Properties

Label 197.3.c.a.14.5
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 14.5
Character \(\chi\) \(=\) 197.14
Dual form 197.3.c.a.183.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.07857 + 2.07857i) q^{2} +(3.03733 - 3.03733i) q^{3} -4.64088i q^{4} +(-3.00380 + 3.00380i) q^{5} +12.6266i q^{6} +7.49199i q^{7} +(1.33210 + 1.33210i) q^{8} -9.45073i q^{9} +O(q^{10})\) \(q+(-2.07857 + 2.07857i) q^{2} +(3.03733 - 3.03733i) q^{3} -4.64088i q^{4} +(-3.00380 + 3.00380i) q^{5} +12.6266i q^{6} +7.49199i q^{7} +(1.33210 + 1.33210i) q^{8} -9.45073i q^{9} -12.4872i q^{10} +(6.13923 - 6.13923i) q^{11} +(-14.0959 - 14.0959i) q^{12} +(-17.5286 + 17.5286i) q^{13} +(-15.5726 - 15.5726i) q^{14} +18.2471i q^{15} +13.0258 q^{16} +(21.5727 + 21.5727i) q^{17} +(19.6440 + 19.6440i) q^{18} +7.26047i q^{19} +(13.9403 + 13.9403i) q^{20} +(22.7556 + 22.7556i) q^{21} +25.5216i q^{22} -34.1557 q^{23} +8.09207 q^{24} +6.95434i q^{25} -72.8687i q^{26} +(-1.36903 - 1.36903i) q^{27} +34.7694 q^{28} +28.8625 q^{29} +(-37.9278 - 37.9278i) q^{30} +(-13.7496 + 13.7496i) q^{31} +(-32.4033 + 32.4033i) q^{32} -37.2937i q^{33} -89.6807 q^{34} +(-22.5045 - 22.5045i) q^{35} -43.8597 q^{36} -31.4783 q^{37} +(-15.0914 - 15.0914i) q^{38} +106.480i q^{39} -8.00275 q^{40} -64.9382i q^{41} -94.5983 q^{42} +45.8464i q^{43} +(-28.4914 - 28.4914i) q^{44} +(28.3881 + 28.3881i) q^{45} +(70.9948 - 70.9948i) q^{46} -30.0693i q^{47} +(39.5636 - 39.5636i) q^{48} -7.12997 q^{49} +(-14.4550 - 14.4550i) q^{50} +131.047 q^{51} +(81.3481 + 81.3481i) q^{52} +70.8242 q^{53} +5.69123 q^{54} +36.8821i q^{55} +(-9.98011 + 9.98011i) q^{56} +(22.0524 + 22.0524i) q^{57} +(-59.9926 + 59.9926i) q^{58} -99.2741 q^{59} +84.6824 q^{60} +40.5350 q^{61} -57.1588i q^{62} +70.8048 q^{63} -82.6019i q^{64} -105.305i q^{65} +(77.5175 + 77.5175i) q^{66} +(-11.5282 + 11.5282i) q^{67} +(100.116 - 100.116i) q^{68} +(-103.742 + 103.742i) q^{69} +93.5541 q^{70} +(16.8818 + 16.8818i) q^{71} +(12.5894 - 12.5894i) q^{72} +(34.9003 - 34.9003i) q^{73} +(65.4298 - 65.4298i) q^{74} +(21.1226 + 21.1226i) q^{75} +33.6949 q^{76} +(45.9951 + 45.9951i) q^{77} +(-221.326 - 221.326i) q^{78} +(-10.5741 - 10.5741i) q^{79} +(-39.1269 + 39.1269i) q^{80} +76.7402 q^{81} +(134.978 + 134.978i) q^{82} -109.901i q^{83} +(105.606 - 105.606i) q^{84} -129.600 q^{85} +(-95.2948 - 95.2948i) q^{86} +(87.6648 - 87.6648i) q^{87} +16.3562 q^{88} +(76.2349 + 76.2349i) q^{89} -118.013 q^{90} +(-131.324 - 131.324i) q^{91} +158.512i q^{92} +83.5239i q^{93} +(62.5010 + 62.5010i) q^{94} +(-21.8090 - 21.8090i) q^{95} +196.839i q^{96} -60.2020i q^{97} +(14.8201 - 14.8201i) q^{98} +(-58.0202 - 58.0202i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.07857 + 2.07857i −1.03928 + 1.03928i −0.0400870 + 0.999196i \(0.512763\pi\)
−0.999196 + 0.0400870i \(0.987237\pi\)
\(3\) 3.03733 3.03733i 1.01244 1.01244i 0.0125214 0.999922i \(-0.496014\pi\)
0.999922 0.0125214i \(-0.00398578\pi\)
\(4\) 4.64088i 1.16022i
\(5\) −3.00380 + 3.00380i −0.600761 + 0.600761i −0.940514 0.339754i \(-0.889656\pi\)
0.339754 + 0.940514i \(0.389656\pi\)
\(6\) 12.6266i 2.10443i
\(7\) 7.49199i 1.07028i 0.844762 + 0.535142i \(0.179742\pi\)
−0.844762 + 0.535142i \(0.820258\pi\)
\(8\) 1.33210 + 1.33210i 0.166513 + 0.166513i
\(9\) 9.45073i 1.05008i
\(10\) 12.4872i 1.24872i
\(11\) 6.13923 6.13923i 0.558112 0.558112i −0.370658 0.928770i \(-0.620868\pi\)
0.928770 + 0.370658i \(0.120868\pi\)
\(12\) −14.0959 14.0959i −1.17466 1.17466i
\(13\) −17.5286 + 17.5286i −1.34835 + 1.34835i −0.460903 + 0.887450i \(0.652475\pi\)
−0.887450 + 0.460903i \(0.847525\pi\)
\(14\) −15.5726 15.5726i −1.11233 1.11233i
\(15\) 18.2471i 1.21647i
\(16\) 13.0258 0.814111
\(17\) 21.5727 + 21.5727i 1.26898 + 1.26898i 0.946613 + 0.322371i \(0.104480\pi\)
0.322371 + 0.946613i \(0.395520\pi\)
\(18\) 19.6440 + 19.6440i 1.09133 + 1.09133i
\(19\) 7.26047i 0.382130i 0.981577 + 0.191065i \(0.0611941\pi\)
−0.981577 + 0.191065i \(0.938806\pi\)
\(20\) 13.9403 + 13.9403i 0.697014 + 0.697014i
\(21\) 22.7556 + 22.7556i 1.08360 + 1.08360i
\(22\) 25.5216i 1.16007i
\(23\) −34.1557 −1.48503 −0.742515 0.669830i \(-0.766367\pi\)
−0.742515 + 0.669830i \(0.766367\pi\)
\(24\) 8.09207 0.337170
\(25\) 6.95434i 0.278173i
\(26\) 72.8687i 2.80264i
\(27\) −1.36903 1.36903i −0.0507047 0.0507047i
\(28\) 34.7694 1.24176
\(29\) 28.8625 0.995258 0.497629 0.867390i \(-0.334204\pi\)
0.497629 + 0.867390i \(0.334204\pi\)
\(30\) −37.9278 37.9278i −1.26426 1.26426i
\(31\) −13.7496 + 13.7496i −0.443535 + 0.443535i −0.893198 0.449663i \(-0.851544\pi\)
0.449663 + 0.893198i \(0.351544\pi\)
\(32\) −32.4033 + 32.4033i −1.01260 + 1.01260i
\(33\) 37.2937i 1.13011i
\(34\) −89.6807 −2.63767
\(35\) −22.5045 22.5045i −0.642985 0.642985i
\(36\) −43.8597 −1.21832
\(37\) −31.4783 −0.850765 −0.425383 0.905014i \(-0.639861\pi\)
−0.425383 + 0.905014i \(0.639861\pi\)
\(38\) −15.0914 15.0914i −0.397141 0.397141i
\(39\) 106.480i 2.73026i
\(40\) −8.00275 −0.200069
\(41\) 64.9382i 1.58386i −0.610613 0.791929i \(-0.709077\pi\)
0.610613 0.791929i \(-0.290923\pi\)
\(42\) −94.5983 −2.25234
\(43\) 45.8464i 1.06620i 0.846054 + 0.533098i \(0.178972\pi\)
−0.846054 + 0.533098i \(0.821028\pi\)
\(44\) −28.4914 28.4914i −0.647532 0.647532i
\(45\) 28.3881 + 28.3881i 0.630848 + 0.630848i
\(46\) 70.9948 70.9948i 1.54337 1.54337i
\(47\) 30.0693i 0.639772i −0.947456 0.319886i \(-0.896355\pi\)
0.947456 0.319886i \(-0.103645\pi\)
\(48\) 39.5636 39.5636i 0.824241 0.824241i
\(49\) −7.12997 −0.145510
\(50\) −14.4550 14.4550i −0.289101 0.289101i
\(51\) 131.047 2.56955
\(52\) 81.3481 + 81.3481i 1.56439 + 1.56439i
\(53\) 70.8242 1.33631 0.668153 0.744024i \(-0.267085\pi\)
0.668153 + 0.744024i \(0.267085\pi\)
\(54\) 5.69123 0.105393
\(55\) 36.8821i 0.670583i
\(56\) −9.98011 + 9.98011i −0.178216 + 0.178216i
\(57\) 22.0524 + 22.0524i 0.386885 + 0.386885i
\(58\) −59.9926 + 59.9926i −1.03435 + 1.03435i
\(59\) −99.2741 −1.68261 −0.841306 0.540559i \(-0.818213\pi\)
−0.841306 + 0.540559i \(0.818213\pi\)
\(60\) 84.6824 1.41137
\(61\) 40.5350 0.664509 0.332254 0.943190i \(-0.392191\pi\)
0.332254 + 0.943190i \(0.392191\pi\)
\(62\) 57.1588i 0.921916i
\(63\) 70.8048 1.12389
\(64\) 82.6019i 1.29066i
\(65\) 105.305i 1.62008i
\(66\) 77.5175 + 77.5175i 1.17451 + 1.17451i
\(67\) −11.5282 + 11.5282i −0.172063 + 0.172063i −0.787885 0.615822i \(-0.788824\pi\)
0.615822 + 0.787885i \(0.288824\pi\)
\(68\) 100.116 100.116i 1.47230 1.47230i
\(69\) −103.742 + 103.742i −1.50351 + 1.50351i
\(70\) 93.5541 1.33649
\(71\) 16.8818 + 16.8818i 0.237771 + 0.237771i 0.815927 0.578155i \(-0.196227\pi\)
−0.578155 + 0.815927i \(0.696227\pi\)
\(72\) 12.5894 12.5894i 0.174852 0.174852i
\(73\) 34.9003 34.9003i 0.478087 0.478087i −0.426433 0.904519i \(-0.640230\pi\)
0.904519 + 0.426433i \(0.140230\pi\)
\(74\) 65.4298 65.4298i 0.884186 0.884186i
\(75\) 21.1226 + 21.1226i 0.281635 + 0.281635i
\(76\) 33.6949 0.443354
\(77\) 45.9951 + 45.9951i 0.597339 + 0.597339i
\(78\) −221.326 221.326i −2.83752 2.83752i
\(79\) −10.5741 10.5741i −0.133849 0.133849i 0.637008 0.770857i \(-0.280172\pi\)
−0.770857 + 0.637008i \(0.780172\pi\)
\(80\) −39.1269 + 39.1269i −0.489086 + 0.489086i
\(81\) 76.7402 0.947410
\(82\) 134.978 + 134.978i 1.64608 + 1.64608i
\(83\) 109.901i 1.32411i −0.749454 0.662056i \(-0.769684\pi\)
0.749454 0.662056i \(-0.230316\pi\)
\(84\) 105.606 105.606i 1.25722 1.25722i
\(85\) −129.600 −1.52471
\(86\) −95.2948 95.2948i −1.10808 1.10808i
\(87\) 87.6648 87.6648i 1.00764 1.00764i
\(88\) 16.3562 0.185866
\(89\) 76.2349 + 76.2349i 0.856572 + 0.856572i 0.990933 0.134360i \(-0.0428979\pi\)
−0.134360 + 0.990933i \(0.542898\pi\)
\(90\) −118.013 −1.31126
\(91\) −131.324 131.324i −1.44312 1.44312i
\(92\) 158.512i 1.72296i
\(93\) 83.5239i 0.898107i
\(94\) 62.5010 + 62.5010i 0.664905 + 0.664905i
\(95\) −21.8090 21.8090i −0.229569 0.229569i
\(96\) 196.839i 2.05041i
\(97\) 60.2020i 0.620639i −0.950632 0.310320i \(-0.899564\pi\)
0.950632 0.310320i \(-0.100436\pi\)
\(98\) 14.8201 14.8201i 0.151226 0.151226i
\(99\) −58.0202 58.0202i −0.586063 0.586063i
\(100\) 32.2742 0.322742
\(101\) 91.8868 0.909771 0.454885 0.890550i \(-0.349680\pi\)
0.454885 + 0.890550i \(0.349680\pi\)
\(102\) −272.390 + 272.390i −2.67049 + 2.67049i
\(103\) 62.2623 62.2623i 0.604489 0.604489i −0.337012 0.941500i \(-0.609416\pi\)
0.941500 + 0.337012i \(0.109416\pi\)
\(104\) −46.6998 −0.449037
\(105\) −136.707 −1.30197
\(106\) −147.213 + 147.213i −1.38880 + 1.38880i
\(107\) 83.3414i 0.778892i −0.921049 0.389446i \(-0.872666\pi\)
0.921049 0.389446i \(-0.127334\pi\)
\(108\) −6.35349 + 6.35349i −0.0588286 + 0.0588286i
\(109\) 36.2540i 0.332606i −0.986075 0.166303i \(-0.946817\pi\)
0.986075 0.166303i \(-0.0531829\pi\)
\(110\) −76.6618 76.6618i −0.696926 0.696926i
\(111\) −95.6100 + 95.6100i −0.861352 + 0.861352i
\(112\) 97.5890i 0.871330i
\(113\) −11.5798 11.5798i −0.102476 0.102476i 0.654010 0.756486i \(-0.273086\pi\)
−0.756486 + 0.654010i \(0.773086\pi\)
\(114\) −91.6749 −0.804166
\(115\) 102.597 102.597i 0.892147 0.892147i
\(116\) 133.947i 1.15472i
\(117\) 165.658 + 165.658i 1.41588 + 1.41588i
\(118\) 206.348 206.348i 1.74871 1.74871i
\(119\) −161.623 + 161.623i −1.35817 + 1.35817i
\(120\) −24.3070 + 24.3070i −0.202558 + 0.202558i
\(121\) 45.6197i 0.377022i
\(122\) −84.2547 + 84.2547i −0.690613 + 0.690613i
\(123\) −197.239 197.239i −1.60357 1.60357i
\(124\) 63.8101 + 63.8101i 0.514597 + 0.514597i
\(125\) −95.9845 95.9845i −0.767876 0.767876i
\(126\) −147.173 + 147.173i −1.16804 + 1.16804i
\(127\) 7.11537i 0.0560265i 0.999608 + 0.0280133i \(0.00891806\pi\)
−0.999608 + 0.0280133i \(0.991082\pi\)
\(128\) 42.0802 + 42.0802i 0.328751 + 0.328751i
\(129\) 139.251 + 139.251i 1.07946 + 1.07946i
\(130\) 218.883 + 218.883i 1.68372 + 1.68372i
\(131\) 25.0179 25.0179i 0.190976 0.190976i −0.605142 0.796118i \(-0.706884\pi\)
0.796118 + 0.605142i \(0.206884\pi\)
\(132\) −173.076 −1.31118
\(133\) −54.3954 −0.408988
\(134\) 47.9244i 0.357644i
\(135\) 8.22458 0.0609228
\(136\) 57.4742i 0.422605i
\(137\) 101.198i 0.738672i 0.929296 + 0.369336i \(0.120415\pi\)
−0.929296 + 0.369336i \(0.879585\pi\)
\(138\) 431.269i 3.12514i
\(139\) −6.07892 6.07892i −0.0437332 0.0437332i 0.684902 0.728635i \(-0.259845\pi\)
−0.728635 + 0.684902i \(0.759845\pi\)
\(140\) −104.440 + 104.440i −0.746003 + 0.746003i
\(141\) −91.3304 91.3304i −0.647733 0.647733i
\(142\) −70.1797 −0.494224
\(143\) 215.224i 1.50506i
\(144\) 123.103i 0.854883i
\(145\) −86.6972 + 86.6972i −0.597912 + 0.597912i
\(146\) 145.085i 0.993735i
\(147\) −21.6561 + 21.6561i −0.147320 + 0.147320i
\(148\) 146.087i 0.987074i
\(149\) −2.99499 2.99499i −0.0201006 0.0201006i 0.696985 0.717086i \(-0.254524\pi\)
−0.717086 + 0.696985i \(0.754524\pi\)
\(150\) −87.8095 −0.585397
\(151\) 43.7021 + 43.7021i 0.289418 + 0.289418i 0.836850 0.547432i \(-0.184395\pi\)
−0.547432 + 0.836850i \(0.684395\pi\)
\(152\) −9.67170 + 9.67170i −0.0636296 + 0.0636296i
\(153\) 203.878 203.878i 1.33254 1.33254i
\(154\) −191.208 −1.24161
\(155\) 82.6020i 0.532916i
\(156\) 494.162 3.16770
\(157\) 63.5874i 0.405015i −0.979281 0.202508i \(-0.935091\pi\)
0.979281 0.202508i \(-0.0649091\pi\)
\(158\) 43.9578 0.278214
\(159\) 215.117 215.117i 1.35293 1.35293i
\(160\) 194.667i 1.21667i
\(161\) 255.894i 1.58940i
\(162\) −159.510 + 159.510i −0.984628 + 0.984628i
\(163\) 237.606i 1.45770i 0.684671 + 0.728852i \(0.259946\pi\)
−0.684671 + 0.728852i \(0.740054\pi\)
\(164\) −301.370 −1.83762
\(165\) 112.023 + 112.023i 0.678927 + 0.678927i
\(166\) 228.437 + 228.437i 1.37613 + 1.37613i
\(167\) −45.3411 + 45.3411i −0.271504 + 0.271504i −0.829705 0.558202i \(-0.811492\pi\)
0.558202 + 0.829705i \(0.311492\pi\)
\(168\) 60.6257i 0.360868i
\(169\) 445.504i 2.63612i
\(170\) 269.383 269.383i 1.58461 1.58461i
\(171\) 68.6168 0.401268
\(172\) 212.767 1.23702
\(173\) 283.952i 1.64134i 0.571403 + 0.820669i \(0.306399\pi\)
−0.571403 + 0.820669i \(0.693601\pi\)
\(174\) 364.434i 2.09445i
\(175\) −52.1018 −0.297725
\(176\) 79.9682 79.9682i 0.454365 0.454365i
\(177\) −301.528 + 301.528i −1.70355 + 1.70355i
\(178\) −316.919 −1.78044
\(179\) 91.1931 91.1931i 0.509459 0.509459i −0.404901 0.914360i \(-0.632694\pi\)
0.914360 + 0.404901i \(0.132694\pi\)
\(180\) 131.746 131.746i 0.731921 0.731921i
\(181\) 121.101i 0.669067i 0.942384 + 0.334533i \(0.108579\pi\)
−0.942384 + 0.334533i \(0.891421\pi\)
\(182\) 545.932 2.99963
\(183\) 123.118 123.118i 0.672777 0.672777i
\(184\) −45.4989 45.4989i −0.247277 0.247277i
\(185\) 94.5547 94.5547i 0.511106 0.511106i
\(186\) −173.610 173.610i −0.933387 0.933387i
\(187\) 264.880 1.41647
\(188\) −139.548 −0.742276
\(189\) 10.2567 10.2567i 0.0542685 0.0542685i
\(190\) 90.6630 0.477174
\(191\) −297.372 −1.55692 −0.778461 0.627693i \(-0.783999\pi\)
−0.778461 + 0.627693i \(0.783999\pi\)
\(192\) −250.889 250.889i −1.30671 1.30671i
\(193\) 275.984 1.42997 0.714984 0.699141i \(-0.246434\pi\)
0.714984 + 0.699141i \(0.246434\pi\)
\(194\) 125.134 + 125.134i 0.645020 + 0.645020i
\(195\) −319.846 319.846i −1.64023 1.64023i
\(196\) 33.0893i 0.168823i
\(197\) −14.5199 + 196.464i −0.0737052 + 0.997280i
\(198\) 241.198 1.21817
\(199\) 96.4865 96.4865i 0.484857 0.484857i −0.421822 0.906679i \(-0.638609\pi\)
0.906679 + 0.421822i \(0.138609\pi\)
\(200\) −9.26389 + 9.26389i −0.0463195 + 0.0463195i
\(201\) 70.0300i 0.348408i
\(202\) −190.993 + 190.993i −0.945509 + 0.945509i
\(203\) 216.237i 1.06521i
\(204\) 608.173i 2.98124i
\(205\) 195.062 + 195.062i 0.951520 + 0.951520i
\(206\) 258.833i 1.25647i
\(207\) 322.796i 1.55940i
\(208\) −228.324 + 228.324i −1.09771 + 1.09771i
\(209\) 44.5737 + 44.5737i 0.213271 + 0.213271i
\(210\) 284.154 284.154i 1.35312 1.35312i
\(211\) 33.2248 + 33.2248i 0.157464 + 0.157464i 0.781442 0.623978i \(-0.214485\pi\)
−0.623978 + 0.781442i \(0.714485\pi\)
\(212\) 328.687i 1.55041i
\(213\) 102.551 0.481460
\(214\) 173.231 + 173.231i 0.809489 + 0.809489i
\(215\) −137.714 137.714i −0.640528 0.640528i
\(216\) 3.64737i 0.0168860i
\(217\) −103.012 103.012i −0.474708 0.474708i
\(218\) 75.3564 + 75.3564i 0.345671 + 0.345671i
\(219\) 212.008i 0.968071i
\(220\) 171.165 0.778023
\(221\) −756.280 −3.42208
\(222\) 397.464i 1.79038i
\(223\) 85.9628i 0.385483i −0.981250 0.192742i \(-0.938262\pi\)
0.981250 0.192742i \(-0.0617379\pi\)
\(224\) −242.766 242.766i −1.08378 1.08378i
\(225\) 65.7236 0.292105
\(226\) 48.1389 0.213004
\(227\) 221.214 + 221.214i 0.974512 + 0.974512i 0.999683 0.0251710i \(-0.00801303\pi\)
−0.0251710 + 0.999683i \(0.508013\pi\)
\(228\) 102.343 102.343i 0.448871 0.448871i
\(229\) −87.0630 + 87.0630i −0.380188 + 0.380188i −0.871170 0.490982i \(-0.836638\pi\)
0.490982 + 0.871170i \(0.336638\pi\)
\(230\) 426.509i 1.85439i
\(231\) 279.404 1.20954
\(232\) 38.4478 + 38.4478i 0.165723 + 0.165723i
\(233\) −334.722 −1.43657 −0.718287 0.695747i \(-0.755073\pi\)
−0.718287 + 0.695747i \(0.755073\pi\)
\(234\) −688.663 −2.94300
\(235\) 90.3223 + 90.3223i 0.384350 + 0.384350i
\(236\) 460.719i 1.95220i
\(237\) −64.2338 −0.271029
\(238\) 671.887i 2.82306i
\(239\) −41.5641 −0.173909 −0.0869543 0.996212i \(-0.527713\pi\)
−0.0869543 + 0.996212i \(0.527713\pi\)
\(240\) 237.682i 0.990343i
\(241\) 56.6293 + 56.6293i 0.234976 + 0.234976i 0.814766 0.579790i \(-0.196865\pi\)
−0.579790 + 0.814766i \(0.696865\pi\)
\(242\) −94.8236 94.8236i −0.391833 0.391833i
\(243\) 245.407 245.407i 1.00990 1.00990i
\(244\) 188.118i 0.770975i
\(245\) 21.4170 21.4170i 0.0874164 0.0874164i
\(246\) 819.947 3.33312
\(247\) −127.266 127.266i −0.515246 0.515246i
\(248\) −36.6317 −0.147708
\(249\) −333.807 333.807i −1.34059 1.34059i
\(250\) 399.020 1.59608
\(251\) −370.912 −1.47774 −0.738869 0.673849i \(-0.764640\pi\)
−0.738869 + 0.673849i \(0.764640\pi\)
\(252\) 328.596i 1.30395i
\(253\) −209.690 + 209.690i −0.828812 + 0.828812i
\(254\) −14.7898 14.7898i −0.0582274 0.0582274i
\(255\) −393.639 + 393.639i −1.54368 + 1.54368i
\(256\) 155.475 0.607323
\(257\) 223.521 0.869733 0.434867 0.900495i \(-0.356795\pi\)
0.434867 + 0.900495i \(0.356795\pi\)
\(258\) −578.883 −2.24373
\(259\) 235.835i 0.910561i
\(260\) −488.707 −1.87964
\(261\) 272.772i 1.04510i
\(262\) 104.003i 0.396956i
\(263\) 236.816 + 236.816i 0.900443 + 0.900443i 0.995474 0.0950316i \(-0.0302952\pi\)
−0.0950316 + 0.995474i \(0.530295\pi\)
\(264\) 49.6791 49.6791i 0.188178 0.188178i
\(265\) −212.742 + 212.742i −0.802800 + 0.802800i
\(266\) 113.064 113.064i 0.425054 0.425054i
\(267\) 463.101 1.73446
\(268\) 53.5011 + 53.5011i 0.199631 + 0.199631i
\(269\) −35.0061 + 35.0061i −0.130134 + 0.130134i −0.769174 0.639040i \(-0.779332\pi\)
0.639040 + 0.769174i \(0.279332\pi\)
\(270\) −17.0953 + 17.0953i −0.0633161 + 0.0633161i
\(271\) 55.3193 55.3193i 0.204130 0.204130i −0.597637 0.801767i \(-0.703893\pi\)
0.801767 + 0.597637i \(0.203893\pi\)
\(272\) 281.002 + 281.002i 1.03309 + 1.03309i
\(273\) −797.749 −2.92216
\(274\) −210.347 210.347i −0.767689 0.767689i
\(275\) 42.6943 + 42.6943i 0.155252 + 0.155252i
\(276\) 481.454 + 481.454i 1.74440 + 1.74440i
\(277\) −367.087 + 367.087i −1.32523 + 1.32523i −0.415743 + 0.909482i \(0.636479\pi\)
−0.909482 + 0.415743i \(0.863521\pi\)
\(278\) 25.2709 0.0909024
\(279\) 129.944 + 129.944i 0.465748 + 0.465748i
\(280\) 59.9566i 0.214131i
\(281\) 331.815 331.815i 1.18084 1.18084i 0.201310 0.979528i \(-0.435480\pi\)
0.979528 0.201310i \(-0.0645199\pi\)
\(282\) 379.672 1.34636
\(283\) 80.4176 + 80.4176i 0.284161 + 0.284161i 0.834766 0.550605i \(-0.185603\pi\)
−0.550605 + 0.834766i \(0.685603\pi\)
\(284\) 78.3462 78.3462i 0.275867 0.275867i
\(285\) −132.482 −0.464850
\(286\) −447.358 447.358i −1.56419 1.56419i
\(287\) 486.517 1.69518
\(288\) 306.235 + 306.235i 1.06332 + 1.06332i
\(289\) 641.766i 2.22064i
\(290\) 360.412i 1.24280i
\(291\) −182.853 182.853i −0.628362 0.628362i
\(292\) −161.968 161.968i −0.554685 0.554685i
\(293\) 113.035i 0.385786i 0.981220 + 0.192893i \(0.0617870\pi\)
−0.981220 + 0.192893i \(0.938213\pi\)
\(294\) 90.0271i 0.306215i
\(295\) 298.200 298.200i 1.01085 1.01085i
\(296\) −41.9324 41.9324i −0.141663 0.141663i
\(297\) −16.8096 −0.0565978
\(298\) 12.4506 0.0417804
\(299\) 598.701 598.701i 2.00234 2.00234i
\(300\) 98.0274 98.0274i 0.326758 0.326758i
\(301\) −343.481 −1.14113
\(302\) −181.675 −0.601574
\(303\) 279.091 279.091i 0.921091 0.921091i
\(304\) 94.5732i 0.311096i
\(305\) −121.759 + 121.759i −0.399211 + 0.399211i
\(306\) 847.549i 2.76977i
\(307\) −290.660 290.660i −0.946775 0.946775i 0.0518785 0.998653i \(-0.483479\pi\)
−0.998653 + 0.0518785i \(0.983479\pi\)
\(308\) 213.457 213.457i 0.693044 0.693044i
\(309\) 378.222i 1.22402i
\(310\) 171.694 + 171.694i 0.553851 + 0.553851i
\(311\) 242.419 0.779484 0.389742 0.920924i \(-0.372564\pi\)
0.389742 + 0.920924i \(0.372564\pi\)
\(312\) −141.843 + 141.843i −0.454624 + 0.454624i
\(313\) 127.668i 0.407884i −0.978983 0.203942i \(-0.934625\pi\)
0.978983 0.203942i \(-0.0653754\pi\)
\(314\) 132.171 + 132.171i 0.420925 + 0.420925i
\(315\) −212.684 + 212.684i −0.675187 + 0.675187i
\(316\) −49.0729 + 49.0729i −0.155294 + 0.155294i
\(317\) 299.989 299.989i 0.946339 0.946339i −0.0522932 0.998632i \(-0.516653\pi\)
0.998632 + 0.0522932i \(0.0166530\pi\)
\(318\) 894.268i 2.81216i
\(319\) 177.193 177.193i 0.555465 0.555465i
\(320\) 248.120 + 248.120i 0.775375 + 0.775375i
\(321\) −253.135 253.135i −0.788584 0.788584i
\(322\) 531.893 + 531.893i 1.65184 + 1.65184i
\(323\) −156.628 + 156.628i −0.484917 + 0.484917i
\(324\) 356.142i 1.09920i
\(325\) −121.900 121.900i −0.375076 0.375076i
\(326\) −493.879 493.879i −1.51497 1.51497i
\(327\) −110.115 110.115i −0.336744 0.336744i
\(328\) 86.5044 86.5044i 0.263733 0.263733i
\(329\) 225.279 0.684739
\(330\) −465.694 −1.41120
\(331\) 262.561i 0.793237i 0.917984 + 0.396618i \(0.129816\pi\)
−0.917984 + 0.396618i \(0.870184\pi\)
\(332\) −510.039 −1.53626
\(333\) 297.493i 0.893373i
\(334\) 188.489i 0.564338i
\(335\) 69.2570i 0.206737i
\(336\) 296.410 + 296.410i 0.882172 + 0.882172i
\(337\) −83.0734 + 83.0734i −0.246509 + 0.246509i −0.819536 0.573027i \(-0.805769\pi\)
0.573027 + 0.819536i \(0.305769\pi\)
\(338\) 926.009 + 926.009i 2.73967 + 2.73967i
\(339\) −70.3435 −0.207503
\(340\) 601.460i 1.76900i
\(341\) 168.824i 0.495084i
\(342\) −142.625 + 142.625i −0.417031 + 0.417031i
\(343\) 313.690i 0.914548i
\(344\) −61.0721 + 61.0721i −0.177535 + 0.177535i
\(345\) 623.241i 1.80650i
\(346\) −590.212 590.212i −1.70582 1.70582i
\(347\) 430.991 1.24205 0.621025 0.783791i \(-0.286717\pi\)
0.621025 + 0.783791i \(0.286717\pi\)
\(348\) −406.842 406.842i −1.16908 1.16908i
\(349\) 55.6315 55.6315i 0.159402 0.159402i −0.622899 0.782302i \(-0.714045\pi\)
0.782302 + 0.622899i \(0.214045\pi\)
\(350\) 108.297 108.297i 0.309420 0.309420i
\(351\) 47.9943 0.136736
\(352\) 397.863i 1.13029i
\(353\) 188.069 0.532773 0.266386 0.963866i \(-0.414170\pi\)
0.266386 + 0.963866i \(0.414170\pi\)
\(354\) 1253.49i 3.54094i
\(355\) −101.419 −0.285687
\(356\) 353.797 353.797i 0.993812 0.993812i
\(357\) 981.803i 2.75015i
\(358\) 379.102i 1.05894i
\(359\) 435.070 435.070i 1.21189 1.21189i 0.241489 0.970403i \(-0.422364\pi\)
0.970403 0.241489i \(-0.0776359\pi\)
\(360\) 75.6319i 0.210089i
\(361\) 308.286 0.853977
\(362\) −251.717 251.717i −0.695350 0.695350i
\(363\) 138.562 + 138.562i 0.381714 + 0.381714i
\(364\) −609.459 + 609.459i −1.67434 + 1.67434i
\(365\) 209.667i 0.574431i
\(366\) 511.819i 1.39841i
\(367\) 227.135 227.135i 0.618895 0.618895i −0.326353 0.945248i \(-0.605820\pi\)
0.945248 + 0.326353i \(0.105820\pi\)
\(368\) −444.904 −1.20898
\(369\) −613.714 −1.66318
\(370\) 393.076i 1.06237i
\(371\) 530.615i 1.43023i
\(372\) 387.624 1.04200
\(373\) 414.029 414.029i 1.11000 1.11000i 0.116848 0.993150i \(-0.462721\pi\)
0.993150 0.116848i \(-0.0372790\pi\)
\(374\) −550.571 + 550.571i −1.47211 + 1.47211i
\(375\) −583.073 −1.55486
\(376\) 40.0554 40.0554i 0.106530 0.106530i
\(377\) −505.919 + 505.919i −1.34196 + 1.34196i
\(378\) 42.6387i 0.112801i
\(379\) −288.367 −0.760863 −0.380432 0.924809i \(-0.624225\pi\)
−0.380432 + 0.924809i \(0.624225\pi\)
\(380\) −101.213 + 101.213i −0.266350 + 0.266350i
\(381\) 21.6117 + 21.6117i 0.0567236 + 0.0567236i
\(382\) 618.108 618.108i 1.61808 1.61808i
\(383\) −164.804 164.804i −0.430297 0.430297i 0.458432 0.888729i \(-0.348411\pi\)
−0.888729 + 0.458432i \(0.848411\pi\)
\(384\) 255.623 0.665684
\(385\) −276.320 −0.717715
\(386\) −573.650 + 573.650i −1.48614 + 1.48614i
\(387\) 433.282 1.11959
\(388\) −279.390 −0.720078
\(389\) −115.237 115.237i −0.296239 0.296239i 0.543300 0.839539i \(-0.317175\pi\)
−0.839539 + 0.543300i \(0.817175\pi\)
\(390\) 1329.64 3.40934
\(391\) −736.831 736.831i −1.88448 1.88448i
\(392\) −9.49785 9.49785i −0.0242292 0.0242292i
\(393\) 151.975i 0.386705i
\(394\) −378.183 438.544i −0.959856 1.11306i
\(395\) 63.5248 0.160822
\(396\) −269.265 + 269.265i −0.679961 + 0.679961i
\(397\) 234.751 234.751i 0.591311 0.591311i −0.346674 0.937986i \(-0.612689\pi\)
0.937986 + 0.346674i \(0.112689\pi\)
\(398\) 401.107i 1.00781i
\(399\) −165.217 + 165.217i −0.414077 + 0.414077i
\(400\) 90.5856i 0.226464i
\(401\) 7.18407i 0.0179154i −0.999960 0.00895769i \(-0.997149\pi\)
0.999960 0.00895769i \(-0.00285136\pi\)
\(402\) −145.562 145.562i −0.362095 0.362095i
\(403\) 482.021i 1.19608i
\(404\) 426.435i 1.05553i
\(405\) −230.513 + 230.513i −0.569167 + 0.569167i
\(406\) −449.464 449.464i −1.10705 1.10705i
\(407\) −193.253 + 193.253i −0.474822 + 0.474822i
\(408\) 174.568 + 174.568i 0.427863 + 0.427863i
\(409\) 517.420i 1.26509i −0.774526 0.632543i \(-0.782011\pi\)
0.774526 0.632543i \(-0.217989\pi\)
\(410\) −810.897 −1.97780
\(411\) 307.372 + 307.372i 0.747863 + 0.747863i
\(412\) −288.952 288.952i −0.701339 0.701339i
\(413\) 743.761i 1.80087i
\(414\) −670.953 670.953i −1.62066 1.62066i
\(415\) 330.122 + 330.122i 0.795475 + 0.795475i
\(416\) 1135.97i 2.73070i
\(417\) −36.9273 −0.0885548
\(418\) −185.299 −0.443298
\(419\) 5.11987i 0.0122193i −0.999981 0.00610963i \(-0.998055\pi\)
0.999981 0.00610963i \(-0.00194477\pi\)
\(420\) 634.440i 1.51057i
\(421\) 429.558 + 429.558i 1.02033 + 1.02033i 0.999789 + 0.0205384i \(0.00653803\pi\)
0.0205384 + 0.999789i \(0.493462\pi\)
\(422\) −138.120 −0.327299
\(423\) −284.177 −0.671813
\(424\) 94.3452 + 94.3452i 0.222512 + 0.222512i
\(425\) −150.024 + 150.024i −0.352998 + 0.352998i
\(426\) −213.159 + 213.159i −0.500373 + 0.500373i
\(427\) 303.688i 0.711213i
\(428\) −386.777 −0.903685
\(429\) 653.707 + 653.707i 1.52379 + 1.52379i
\(430\) 572.494 1.33138
\(431\) 297.003 0.689102 0.344551 0.938768i \(-0.388031\pi\)
0.344551 + 0.938768i \(0.388031\pi\)
\(432\) −17.8326 17.8326i −0.0412793 0.0412793i
\(433\) 829.652i 1.91605i 0.286677 + 0.958027i \(0.407449\pi\)
−0.286677 + 0.958027i \(0.592551\pi\)
\(434\) 428.233 0.986713
\(435\) 526.656i 1.21070i
\(436\) −168.250 −0.385895
\(437\) 247.986i 0.567474i
\(438\) 440.672 + 440.672i 1.00610 + 1.00610i
\(439\) 40.8351 + 40.8351i 0.0930184 + 0.0930184i 0.752085 0.659066i \(-0.229048\pi\)
−0.659066 + 0.752085i \(0.729048\pi\)
\(440\) −49.1307 + 49.1307i −0.111661 + 0.111661i
\(441\) 67.3834i 0.152797i
\(442\) 1571.98 1571.98i 3.55651 3.55651i
\(443\) −131.765 −0.297438 −0.148719 0.988879i \(-0.547515\pi\)
−0.148719 + 0.988879i \(0.547515\pi\)
\(444\) 443.714 + 443.714i 0.999356 + 0.999356i
\(445\) −457.990 −1.02919
\(446\) 178.679 + 178.679i 0.400626 + 0.400626i
\(447\) −18.1935 −0.0407014
\(448\) 618.853 1.38137
\(449\) 0.494078i 0.00110040i 1.00000 0.000550198i \(0.000175133\pi\)
−1.00000 0.000550198i \(0.999825\pi\)
\(450\) −136.611 + 136.611i −0.303580 + 0.303580i
\(451\) −398.671 398.671i −0.883970 0.883970i
\(452\) −53.7406 + 53.7406i −0.118895 + 0.118895i
\(453\) 265.475 0.586038
\(454\) −919.617 −2.02559
\(455\) 788.944 1.73394
\(456\) 58.7522i 0.128843i
\(457\) −411.956 −0.901436 −0.450718 0.892666i \(-0.648832\pi\)
−0.450718 + 0.892666i \(0.648832\pi\)
\(458\) 361.933i 0.790246i
\(459\) 59.0674i 0.128687i
\(460\) −476.140 476.140i −1.03509 1.03509i
\(461\) 145.926 145.926i 0.316542 0.316542i −0.530895 0.847437i \(-0.678144\pi\)
0.847437 + 0.530895i \(0.178144\pi\)
\(462\) −580.760 + 580.760i −1.25706 + 1.25706i
\(463\) 425.789 425.789i 0.919631 0.919631i −0.0773713 0.997002i \(-0.524653\pi\)
0.997002 + 0.0773713i \(0.0246527\pi\)
\(464\) 375.956 0.810250
\(465\) −250.889 250.889i −0.539547 0.539547i
\(466\) 695.741 695.741i 1.49301 1.49301i
\(467\) −499.997 + 499.997i −1.07066 + 1.07066i −0.0733515 + 0.997306i \(0.523369\pi\)
−0.997306 + 0.0733515i \(0.976631\pi\)
\(468\) 768.799 768.799i 1.64273 1.64273i
\(469\) −86.3694 86.3694i −0.184156 0.184156i
\(470\) −375.482 −0.798897
\(471\) −193.136 193.136i −0.410055 0.410055i
\(472\) −132.243 132.243i −0.280177 0.280177i
\(473\) 281.462 + 281.462i 0.595056 + 0.595056i
\(474\) 133.514 133.514i 0.281675 0.281675i
\(475\) −50.4917 −0.106298
\(476\) 750.071 + 750.071i 1.57578 + 1.57578i
\(477\) 669.341i 1.40323i
\(478\) 86.3938 86.3938i 0.180740 0.180740i
\(479\) −54.4156 −0.113602 −0.0568012 0.998386i \(-0.518090\pi\)
−0.0568012 + 0.998386i \(0.518090\pi\)
\(480\) −591.266 591.266i −1.23180 1.23180i
\(481\) 551.771 551.771i 1.14713 1.14713i
\(482\) −235.415 −0.488414
\(483\) −777.234 777.234i −1.60918 1.60918i
\(484\) 211.715 0.437429
\(485\) 180.835 + 180.835i 0.372856 + 0.372856i
\(486\) 1020.19i 2.09915i
\(487\) 170.938i 0.351001i 0.984479 + 0.175501i \(0.0561544\pi\)
−0.984479 + 0.175501i \(0.943846\pi\)
\(488\) 53.9968 + 53.9968i 0.110649 + 0.110649i
\(489\) 721.687 + 721.687i 1.47584 + 1.47584i
\(490\) 89.0334i 0.181701i
\(491\) 926.921i 1.88782i 0.330198 + 0.943912i \(0.392885\pi\)
−0.330198 + 0.943912i \(0.607115\pi\)
\(492\) −915.360 + 915.360i −1.86049 + 1.86049i
\(493\) 622.643 + 622.643i 1.26297 + 1.26297i
\(494\) 529.061 1.07097
\(495\) 348.563 0.704167
\(496\) −179.099 + 179.099i −0.361086 + 0.361086i
\(497\) −126.478 + 126.478i −0.254483 + 0.254483i
\(498\) 1387.68 2.78650
\(499\) −239.571 −0.480102 −0.240051 0.970760i \(-0.577164\pi\)
−0.240051 + 0.970760i \(0.577164\pi\)
\(500\) −445.452 + 445.452i −0.890905 + 0.890905i
\(501\) 275.432i 0.549764i
\(502\) 770.965 770.965i 1.53579 1.53579i
\(503\) 723.826i 1.43902i −0.694483 0.719509i \(-0.744367\pi\)
0.694483 0.719509i \(-0.255633\pi\)
\(504\) 94.3194 + 94.3194i 0.187142 + 0.187142i
\(505\) −276.010 + 276.010i −0.546554 + 0.546554i
\(506\) 871.707i 1.72274i
\(507\) −1353.14 1353.14i −2.66892 2.66892i
\(508\) 33.0215 0.0650030
\(509\) −0.481353 + 0.481353i −0.000945683 + 0.000945683i −0.707579 0.706634i \(-0.750213\pi\)
0.706634 + 0.707579i \(0.250213\pi\)
\(510\) 1636.41i 3.20865i
\(511\) 261.473 + 261.473i 0.511689 + 0.511689i
\(512\) −491.485 + 491.485i −0.959932 + 0.959932i
\(513\) 9.93979 9.93979i 0.0193758 0.0193758i
\(514\) −464.604 + 464.604i −0.903899 + 0.903899i
\(515\) 374.048i 0.726306i
\(516\) 646.245 646.245i 1.25241 1.25241i
\(517\) −184.602 184.602i −0.357065 0.357065i
\(518\) 490.199 + 490.199i 0.946331 + 0.946331i
\(519\) 862.454 + 862.454i 1.66176 + 1.66176i
\(520\) 140.277 140.277i 0.269763 0.269763i
\(521\) 586.451i 1.12563i −0.826584 0.562813i \(-0.809719\pi\)
0.826584 0.562813i \(-0.190281\pi\)
\(522\) 566.974 + 566.974i 1.08616 + 1.08616i
\(523\) −723.390 723.390i −1.38315 1.38315i −0.838958 0.544196i \(-0.816835\pi\)
−0.544196 0.838958i \(-0.683165\pi\)
\(524\) −116.105 116.105i −0.221574 0.221574i
\(525\) −158.250 + 158.250i −0.301429 + 0.301429i
\(526\) −984.477 −1.87163
\(527\) −593.232 −1.12568
\(528\) 485.780i 0.920037i
\(529\) 637.610 1.20531
\(530\) 884.397i 1.66867i
\(531\) 938.213i 1.76688i
\(532\) 252.442i 0.474516i
\(533\) 1138.28 + 1138.28i 2.13560 + 2.13560i
\(534\) −962.587 + 962.587i −1.80260 + 1.80260i
\(535\) 250.341 + 250.341i 0.467928 + 0.467928i
\(536\) −30.7136 −0.0573014
\(537\) 553.967i 1.03160i
\(538\) 145.525i 0.270493i
\(539\) −43.7725 + 43.7725i −0.0812106 + 0.0812106i
\(540\) 38.1693i 0.0706838i
\(541\) −164.561 + 164.561i −0.304180 + 0.304180i −0.842647 0.538467i \(-0.819004\pi\)
0.538467 + 0.842647i \(0.319004\pi\)
\(542\) 229.970i 0.424299i
\(543\) 367.824 + 367.824i 0.677392 + 0.677392i
\(544\) −1398.06 −2.56996
\(545\) 108.900 + 108.900i 0.199816 + 0.199816i
\(546\) 1658.17 1658.17i 3.03695 3.03695i
\(547\) 172.602 172.602i 0.315543 0.315543i −0.531510 0.847052i \(-0.678375\pi\)
0.847052 + 0.531510i \(0.178375\pi\)
\(548\) 469.648 0.857021
\(549\) 383.086i 0.697788i
\(550\) −177.486 −0.322701
\(551\) 209.555i 0.380318i
\(552\) −276.390 −0.500707
\(553\) 79.2208 79.2208i 0.143256 0.143256i
\(554\) 1526.03i 2.75457i
\(555\) 574.387i 1.03493i
\(556\) −28.2115 + 28.2115i −0.0507401 + 0.0507401i
\(557\) 305.484i 0.548446i −0.961666 0.274223i \(-0.911579\pi\)
0.961666 0.274223i \(-0.0884206\pi\)
\(558\) −540.193 −0.968087
\(559\) −803.623 803.623i −1.43761 1.43761i
\(560\) −293.138 293.138i −0.523461 0.523461i
\(561\) 804.528 804.528i 1.43410 1.43410i
\(562\) 1379.40i 2.45445i
\(563\) 843.323i 1.49791i −0.662621 0.748955i \(-0.730556\pi\)
0.662621 0.748955i \(-0.269444\pi\)
\(564\) −423.853 + 423.853i −0.751512 + 0.751512i
\(565\) 69.5670 0.123128
\(566\) −334.306 −0.590648
\(567\) 574.937i 1.01400i
\(568\) 44.9765i 0.0791840i
\(569\) −638.597 −1.12232 −0.561158 0.827709i \(-0.689644\pi\)
−0.561158 + 0.827709i \(0.689644\pi\)
\(570\) 275.373 275.373i 0.483111 0.483111i
\(571\) 26.5077 26.5077i 0.0464233 0.0464233i −0.683514 0.729937i \(-0.739549\pi\)
0.729937 + 0.683514i \(0.239549\pi\)
\(572\) 998.829 1.74620
\(573\) −903.217 + 903.217i −1.57630 + 1.57630i
\(574\) −1011.26 + 1011.26i −1.76177 + 1.76177i
\(575\) 237.530i 0.413096i
\(576\) −780.649 −1.35529
\(577\) 609.598 609.598i 1.05650 1.05650i 0.0581909 0.998305i \(-0.481467\pi\)
0.998305 0.0581909i \(-0.0185332\pi\)
\(578\) −1333.95 1333.95i −2.30788 2.30788i
\(579\) 838.253 838.253i 1.44776 1.44776i
\(580\) 402.351 + 402.351i 0.693708 + 0.693708i
\(581\) 823.380 1.41718
\(582\) 760.146 1.30609
\(583\) 434.806 434.806i 0.745809 0.745809i
\(584\) 92.9817 0.159215
\(585\) −995.209 −1.70121
\(586\) −234.951 234.951i −0.400941 0.400941i
\(587\) −111.031 −0.189150 −0.0945752 0.995518i \(-0.530149\pi\)
−0.0945752 + 0.995518i \(0.530149\pi\)
\(588\) 100.503 + 100.503i 0.170924 + 0.170924i
\(589\) −99.8284 99.8284i −0.169488 0.169488i
\(590\) 1239.66i 2.10111i
\(591\) 552.625 + 640.828i 0.935067 + 1.08431i
\(592\) −410.030 −0.692617
\(593\) 27.6721 27.6721i 0.0466645 0.0466645i −0.683389 0.730054i \(-0.739495\pi\)
0.730054 + 0.683389i \(0.239495\pi\)
\(594\) 34.9398 34.9398i 0.0588212 0.0588212i
\(595\) 970.966i 1.63188i
\(596\) −13.8994 + 13.8994i −0.0233211 + 0.0233211i
\(597\) 586.122i 0.981780i
\(598\) 2488.88i 4.16201i
\(599\) 471.601 + 471.601i 0.787314 + 0.787314i 0.981053 0.193739i \(-0.0620616\pi\)
−0.193739 + 0.981053i \(0.562062\pi\)
\(600\) 56.2750i 0.0937916i
\(601\) 646.144i 1.07511i 0.843227 + 0.537557i \(0.180653\pi\)
−0.843227 + 0.537557i \(0.819347\pi\)
\(602\) 713.948 713.948i 1.18596 1.18596i
\(603\) 108.950 + 108.950i 0.180680 + 0.180680i
\(604\) 202.816 202.816i 0.335788 0.335788i
\(605\) −137.033 137.033i −0.226500 0.226500i
\(606\) 1160.22i 1.91455i
\(607\) 668.000 1.10049 0.550247 0.835002i \(-0.314534\pi\)
0.550247 + 0.835002i \(0.314534\pi\)
\(608\) −235.264 235.264i −0.386947 0.386947i
\(609\) 656.784 + 656.784i 1.07846 + 1.07846i
\(610\) 506.169i 0.829786i
\(611\) 527.073 + 527.073i 0.862640 + 0.862640i
\(612\) −946.173 946.173i −1.54604 1.54604i
\(613\) 1048.57i 1.71055i 0.518170 + 0.855277i \(0.326613\pi\)
−0.518170 + 0.855277i \(0.673387\pi\)
\(614\) 1208.31 1.96793
\(615\) 1184.93 1.92672
\(616\) 122.540i 0.198929i
\(617\) 233.005i 0.377642i −0.982012 0.188821i \(-0.939533\pi\)
0.982012 0.188821i \(-0.0604665\pi\)
\(618\) 786.160 + 786.160i 1.27210 + 1.27210i
\(619\) 188.558 0.304618 0.152309 0.988333i \(-0.451329\pi\)
0.152309 + 0.988333i \(0.451329\pi\)
\(620\) −383.346 −0.618300
\(621\) 46.7601 + 46.7601i 0.0752980 + 0.0752980i
\(622\) −503.885 + 503.885i −0.810104 + 0.810104i
\(623\) −571.152 + 571.152i −0.916776 + 0.916776i
\(624\) 1386.99i 2.22274i
\(625\) 402.779 0.644446
\(626\) 265.366 + 265.366i 0.423907 + 0.423907i
\(627\) 270.770 0.431850
\(628\) −295.101 −0.469906
\(629\) −679.074 679.074i −1.07961 1.07961i
\(630\) 884.155i 1.40342i
\(631\) 13.8463 0.0219435 0.0109717 0.999940i \(-0.496508\pi\)
0.0109717 + 0.999940i \(0.496508\pi\)
\(632\) 28.1715i 0.0445751i
\(633\) 201.829 0.318846
\(634\) 1247.10i 1.96703i
\(635\) −21.3732 21.3732i −0.0336585 0.0336585i
\(636\) −998.329 998.329i −1.56970 1.56970i
\(637\) 124.978 124.978i 0.196198 0.196198i
\(638\) 736.616i 1.15457i
\(639\) 159.545 159.545i 0.249679 0.249679i
\(640\) −252.801 −0.395002
\(641\) −309.541 309.541i −0.482904 0.482904i 0.423154 0.906058i \(-0.360923\pi\)
−0.906058 + 0.423154i \(0.860923\pi\)
\(642\) 1052.32 1.63912
\(643\) 390.496 + 390.496i 0.607303 + 0.607303i 0.942240 0.334937i \(-0.108715\pi\)
−0.334937 + 0.942240i \(0.608715\pi\)
\(644\) −1187.57 −1.84406
\(645\) −836.563 −1.29700
\(646\) 651.124i 1.00793i
\(647\) −337.691 + 337.691i −0.521933 + 0.521933i −0.918155 0.396222i \(-0.870321\pi\)
0.396222 + 0.918155i \(0.370321\pi\)
\(648\) 102.226 + 102.226i 0.157756 + 0.157756i
\(649\) −609.467 + 609.467i −0.939086 + 0.939086i
\(650\) 506.754 0.779621
\(651\) −625.761 −0.961230
\(652\) 1102.70 1.69126
\(653\) 59.6732i 0.0913832i −0.998956 0.0456916i \(-0.985451\pi\)
0.998956 0.0456916i \(-0.0145492\pi\)
\(654\) 457.764 0.699945
\(655\) 150.297i 0.229462i
\(656\) 845.870i 1.28944i
\(657\) −329.834 329.834i −0.502030 0.502030i
\(658\) −468.257 + 468.257i −0.711637 + 0.711637i
\(659\) 637.786 637.786i 0.967808 0.967808i −0.0316896 0.999498i \(-0.510089\pi\)
0.999498 + 0.0316896i \(0.0100888\pi\)
\(660\) 519.885 519.885i 0.787704 0.787704i
\(661\) −187.415 −0.283533 −0.141766 0.989900i \(-0.545278\pi\)
−0.141766 + 0.989900i \(0.545278\pi\)
\(662\) −545.751 545.751i −0.824397 0.824397i
\(663\) −2297.07 + 2297.07i −3.46466 + 3.46466i
\(664\) 146.400 146.400i 0.220482 0.220482i
\(665\) 163.393 163.393i 0.245704 0.245704i
\(666\) −618.359 618.359i −0.928468 0.928468i
\(667\) −985.817 −1.47799
\(668\) 210.422 + 210.422i 0.315004 + 0.315004i
\(669\) −261.097 261.097i −0.390280 0.390280i
\(670\) 143.955 + 143.955i 0.214859 + 0.214859i
\(671\) 248.854 248.854i 0.370870 0.370870i
\(672\) −1474.72 −2.19452
\(673\) −131.085 131.085i −0.194777 0.194777i 0.602980 0.797756i \(-0.293980\pi\)
−0.797756 + 0.602980i \(0.793980\pi\)
\(674\) 345.347i 0.512385i
\(675\) 9.52068 9.52068i 0.0141047 0.0141047i
\(676\) −2067.53 −3.05847
\(677\) −312.026 312.026i −0.460896 0.460896i 0.438053 0.898949i \(-0.355668\pi\)
−0.898949 + 0.438053i \(0.855668\pi\)
\(678\) 146.214 146.214i 0.215654 0.215654i
\(679\) 451.033 0.664261
\(680\) −172.641 172.641i −0.253884 0.253884i
\(681\) 1343.80 1.97328
\(682\) −350.911 350.911i −0.514532 0.514532i
\(683\) 134.662i 0.197162i −0.995129 0.0985812i \(-0.968570\pi\)
0.995129 0.0985812i \(-0.0314304\pi\)
\(684\) 318.442i 0.465558i
\(685\) −303.979 303.979i −0.443765 0.443765i
\(686\) −652.026 652.026i −0.950475 0.950475i
\(687\) 528.878i 0.769837i
\(688\) 597.185i 0.868001i
\(689\) −1241.45 + 1241.45i −1.80181 + 1.80181i
\(690\) 1295.45 + 1295.45i 1.87746 + 1.87746i
\(691\) −300.298 −0.434585 −0.217293 0.976107i \(-0.569723\pi\)
−0.217293 + 0.976107i \(0.569723\pi\)
\(692\) 1317.78 1.90431
\(693\) 434.687 434.687i 0.627254 0.627254i
\(694\) −895.844 + 895.844i −1.29084 + 1.29084i
\(695\) 36.5197 0.0525464
\(696\) 233.557 0.335571
\(697\) 1400.89 1400.89i 2.00989 2.00989i
\(698\) 231.267i 0.331329i
\(699\) −1016.66 + 1016.66i −1.45445 + 1.45445i
\(700\) 241.798i 0.345426i
\(701\) −390.491 390.491i −0.557049 0.557049i 0.371417 0.928466i \(-0.378872\pi\)
−0.928466 + 0.371417i \(0.878872\pi\)
\(702\) −99.7593 + 99.7593i −0.142107 + 0.142107i
\(703\) 228.547i 0.325103i
\(704\) −507.112 507.112i −0.720330 0.720330i
\(705\) 548.677 0.778265
\(706\) −390.914 + 390.914i −0.553702 + 0.553702i
\(707\) 688.416i 0.973714i
\(708\) 1399.36 + 1399.36i 1.97649 + 1.97649i
\(709\) −456.434 + 456.434i −0.643771 + 0.643771i −0.951480 0.307709i \(-0.900438\pi\)
0.307709 + 0.951480i \(0.400438\pi\)
\(710\) 210.806 210.806i 0.296910 0.296910i
\(711\) −99.9326 + 99.9326i −0.140552 + 0.140552i
\(712\) 203.106i 0.285261i
\(713\) 469.626 469.626i 0.658662 0.658662i
\(714\) −2040.74 2040.74i −2.85818 2.85818i
\(715\) −646.491 646.491i −0.904183 0.904183i
\(716\) −423.216 423.216i −0.591084 0.591084i
\(717\) −126.244 + 126.244i −0.176072 + 0.176072i
\(718\) 1808.64i 2.51900i
\(719\) −197.634 197.634i −0.274873 0.274873i 0.556185 0.831058i \(-0.312264\pi\)
−0.831058 + 0.556185i \(0.812264\pi\)
\(720\) 369.778 + 369.778i 0.513580 + 0.513580i
\(721\) 466.469 + 466.469i 0.646975 + 0.646975i
\(722\) −640.792 + 640.792i −0.887524 + 0.887524i
\(723\) 344.003 0.475800
\(724\) 562.015 0.776264
\(725\) 200.719i 0.276854i
\(726\) −576.021 −0.793417
\(727\) 265.374i 0.365026i 0.983203 + 0.182513i \(0.0584232\pi\)
−0.983203 + 0.182513i \(0.941577\pi\)
\(728\) 349.875i 0.480597i
\(729\) 800.099i 1.09753i
\(730\) −435.808 435.808i −0.596997 0.596997i
\(731\) −989.032 + 989.032i −1.35299 + 1.35299i
\(732\) −571.376 571.376i −0.780569 0.780569i
\(733\) 132.197 0.180350 0.0901750 0.995926i \(-0.471257\pi\)
0.0901750 + 0.995926i \(0.471257\pi\)
\(734\) 944.229i 1.28642i
\(735\) 130.101i 0.177008i
\(736\) 1106.76 1106.76i 1.50375 1.50375i
\(737\) 141.549i 0.192061i
\(738\) 1275.64 1275.64i 1.72852 1.72852i
\(739\) 686.568i 0.929050i 0.885560 + 0.464525i \(0.153775\pi\)
−0.885560 + 0.464525i \(0.846225\pi\)
\(740\) −438.817 438.817i −0.592995 0.592995i
\(741\) −773.097 −1.04332
\(742\) −1102.92 1102.92i −1.48641 1.48641i
\(743\) 84.7647 84.7647i 0.114084 0.114084i −0.647760 0.761844i \(-0.724294\pi\)
0.761844 + 0.647760i \(0.224294\pi\)
\(744\) −111.263 + 111.263i −0.149546 + 0.149546i
\(745\) 17.9927 0.0241513
\(746\) 1721.17i 2.30720i
\(747\) −1038.65 −1.39043
\(748\) 1229.28i 1.64342i
\(749\) 624.394 0.833636
\(750\) 1211.96 1211.96i 1.61594 1.61594i
\(751\) 385.719i 0.513608i −0.966464 0.256804i \(-0.917331\pi\)
0.966464 0.256804i \(-0.0826694\pi\)
\(752\) 391.676i 0.520846i
\(753\) −1126.58 + 1126.58i −1.49612 + 1.49612i
\(754\) 2103.17i 2.78935i
\(755\) −262.545 −0.347742
\(756\) −47.6003 47.6003i −0.0629634 0.0629634i
\(757\) 358.245 + 358.245i 0.473243 + 0.473243i 0.902963 0.429719i \(-0.141387\pi\)
−0.429719 + 0.902963i \(0.641387\pi\)
\(758\) 599.390 599.390i 0.790753 0.790753i
\(759\) 1273.79i 1.67825i
\(760\) 58.1037i 0.0764523i
\(761\) −628.732 + 628.732i −0.826192 + 0.826192i −0.986988 0.160796i \(-0.948594\pi\)
0.160796 + 0.986988i \(0.448594\pi\)
\(762\) −89.8427 −0.117904
\(763\) 271.615 0.355983
\(764\) 1380.07i 1.80637i
\(765\) 1224.82i 1.60107i
\(766\) 685.111 0.894401
\(767\) 1740.14 1740.14i 2.26876 2.26876i
\(768\) 472.228 472.228i 0.614880 0.614880i
\(769\) 297.969 0.387476 0.193738 0.981053i \(-0.437939\pi\)
0.193738 + 0.981053i \(0.437939\pi\)
\(770\) 574.350 574.350i 0.745909 0.745909i
\(771\) 678.908 678.908i 0.880556 0.880556i
\(772\) 1280.81i 1.65907i
\(773\) −944.042 −1.22127 −0.610635 0.791912i \(-0.709086\pi\)
−0.610635 + 0.791912i \(0.709086\pi\)
\(774\) −900.606 + 900.606i −1.16357 + 1.16357i
\(775\) −95.6192 95.6192i −0.123380 0.123380i