 21.3256i −0.0525261 0.0525261i
\(407\) 152.747 152.747i 0.375301 0.375301i
\(408\) −30.1657 30.1657i −0.0739356 0.0739356i
\(409\) 451.916i 1.10493i 0.833536 + 0.552465i \(0.186313\pi\)
−0.833536 + 0.552465i \(0.813687\pi\)
\(410\) −2.11257 −0.00515261
\(411\) −341.807 341.807i −0.831648 0.831648i
\(412\) 371.123 + 371.123i 0.900785 + 0.900785i
\(413\) 368.596i 0.892485i
\(414\) 4.60614 + 4.60614i 0.0111259 + 0.0111259i
\(415\) −418.706 418.706i −1.00893 1.00893i
\(416\) 58.5167i 0.140665i
\(417\) 193.625 0.464328
\(418\) −15.6240 −0.0373779
\(419\) 103.151i 0.246183i −0.992395 0.123091i \(-0.960719\pi\)
0.992395 0.123091i \(-0.0392808\pi\)
\(420\) 442.100i 1.05262i
\(421\) −190.693 190.693i −0.452953 0.452953i 0.443380 0.896334i \(-0.353779\pi\)
−0.896334 + 0.443380i \(0.853779\pi\)
\(422\) 16.7571 0.0397088
\(423\) 16.7881 0.0396882
\(424\) 12.3445 + 12.3445i 0.0291144 + 0.0291144i
\(425\) −74.8153 + 74.8153i −0.176036 + 0.176036i
\(426\) 8.63780 8.63780i 0.0202765 0.0202765i
\(427\) 129.828i 0.304048i
\(428\) −807.997 −1.88784
\(429\) 122.049 + 122.049i 0.284495 + 0.284495i
\(430\) 31.5286 0.0733223
\(431\) −292.192 −0.677940 −0.338970 0.940797i \(-0.610078\pi\)
−0.338970 + 0.940797i \(0.610078\pi\)
\(432\) −327.036 327.036i −0.757029 0.757029i
\(433\) 217.605i 0.502553i 0.967915 + 0.251276i \(0.0808503\pi\)
−0.967915 + 0.251276i \(0.919150\pi\)
\(434\) −29.0162 −0.0668576
\(435\) 325.881i 0.749151i
\(436\) −92.4274 −0.211989
\(437\) 587.733i 1.34493i
\(438\) −7.32968 7.32968i −0.0167344 0.0167344i
\(439\) −74.6551 74.6551i −0.170057 0.170057i 0.616947 0.787004i \(-0.288369\pi\)
−0.787004 + 0.616947i \(0.788369\pi\)
\(440\) 12.7587 12.7587i 0.0289971 0.0289971i
\(441\) 267.626i 0.606861i
\(442\) −23.3443 + 23.3443i −0.0528152 + 0.0528152i
\(443\) 0.441477 0.000996562 0.000498281 1.00000i \(-0.499841\pi\)
0.000498281 1.00000i \(0.499841\pi\)
\(444\) −245.092 245.092i −0.552009 0.552009i
\(445\) 143.806 0.323160
\(446\) −0.262376 0.262376i −0.000588286 0.000588286i
\(447\) 514.485 1.15097
\(448\) 681.511 1.52123
\(449\) 766.648i 1.70746i 0.520720 + 0.853728i \(0.325664\pi\)
−0.520720 + 0.853728i \(0.674336\pi\)
\(450\) 0.975514 0.975514i 0.00216781 0.00216781i
\(451\) −20.5239 20.5239i −0.0455075 0.0455075i
\(452\) −399.484 + 399.484i −0.883815 + 0.883815i
\(453\) −355.418 −0.784587
\(454\) −32.3615 −0.0712809
\(455\) 684.923 1.50533
\(456\) 50.1881i 0.110062i
\(457\) −534.249 −1.16904 −0.584518 0.811381i \(-0.698716\pi\)
−0.584518 + 0.811381i \(0.698716\pi\)
\(458\) 25.9335i 0.0566234i
\(459\) 785.351i 1.71100i
\(460\) −239.741 239.741i −0.521176 0.521176i
\(461\) 273.447 273.447i 0.593160 0.593160i −0.345324 0.938484i \(-0.612231\pi\)
0.938484 + 0.345324i \(0.112231\pi\)
\(462\) 8.38533 8.38533i 0.0181501 0.0181501i
\(463\) 265.533 265.533i 0.573505 0.573505i −0.359601 0.933106i \(-0.617087\pi\)
0.933106 + 0.359601i \(0.117087\pi\)
\(464\) −504.334 −1.08693
\(465\) −221.701 221.701i −0.476777 0.476777i
\(466\) 12.2049 12.2049i 0.0261907 0.0261907i
\(467\) 253.123 253.123i 0.542019 0.542019i −0.382101 0.924120i \(-0.624799\pi\)
0.924120 + 0.382101i \(0.124799\pi\)
\(468\) −155.910 + 155.910i −0.333141 + 0.333141i
\(469\) −31.8440 31.8440i −0.0678977 0.0678977i
\(470\) 1.70592 0.00362961
\(471\) 161.430 + 161.430i 0.342739 + 0.342739i
\(472\) 17.0684 + 17.0684i 0.0361618 + 0.0361618i
\(473\) 306.304 + 306.304i 0.647578 + 0.647578i
\(474\) 8.80624 8.80624i 0.0185786 0.0185786i
\(475\) 124.474 0.262050
\(476\) −821.519 821.519i −1.72588 1.72588i
\(477\) 98.7027i 0.206924i
\(478\) 12.2471 12.2471i 0.0256215 0.0256215i
\(479\) −781.396 −1.63131 −0.815654 0.578540i \(-0.803622\pi\)
−0.815654 + 0.578540i \(0.803622\pi\)
\(480\) −30.7181 30.7181i −0.0639961 0.0639961i
\(481\) −379.709 + 379.709i −0.789415 + 0.789415i
\(482\) 2.80105 0.00581131
\(483\) −315.435 315.435i −0.653074 0.653074i
\(484\) −359.225 −0.742201
\(485\) −420.351 420.351i −0.866702 0.866702i
\(486\) 17.3354i 0.0356695i
\(487\) 273.012i 0.560600i 0.959913 + 0.280300i \(0.0904339\pi\)
−0.959913 + 0.280300i \(0.909566\pi\)
\(488\) 6.01190 + 6.01190i 0.0123195 + 0.0123195i
\(489\) −388.971 388.971i −0.795442 0.795442i
\(490\) 27.1947i 0.0554994i
\(491\) 591.880i 1.20546i 0.797946 + 0.602729i \(0.205920\pi\)
−0.797946 + 0.602729i \(0.794080\pi\)
\(492\) −32.9318 + 32.9318i −0.0669345 + 0.0669345i
\(493\) 605.558 + 605.558i 1.22831 + 1.22831i
\(494\) 38.8390 0.0786214
\(495\) −102.015 −0.206090
\(496\) −343.105 + 343.105i −0.691744 + 0.691744i
\(497\) 470.935 470.935i 0.947556 0.947556i
\(498\) 25.4856 0.0511758
\(499\) 380.370 0.762264 0.381132 0.924521i \(-0.375534\pi\)
0.381132 + 0.924521i \(0.375534\pi\)
\(500\) −374.816 + 374.816i −0.749632 + 0.749632i
\(501\) 146.976i 0.293366i
\(502\) 19.9117 19.9117i 0.0396648 0.0396648i
\(503\) 240.775i 0.478678i −0.970936 0.239339i \(-0.923069\pi\)
0.970936 0.239339i \(-0.0769308\pi\)
\(504\) 21.4444 + 21.4444i 0.0425485 + 0.0425485i
\(505\) 92.9195 92.9195i 0.183999 0.183999i
\(506\) 9.09435i 0.0179730i
\(507\) −35.8956 35.8956i −0.0708000 0.0708000i
\(508\) −524.839 −1.03315
\(509\) 1.12121 1.12121i 0.00220277 0.00220277i −0.706005 0.708207i \(-0.749504\pi\)
0.708207 + 0.706005i \(0.249504\pi\)
\(510\) 24.5090i 0.0480569i
\(511\) −399.616 399.616i −0.782027 0.782027i
\(512\) −79.2840 + 79.2840i −0.154852 + 0.154852i
\(513\) 653.312 653.312i 1.27351 1.27351i
\(514\) −14.6465 + 14.6465i −0.0284952 + 0.0284952i
\(515\) 603.649i 1.17213i
\(516\) 491.483 491.483i 0.952487 0.952487i
\(517\) 16.5732 + 16.5732i 0.0320565 + 0.0320565i
\(518\) 26.0878 + 26.0878i 0.0503626 + 0.0503626i
\(519\) −450.942 450.942i −0.868867 0.868867i
\(520\) −31.7164 + 31.7164i −0.0609930 + 0.0609930i
\(521\) 540.852i 1.03810i −0.854743 0.519051i \(-0.826285\pi\)
0.854743 0.519051i \(-0.173715\pi\)
\(522\) −7.89585 7.89585i −0.0151261 0.0151261i
\(523\) −99.9221 99.9221i −0.191056 0.191056i 0.605096 0.796152i \(-0.293135\pi\)
−0.796152 + 0.605096i \(0.793135\pi\)
\(524\) −144.041 144.041i −0.274887 0.274887i
\(525\) −66.8046 + 66.8046i −0.127247 + 0.127247i
\(526\) −28.5584 −0.0542936
\(527\) 823.938 1.56345
\(528\) 198.307i 0.375581i
\(529\) −186.894 −0.353296
\(530\) 10.0296i 0.0189239i
\(531\) 136.474i 0.257012i
\(532\) 1366.80i 2.56917i
\(533\) 51.0195 + 51.0195i 0.0957214 + 0.0957214i
\(534\) −4.37656 + 4.37656i −0.00819581 + 0.00819581i
\(535\) 657.122 + 657.122i 1.22826 + 1.22826i
\(536\) 2.94917 0.00550218
\(537\) 492.210i 0.916593i
\(538\) 5.40003i 0.0100372i
\(539\) 264.200 264.200i 0.490167 0.490167i
\(540\) 532.982i 0.987004i
\(541\) −9.73596 + 9.73596i −0.0179962 + 0.0179962i −0.716048 0.698051i \(-0.754051\pi\)
0.698051 + 0.716048i \(0.254051\pi\)
\(542\) 11.9879i 0.0221178i
\(543\) 181.850 + 181.850i 0.334899 + 0.334899i
\(544\) 114.162 0.209857
\(545\) 75.1686 + 75.1686i 0.137924 + 0.137924i
\(546\) −20.8448 + 20.8448i −0.0381772 + 0.0381772i
\(547\) −537.310 + 537.310i −0.982285 + 0.982285i −0.999846 0.0175605i \(-0.994410\pi\)
0.0175605 + 0.999846i \(0.494410\pi\)
\(548\) 862.099 1.57317
\(549\) 48.0692i 0.0875578i
\(550\) 1.92605 0.00350192
\(551\) 1007.49i 1.82848i
\(552\) 29.2133 0.0529227
\(553\) 480.119 480.119i 0.868207 0.868207i
\(554\) 39.3730i 0.0710704i
\(555\) 398.653i 0.718294i
\(556\) −244.178 + 244.178i −0.439169 + 0.439169i
\(557\) 430.206i 0.772362i −0.922423 0.386181i \(-0.873794\pi\)
0.922423 0.386181i \(-0.126206\pi\)
\(558\) −10.7433 −0.0192532
\(559\) −761.430 761.430i −1.36213 1.36213i
\(560\) −556.437 556.437i −0.993638 0.993638i
\(561\) −238.108 + 238.108i −0.424435 + 0.424435i
\(562\) 14.4418i 0.0256971i
\(563\) 629.872i 1.11878i 0.828905 + 0.559389i \(0.188964\pi\)
−0.828905 + 0.559389i \(0.811036\pi\)
\(564\) 26.5927 26.5927i 0.0471502 0.0471502i
\(565\) 649.779 1.15005
\(566\) 29.0146 0.0512625
\(567\) 314.428i 0.554546i
\(568\) 43.6147i 0.0767864i
\(569\) −229.758 −0.403793 −0.201897 0.979407i \(-0.564711\pi\)
−0.201897 + 0.979407i \(0.564711\pi\)
\(570\) 20.3884 20.3884i 0.0357691 0.0357691i
\(571\) −708.422 + 708.422i −1.24067 + 1.24067i −0.280946 + 0.959723i \(0.590648\pi\)
−0.959723 + 0.280946i \(0.909352\pi\)
\(572\) −307.828 −0.538161
\(573\) 240.700 240.700i 0.420069 0.420069i
\(574\) 3.50529 3.50529i 0.00610678 0.00610678i
\(575\) 72.4533i 0.126006i
\(576\) 252.331 0.438074
\(577\) −26.0769 + 26.0769i −0.0451939 + 0.0451939i −0.729343 0.684149i \(-0.760174\pi\)
0.684149 + 0.729343i \(0.260174\pi\)
\(578\) −27.5020 27.5020i −0.0475812 0.0475812i
\(579\) −463.276 + 463.276i −0.800131 + 0.800131i
\(580\) 410.965 + 410.965i 0.708560 + 0.708560i
\(581\) 1389.48 2.39153
\(582\) 25.5857 0.0439616
\(583\) 97.4393 97.4393i 0.167134 0.167134i
\(584\) 37.0096 0.0633726
\(585\) 253.594 0.433494
\(586\) −9.05273 9.05273i −0.0154483 0.0154483i
\(587\) −605.591 −1.03167 −0.515836 0.856688i \(-0.672518\pi\)
−0.515836 + 0.856688i \(0.672518\pi\)
\(588\) −423.925 423.925i −0.720960 0.720960i
\(589\) −685.412 685.412i −1.16369 1.16369i
\(590\) 13.8677i 0.0235046i
\(591\) −330.079 + 292.422i −0.558510 + 0.494791i
\(592\) 616.957 1.04216
\(593\) 149.638 149.638i 0.252340 0.252340i −0.569589 0.821930i \(-0.692898\pi\)
0.821930 + 0.569589i \(0.192898\pi\)
\(594\) 10.1091 10.1091i 0.0170187 0.0170187i
\(595\) 1336.24i 2.24578i
\(596\) −648.812 + 648.812i −1.08861 + 1.08861i
\(597\) 0.573892i 0.000961294i
\(598\) 22.6073i 0.0378048i
\(599\) 84.5357 + 84.5357i 0.141128 + 0.141128i 0.774141 0.633013i \(-0.218182\pi\)
−0.633013 + 0.774141i \(0.718182\pi\)
\(600\) 6.18697i 0.0103116i
\(601\) 393.271i 0.654362i 0.944962 + 0.327181i \(0.106099\pi\)
−0.944962 + 0.327181i \(0.893901\pi\)
\(602\) −52.3139 + 52.3139i −0.0869002 + 0.0869002i
\(603\) −11.7903 11.7903i −0.0195528 0.0195528i
\(604\) 448.214 448.214i 0.742075 0.742075i
\(605\) 292.148 + 292.148i 0.482889 + 0.482889i
\(606\) 5.65577i 0.00933296i
\(607\) −706.714 −1.16427 −0.582136 0.813091i \(-0.697783\pi\)
−0.582136 + 0.813091i \(0.697783\pi\)
\(608\) −94.9683 94.9683i −0.156198 0.156198i
\(609\) 540.719 + 540.719i 0.887880 + 0.887880i
\(610\) 4.88454i 0.00800745i
\(611\) −41.1987 41.1987i −0.0674283 0.0674283i
\(612\) −304.169 304.169i −0.497008 0.497008i
\(613\) 589.730i 0.962038i −0.876710 0.481019i \(-0.840267\pi\)
0.876710 0.481019i \(-0.159733\pi\)
\(614\) −37.9370 −0.0617866
\(615\) 53.5650 0.0870976
\(616\) 42.3399i 0.0687336i
\(617\) 307.544i 0.498450i 0.968446 + 0.249225i \(0.0801758\pi\)
−0.968446 + 0.249225i \(0.919824\pi\)
\(618\) 18.3713 + 18.3713i 0.0297270 + 0.0297270i
\(619\) 499.962 0.807693 0.403846 0.914827i \(-0.367673\pi\)
0.403846 + 0.914827i \(0.367673\pi\)
\(620\) 559.170 0.901887
\(621\) −380.278 380.278i −0.612364 0.612364i
\(622\) −9.89795 + 9.89795i −0.0159131 + 0.0159131i
\(623\) −238.611 + 238.611i −0.383004 + 0.383004i
\(624\) 492.962i 0.790004i
\(625\) 511.725 0.818760
\(626\) 5.24656 + 5.24656i 0.00838109 + 0.00838109i
\(627\) 396.151 0.631820
\(628\) −407.155 −0.648336
\(629\) −740.785 740.785i −1.17772 1.17772i
\(630\) 17.4232i 0.0276558i
\(631\) 655.032 1.03809 0.519043 0.854748i \(-0.326289\pi\)
0.519043 + 0.854748i \(0.326289\pi\)
\(632\) 44.4652i 0.0703563i
\(633\) −424.883 −0.671222
\(634\) 31.8725i 0.0502720i
\(635\) 426.837 + 426.837i 0.672185 + 0.672185i
\(636\) −156.347 156.347i −0.245829 0.245829i
\(637\) −656.764 + 656.764i −1.03103 + 1.03103i
\(638\) 15.5896i 0.0244350i
\(639\) 174.365 174.365i 0.272871 0.272871i
\(640\) 103.268 0.161357
\(641\) 659.625 + 659.625i 1.02906 + 1.02906i 0.999565 + 0.0294910i \(0.00938862\pi\)
0.0294910 + 0.999565i \(0.490611\pi\)
\(642\) −39.9973 −0.0623011
\(643\) −140.974 140.974i −0.219244 0.219244i 0.588936 0.808180i \(-0.299547\pi\)
−0.808180 + 0.588936i \(0.799547\pi\)
\(644\) 795.583 1.23538
\(645\) −799.420 −1.23941
\(646\) 75.7721i 0.117294i
\(647\) 622.152 622.152i 0.961596 0.961596i −0.0376936 0.999289i \(-0.512001\pi\)
0.999289 + 0.0376936i \(0.0120011\pi\)
\(648\) −14.5600 14.5600i −0.0224692 0.0224692i
\(649\) 134.727 134.727i 0.207591 0.207591i
\(650\) −4.78790 −0.00736600
\(651\) 735.717 1.13013
\(652\) 981.055 1.50469
\(653\) 515.139i 0.788880i −0.918922 0.394440i \(-0.870939\pi\)
0.918922 0.394440i \(-0.129061\pi\)
\(654\) −4.57532 −0.00699590
\(655\) 234.288i 0.357692i
\(656\) 82.8973i 0.126368i
\(657\) −147.959 147.959i −0.225203 0.225203i
\(658\) −2.83055 + 2.83055i −0.00430175 + 0.00430175i
\(659\) −696.628 + 696.628i −1.05710 + 1.05710i −0.0588305 + 0.998268i \(0.518737\pi\)
−0.998268 + 0.0588305i \(0.981263\pi\)
\(660\) −161.593 + 161.593i −0.244838 + 0.244838i
\(661\) −582.787 −0.881674 −0.440837 0.897587i \(-0.645318\pi\)
−0.440837 + 0.897587i \(0.645318\pi\)
\(662\) −20.1082 20.1082i −0.0303749 0.0303749i
\(663\) 591.904 591.904i 0.892766 0.892766i
\(664\) −64.3419 + 64.3419i −0.0969004 + 0.0969004i
\(665\) 1111.58 1111.58i 1.67155 1.67155i
\(666\) 9.65907 + 9.65907i 0.0145031 + 0.0145031i
\(667\) −586.439 −0.879219
\(668\) 185.350 + 185.350i 0.277471 + 0.277471i
\(669\) 6.65264 + 6.65264i 0.00994415 + 0.00994415i
\(670\) −1.19807 1.19807i −0.00178816 0.00178816i
\(671\) 47.4539 47.4539i 0.0707212 0.0707212i
\(672\) 101.938 0.151694
\(673\) −714.473 714.473i −1.06162 1.06162i −0.997972 0.0636517i \(-0.979725\pi\)
−0.0636517 0.997972i \(-0.520275\pi\)
\(674\) 14.7309i 0.0218560i
\(675\) −80.5374 + 80.5374i −0.119315 + 0.119315i
\(676\) 90.5351 0.133928
\(677\) −765.767 765.767i −1.13112 1.13112i −0.989992 0.141127i \(-0.954927\pi\)
−0.141127 0.989992i \(-0.545073\pi\)
\(678\) −19.7752 + 19.7752i −0.0291670 + 0.0291670i
\(679\) 1394.94 2.05440
\(680\) −61.8765 61.8765i −0.0909948 0.0909948i
\(681\) 820.539 1.20490
\(682\) −10.6058 10.6058i −0.0155510 0.0155510i
\(683\) 886.045i 1.29728i 0.761094 + 0.648642i \(0.224663\pi\)
−0.761094 + 0.648642i \(0.775337\pi\)
\(684\) 506.060i 0.739854i
\(685\) −701.121 701.121i −1.02353 1.02353i
\(686\) 12.1654 + 12.1654i 0.0177338 + 0.0177338i
\(687\) 657.554i 0.957138i
\(688\) 1237.18i 1.79823i
\(689\) −242.220 + 242.220i −0.351554 + 0.351554i
\(690\) −11.8676 11.8676i −0.0171995 0.0171995i
\(691\) −862.012 −1.24749 −0.623743 0.781630i \(-0.714389\pi\)
−0.623743 + 0.781630i \(0.714389\pi\)
\(692\) 1137.36 1.64358
\(693\) 169.268 169.268i 0.244254 0.244254i
\(694\) 37.8304 37.8304i 0.0545106 0.0545106i
\(695\) 397.167 0.571463
\(696\) −50.0776 −0.0719505
\(697\) −99.5355 + 99.5355i −0.142806 + 0.142806i
\(698\) 8.36053i 0.0119778i
\(699\) −309.459 + 309.459i −0.442717 + 0.442717i
\(700\) 168.493i 0.240704i
\(701\) 123.879 + 123.879i 0.176717 + 0.176717i 0.789923 0.613206i \(-0.210120\pi\)
−0.613206 + 0.789923i \(0.710120\pi\)
\(702\) −25.1298 + 25.1298i −0.0357974 + 0.0357974i
\(703\) 1232.48i 1.75317i
\(704\) 249.101 + 249.101i 0.353837 + 0.353837i
\(705\) −43.2542 −0.0613535
\(706\) 3.53822 3.53822i 0.00501165 0.00501165i
\(707\) 308.354i 0.436144i
\(708\) −216.177 216.177i −0.305335 0.305335i
\(709\) −237.619 + 237.619i −0.335147 + 0.335147i −0.854537 0.519390i \(-0.826159\pi\)
0.519390 + 0.854537i \(0.326159\pi\)
\(710\) 17.7180 17.7180i 0.0249550 0.0249550i
\(711\) 177.765 177.765i 0.250021 0.250021i
\(712\) 22.0985i 0.0310372i
\(713\) −398.963 + 398.963i −0.559555 + 0.559555i
\(714\) −40.6667 40.6667i −0.0569561 0.0569561i
\(715\) 250.348 + 250.348i 0.350137 + 0.350137i
\(716\) 620.721 + 620.721i 0.866929 + 0.866929i
\(717\) −310.529 + 310.529i −0.433095 + 0.433095i
\(718\) 49.4703i 0.0689001i
\(719\) 475.093 + 475.093i 0.660769 + 0.660769i 0.955561 0.294793i \(-0.0952505\pi\)
−0.294793 + 0.955561i \(0.595251\pi\)
\(720\) −206.022 206.022i −0.286142 0.286142i
\(721\) 1001.61 + 1001.61i 1.38919 + 1.38919i
\(722\) 40.4969 40.4969i 0.0560899 0.0560899i
\(723\) −71.0217 −0.0982320
\(724\) −458.659 −0.633507
\(725\) 124.199i 0.171310i
\(726\) −17.7823 −0.0244935
\(727\) 158.825i 0.218466i −0.994016 0.109233i \(-0.965161\pi\)
0.994016 0.109233i \(-0.0348394\pi\)
\(728\) 105.251i 0.144576i
\(729\) 702.192i 0.963226i
\(730\) −15.0348 15.0348i −0.0205956 0.0205956i
\(731\) 1485.50 1485.50i 2.03214 2.03214i
\(732\) −76.1427 76.1427i −0.104020 0.104020i
\(733\) 464.653 0.633905 0.316953 0.948441i \(-0.397340\pi\)
0.316953 + 0.948441i \(0.397340\pi\)
\(734\) 13.8138i 0.0188199i
\(735\) 689.532i 0.938139i
\(736\) −55.2789 + 55.2789i −0.0751072 + 0.0751072i
\(737\) 23.2788i 0.0315859i
\(738\) 1.29784 1.29784i 0.00175859 0.00175859i
\(739\) 882.725i 1.19449i 0.802061 + 0.597243i \(0.203737\pi\)
−0.802061 + 0.597243i \(0.796263\pi\)
\(740\) −502.738 502.738i −0.679375 0.679375i
\(741\) −984.777 −1.32898
\(742\) 16.6417 + 16.6417i 0.0224282 + 0.0224282i
\(743\) 358.789 358.789i 0.482892 0.482892i −0.423162 0.906054i \(-0.639080\pi\)
0.906054 + 0.423162i \(0.139080\pi\)
\(744\) −34.0685 + 34.0685i −0.0457909 + 0.0457909i
\(745\) 1055.32 1.41654
\(746\) 33.5997i 0.0450398i
\(747\) 514.457 0.688698
\(748\) 600.551i 0.802876i
\(749\) −2180.66 −2.91143
\(750\) −18.5541 + 18.5541i −0.0247388 + 0.0247388i
\(751\) 539.408i 0.718253i 0.933289 + 0.359126i \(0.116925\pi\)
−0.933289 + 0.359126i \(0.883075\pi\)
\(752\) 66.9403i 0.0890164i
\(753\) −504.869 + 504.869i −0.670477 + 0.670477i
\(754\) 38.7535i 0.0513972i
\(755\) −729.039 −0.965615
\(756\) −884.352 884.352i −1.16978 1.16978i
\(757\) −813.271 813.271i −1.07433 1.07433i −0.997006 0.0773282i \(-0.975361\pi\)
−0.0773282 0.997006i \(-0.524639\pi\)
\(758\) 31.8264 31.8264i 0.0419873 0.0419873i
\(759\) 230.591i 0.303809i
\(760\) 102.947i 0.135456i
\(761\) 362.515 362.515i 0.476367 0.476367i −0.427601 0.903968i \(-0.640641\pi\)
0.903968 + 0.427601i \(0.140641\pi\)
\(762\) −25.9805 −0.0340951
\(763\) −249.448 −0.326930
\(764\) 607.087i 0.794617i
\(765\) 494.745i 0.646725i
\(766\) 1.36353 0.00178007
\(767\) −334.912 + 334.912i −0.436651 + 0.436651i
\(768\) 397.335 397.335i 0.517363 0.517363i
\(769\) 256.078 0.333001 0.166501 0.986041i \(-0.446753\pi\)
0.166501 + 0.986041i \(0.446753\pi\)
\(770\) 17.2001 17.2001i 0.0223378 0.0223378i
\(771\) 371.368 371.368i 0.481671 0.481671i
\(772\) 1168.46i 1.51355i
\(773\) 1257.80 1.62717 0.813584 0.581447i \(-0.197513\pi\)
0.813584 + 0.581447i \(0.197513\pi\)
\(774\) −19.3693 + 19.3693i −0.0250250 + 0.0250250i