Properties

Label 225.4.h.d.91.2
Level $225$
Weight $4$
Character 225.91
Analytic conductor $13.275$
Analytic rank $0$
Dimension $64$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [225,4,Mod(46,225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(225, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 6]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("225.46");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), 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: \(13.2754297513\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(16\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.2
Character \(\chi\) \(=\) 225.91
Dual form 225.4.h.d.136.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.81348 - 2.77066i) q^{2} +(4.39397 + 13.5233i) q^{4} +(-0.520226 + 11.1682i) q^{5} +30.0229 q^{7} +(9.05902 - 27.8808i) q^{8} +O(q^{10})\) \(q+(-3.81348 - 2.77066i) q^{2} +(4.39397 + 13.5233i) q^{4} +(-0.520226 + 11.1682i) q^{5} +30.0229 q^{7} +(9.05902 - 27.8808i) q^{8} +(32.9272 - 41.1485i) q^{10} +(-14.7874 - 10.7436i) q^{11} +(-8.18200 + 5.94457i) q^{13} +(-114.492 - 83.1833i) q^{14} +(-19.7659 + 14.3608i) q^{16} +(-16.0525 + 49.4045i) q^{17} +(-38.2859 + 117.832i) q^{19} +(-153.317 + 42.0378i) q^{20} +(26.6244 + 81.9414i) q^{22} +(1.42621 + 1.03620i) q^{23} +(-124.459 - 11.6200i) q^{25} +47.6723 q^{26} +(131.920 + 406.008i) q^{28} +(-27.4424 - 84.4591i) q^{29} +(46.1542 - 142.048i) q^{31} -119.359 q^{32} +(198.099 - 143.927i) q^{34} +(-15.6187 + 335.303i) q^{35} +(-325.811 + 236.715i) q^{37} +(472.474 - 343.273i) q^{38} +(306.666 + 115.678i) q^{40} +(292.892 - 212.798i) q^{41} +154.458 q^{43} +(80.3139 - 247.181i) q^{44} +(-2.56786 - 7.90307i) q^{46} +(148.872 + 458.182i) q^{47} +558.378 q^{49} +(442.426 + 389.145i) q^{50} +(-116.342 - 84.5271i) q^{52} +(224.200 + 690.016i) q^{53} +(127.680 - 159.560i) q^{55} +(271.978 - 837.064i) q^{56} +(-129.356 + 398.117i) q^{58} +(-535.101 + 388.774i) q^{59} +(-400.775 - 291.180i) q^{61} +(-569.575 + 413.820i) q^{62} +(613.300 + 445.589i) q^{64} +(-62.1339 - 94.4710i) q^{65} +(-151.236 + 465.456i) q^{67} -738.644 q^{68} +(988.572 - 1235.40i) q^{70} +(7.20675 + 22.1801i) q^{71} +(-279.997 - 203.430i) q^{73} +1898.33 q^{74} -1761.70 q^{76} +(-443.960 - 322.556i) q^{77} +(220.932 + 679.959i) q^{79} +(-150.102 - 228.221i) q^{80} -1706.53 q^{82} +(94.0318 - 289.400i) q^{83} +(-543.410 - 204.979i) q^{85} +(-589.024 - 427.951i) q^{86} +(-433.500 + 314.956i) q^{88} +(242.287 + 176.032i) q^{89} +(-245.648 + 178.474i) q^{91} +(-7.74609 + 23.8400i) q^{92} +(701.744 - 2159.74i) q^{94} +(-1296.06 - 488.885i) q^{95} +(-79.7315 - 245.388i) q^{97} +(-2129.36 - 1547.07i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q - 72 q^{4} + 20 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 64 q - 72 q^{4} + 20 q^{7} + 50 q^{10} + 180 q^{13} - 244 q^{16} - 116 q^{19} - 210 q^{22} + 440 q^{25} + 980 q^{28} + 42 q^{31} + 40 q^{34} - 1170 q^{37} - 3040 q^{40} + 1040 q^{43} + 700 q^{46} + 4188 q^{49} + 3280 q^{52} + 2640 q^{55} - 4530 q^{58} + 88 q^{61} - 3018 q^{64} - 2860 q^{67} - 3720 q^{70} - 5280 q^{73} + 9288 q^{76} - 1144 q^{79} + 2840 q^{82} + 470 q^{85} + 7610 q^{88} - 1180 q^{91} + 2170 q^{94} + 2050 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.81348 2.77066i −1.34827 0.979575i −0.999096 0.0425177i \(-0.986462\pi\)
−0.349174 0.937058i \(-0.613538\pi\)
\(3\) 0 0
\(4\) 4.39397 + 13.5233i 0.549247 + 1.69041i
\(5\) −0.520226 + 11.1682i −0.0465304 + 0.998917i
\(6\) 0 0
\(7\) 30.0229 1.62109 0.810543 0.585678i \(-0.199172\pi\)
0.810543 + 0.585678i \(0.199172\pi\)
\(8\) 9.05902 27.8808i 0.400356 1.23217i
\(9\) 0 0
\(10\) 32.9272 41.1485i 1.04125 1.30123i
\(11\) −14.7874 10.7436i −0.405323 0.294485i 0.366382 0.930464i \(-0.380596\pi\)
−0.771706 + 0.635980i \(0.780596\pi\)
\(12\) 0 0
\(13\) −8.18200 + 5.94457i −0.174560 + 0.126825i −0.671635 0.740883i \(-0.734408\pi\)
0.497075 + 0.867708i \(0.334408\pi\)
\(14\) −114.492 83.1833i −2.18566 1.58798i
\(15\) 0 0
\(16\) −19.7659 + 14.3608i −0.308843 + 0.224387i
\(17\) −16.0525 + 49.4045i −0.229018 + 0.704844i 0.768841 + 0.639440i \(0.220834\pi\)
−0.997859 + 0.0654044i \(0.979166\pi\)
\(18\) 0 0
\(19\) −38.2859 + 117.832i −0.462283 + 1.42276i 0.400084 + 0.916479i \(0.368981\pi\)
−0.862367 + 0.506283i \(0.831019\pi\)
\(20\) −153.317 + 42.0378i −1.71413 + 0.469996i
\(21\) 0 0
\(22\) 26.6244 + 81.9414i 0.258015 + 0.794090i
\(23\) 1.42621 + 1.03620i 0.0129298 + 0.00939403i 0.594231 0.804294i \(-0.297456\pi\)
−0.581302 + 0.813688i \(0.697456\pi\)
\(24\) 0 0
\(25\) −124.459 11.6200i −0.995670 0.0929601i
\(26\) 47.6723 0.359589
\(27\) 0 0
\(28\) 131.920 + 406.008i 0.890377 + 2.74030i
\(29\) −27.4424 84.4591i −0.175722 0.540816i 0.823944 0.566671i \(-0.191769\pi\)
−0.999666 + 0.0258556i \(0.991769\pi\)
\(30\) 0 0
\(31\) 46.1542 142.048i 0.267405 0.822987i −0.723725 0.690088i \(-0.757572\pi\)
0.991130 0.132898i \(-0.0424283\pi\)
\(32\) −119.359 −0.659371
\(33\) 0 0
\(34\) 198.099 143.927i 0.999226 0.725980i
\(35\) −15.6187 + 335.303i −0.0754299 + 1.61933i
\(36\) 0 0
\(37\) −325.811 + 236.715i −1.44765 + 1.05178i −0.461273 + 0.887258i \(0.652607\pi\)
−0.986374 + 0.164519i \(0.947393\pi\)
\(38\) 472.474 343.273i 2.01699 1.46543i
\(39\) 0 0
\(40\) 306.666 + 115.678i 1.21221 + 0.457255i
\(41\) 292.892 212.798i 1.11566 0.810573i 0.132113 0.991235i \(-0.457824\pi\)
0.983545 + 0.180661i \(0.0578238\pi\)
\(42\) 0 0
\(43\) 154.458 0.547782 0.273891 0.961761i \(-0.411689\pi\)
0.273891 + 0.961761i \(0.411689\pi\)
\(44\) 80.3139 247.181i 0.275177 0.846907i
\(45\) 0 0
\(46\) −2.56786 7.90307i −0.00823067 0.0253314i
\(47\) 148.872 + 458.182i 0.462027 + 1.42197i 0.862683 + 0.505745i \(0.168782\pi\)
−0.400656 + 0.916228i \(0.631218\pi\)
\(48\) 0 0
\(49\) 558.378 1.62792
\(50\) 442.426 + 389.145i 1.25137 + 1.10067i
\(51\) 0 0
\(52\) −116.342 84.5271i −0.310263 0.225419i
\(53\) 224.200 + 690.016i 0.581061 + 1.78832i 0.614545 + 0.788882i \(0.289340\pi\)
−0.0334842 + 0.999439i \(0.510660\pi\)
\(54\) 0 0
\(55\) 127.680 159.560i 0.313026 0.391182i
\(56\) 271.978 837.064i 0.649012 1.99745i
\(57\) 0 0
\(58\) −129.356 + 398.117i −0.292849 + 0.901298i
\(59\) −535.101 + 388.774i −1.18075 + 0.857865i −0.992256 0.124209i \(-0.960361\pi\)
−0.188494 + 0.982074i \(0.560361\pi\)
\(60\) 0 0
\(61\) −400.775 291.180i −0.841213 0.611177i 0.0814965 0.996674i \(-0.474030\pi\)
−0.922709 + 0.385497i \(0.874030\pi\)
\(62\) −569.575 + 413.820i −1.16671 + 0.847665i
\(63\) 0 0
\(64\) 613.300 + 445.589i 1.19785 + 0.870291i
\(65\) −62.1339 94.4710i −0.118566 0.180272i
\(66\) 0 0
\(67\) −151.236 + 465.456i −0.275767 + 0.848724i 0.713248 + 0.700911i \(0.247223\pi\)
−0.989015 + 0.147812i \(0.952777\pi\)
\(68\) −738.644 −1.31726
\(69\) 0 0
\(70\) 988.572 1235.40i 1.68796 2.10941i
\(71\) 7.20675 + 22.1801i 0.0120463 + 0.0370746i 0.956899 0.290421i \(-0.0937953\pi\)
−0.944853 + 0.327496i \(0.893795\pi\)
\(72\) 0 0
\(73\) −279.997 203.430i −0.448921 0.326160i 0.340249 0.940335i \(-0.389489\pi\)
−0.789170 + 0.614175i \(0.789489\pi\)
\(74\) 1898.33 2.98211
\(75\) 0 0
\(76\) −1761.70 −2.65896
\(77\) −443.960 322.556i −0.657064 0.477385i
\(78\) 0 0
\(79\) 220.932 + 679.959i 0.314643 + 0.968372i 0.975901 + 0.218213i \(0.0700229\pi\)
−0.661258 + 0.750159i \(0.729977\pi\)
\(80\) −150.102 228.221i −0.209774 0.318949i
\(81\) 0 0
\(82\) −1706.53 −2.29823
\(83\) 94.0318 289.400i 0.124353 0.382720i −0.869429 0.494057i \(-0.835513\pi\)
0.993783 + 0.111337i \(0.0355133\pi\)
\(84\) 0 0
\(85\) −543.410 204.979i −0.693425 0.261566i
\(86\) −589.024 427.951i −0.738559 0.536594i
\(87\) 0 0
\(88\) −433.500 + 314.956i −0.525128 + 0.381528i
\(89\) 242.287 + 176.032i 0.288566 + 0.209655i 0.722645 0.691219i \(-0.242926\pi\)
−0.434079 + 0.900875i \(0.642926\pi\)
\(90\) 0 0
\(91\) −245.648 + 178.474i −0.282977 + 0.205595i
\(92\) −7.74609 + 23.8400i −0.00877811 + 0.0270162i
\(93\) 0 0
\(94\) 701.744 2159.74i 0.769993 2.36979i
\(95\) −1296.06 488.885i −1.39971 0.527984i
\(96\) 0 0
\(97\) −79.7315 245.388i −0.0834589 0.256860i 0.900616 0.434616i \(-0.143116\pi\)
−0.984075 + 0.177756i \(0.943116\pi\)
\(98\) −2129.36 1547.07i −2.19488 1.59467i
\(99\) 0 0
\(100\) −389.728 1734.15i −0.389728 1.73415i
\(101\) −325.055 −0.320239 −0.160119 0.987098i \(-0.551188\pi\)
−0.160119 + 0.987098i \(0.551188\pi\)
\(102\) 0 0
\(103\) 511.836 + 1575.27i 0.489638 + 1.50695i 0.825149 + 0.564915i \(0.191091\pi\)
−0.335511 + 0.942036i \(0.608909\pi\)
\(104\) 91.6185 + 281.973i 0.0863840 + 0.265862i
\(105\) 0 0
\(106\) 1056.82 3252.55i 0.968369 2.98033i
\(107\) 1423.10 1.28576 0.642881 0.765966i \(-0.277739\pi\)
0.642881 + 0.765966i \(0.277739\pi\)
\(108\) 0 0
\(109\) −1012.25 + 735.444i −0.889506 + 0.646264i −0.935749 0.352667i \(-0.885275\pi\)
0.0462434 + 0.998930i \(0.485275\pi\)
\(110\) −928.992 + 254.719i −0.805235 + 0.220787i
\(111\) 0 0
\(112\) −593.432 + 431.153i −0.500661 + 0.363752i
\(113\) −1288.60 + 936.225i −1.07276 + 0.779404i −0.976406 0.215944i \(-0.930717\pi\)
−0.0963512 + 0.995347i \(0.530717\pi\)
\(114\) 0 0
\(115\) −12.3145 + 15.3892i −0.00998549 + 0.0124787i
\(116\) 1021.58 742.222i 0.817684 0.594082i
\(117\) 0 0
\(118\) 3117.76 2.43231
\(119\) −481.943 + 1483.27i −0.371258 + 1.14261i
\(120\) 0 0
\(121\) −308.061 948.116i −0.231451 0.712333i
\(122\) 721.588 + 2220.82i 0.535488 + 1.64806i
\(123\) 0 0
\(124\) 2123.75 1.53805
\(125\) 194.522 1383.94i 0.139188 0.990266i
\(126\) 0 0
\(127\) −338.303 245.791i −0.236374 0.171736i 0.463292 0.886206i \(-0.346668\pi\)
−0.699666 + 0.714470i \(0.746668\pi\)
\(128\) −809.165 2490.36i −0.558756 1.71967i
\(129\) 0 0
\(130\) −24.8004 + 532.415i −0.0167318 + 0.359199i
\(131\) −422.519 + 1300.38i −0.281799 + 0.867287i 0.705541 + 0.708669i \(0.250704\pi\)
−0.987340 + 0.158618i \(0.949296\pi\)
\(132\) 0 0
\(133\) −1149.46 + 3537.66i −0.749402 + 2.30642i
\(134\) 1866.35 1355.99i 1.20320 0.874174i
\(135\) 0 0
\(136\) 1232.02 + 895.113i 0.776798 + 0.564377i
\(137\) 1592.09 1156.72i 0.992858 0.721354i 0.0323129 0.999478i \(-0.489713\pi\)
0.960545 + 0.278124i \(0.0897127\pi\)
\(138\) 0 0
\(139\) −1889.03 1372.46i −1.15270 0.837486i −0.163864 0.986483i \(-0.552396\pi\)
−0.988838 + 0.148997i \(0.952396\pi\)
\(140\) −4603.02 + 1262.10i −2.77876 + 0.761905i
\(141\) 0 0
\(142\) 33.9706 104.551i 0.0200757 0.0617867i
\(143\) 184.857 0.108101
\(144\) 0 0
\(145\) 957.534 262.545i 0.548406 0.150367i
\(146\) 504.130 + 1551.55i 0.285768 + 0.879503i
\(147\) 0 0
\(148\) −4632.77 3365.90i −2.57305 1.86943i
\(149\) 2145.99 1.17991 0.589955 0.807436i \(-0.299146\pi\)
0.589955 + 0.807436i \(0.299146\pi\)
\(150\) 0 0
\(151\) −1985.41 −1.07000 −0.535001 0.844851i \(-0.679689\pi\)
−0.535001 + 0.844851i \(0.679689\pi\)
\(152\) 2938.41 + 2134.88i 1.56800 + 1.13922i
\(153\) 0 0
\(154\) 799.343 + 2460.12i 0.418265 + 1.28729i
\(155\) 1562.41 + 589.358i 0.809653 + 0.305409i
\(156\) 0 0
\(157\) 2046.55 1.04034 0.520168 0.854064i \(-0.325869\pi\)
0.520168 + 0.854064i \(0.325869\pi\)
\(158\) 1041.41 3205.14i 0.524370 1.61384i
\(159\) 0 0
\(160\) 62.0936 1333.03i 0.0306808 0.658656i
\(161\) 42.8190 + 31.1098i 0.0209603 + 0.0152285i
\(162\) 0 0
\(163\) 1368.30 994.130i 0.657508 0.477707i −0.208313 0.978062i \(-0.566797\pi\)
0.865820 + 0.500355i \(0.166797\pi\)
\(164\) 4164.69 + 3025.82i 1.98297 + 1.44071i
\(165\) 0 0
\(166\) −1160.42 + 843.092i −0.542565 + 0.394197i
\(167\) −252.425 + 776.885i −0.116966 + 0.359983i −0.992352 0.123441i \(-0.960607\pi\)
0.875386 + 0.483424i \(0.160607\pi\)
\(168\) 0 0
\(169\) −647.303 + 1992.19i −0.294630 + 0.906779i
\(170\) 1504.36 + 2287.29i 0.678699 + 1.03192i
\(171\) 0 0
\(172\) 678.685 + 2088.78i 0.300868 + 0.925976i
\(173\) −253.871 184.448i −0.111569 0.0810597i 0.530602 0.847621i \(-0.321966\pi\)
−0.642171 + 0.766562i \(0.721966\pi\)
\(174\) 0 0
\(175\) −3736.62 348.867i −1.61407 0.150696i
\(176\) 446.573 0.191260
\(177\) 0 0
\(178\) −436.234 1342.59i −0.183691 0.565344i
\(179\) −745.389 2294.07i −0.311246 0.957915i −0.977272 0.211988i \(-0.932006\pi\)
0.666027 0.745928i \(-0.267994\pi\)
\(180\) 0 0
\(181\) −299.683 + 922.330i −0.123068 + 0.378764i −0.993544 0.113446i \(-0.963811\pi\)
0.870476 + 0.492210i \(0.163811\pi\)
\(182\) 1431.26 0.582925
\(183\) 0 0
\(184\) 41.8101 30.3768i 0.0167515 0.0121707i
\(185\) −2474.20 3761.87i −0.983278 1.49502i
\(186\) 0 0
\(187\) 768.159 558.100i 0.300392 0.218248i
\(188\) −5541.98 + 4026.48i −2.14995 + 1.56203i
\(189\) 0 0
\(190\) 3587.95 + 5455.28i 1.36999 + 2.08299i
\(191\) 4080.24 2964.47i 1.54574 1.12305i 0.599134 0.800649i \(-0.295512\pi\)
0.946605 0.322396i \(-0.104488\pi\)
\(192\) 0 0
\(193\) 3589.89 1.33889 0.669445 0.742862i \(-0.266532\pi\)
0.669445 + 0.742862i \(0.266532\pi\)
\(194\) −375.832 + 1156.69i −0.139089 + 0.428071i
\(195\) 0 0
\(196\) 2453.50 + 7551.09i 0.894131 + 2.75185i
\(197\) 217.719 + 670.072i 0.0787404 + 0.242338i 0.982676 0.185330i \(-0.0593353\pi\)
−0.903936 + 0.427668i \(0.859335\pi\)
\(198\) 0 0
\(199\) 2502.96 0.891609 0.445804 0.895130i \(-0.352918\pi\)
0.445804 + 0.895130i \(0.352918\pi\)
\(200\) −1451.45 + 3364.74i −0.513165 + 1.18962i
\(201\) 0 0
\(202\) 1239.59 + 900.615i 0.431769 + 0.313698i
\(203\) −823.902 2535.71i −0.284860 0.876709i
\(204\) 0 0
\(205\) 2224.21 + 3381.79i 0.757783 + 1.15217i
\(206\) 2412.66 7425.39i 0.816008 2.51141i
\(207\) 0 0
\(208\) 76.3562 235.000i 0.0254536 0.0783381i
\(209\) 1832.09 1331.09i 0.606356 0.440543i
\(210\) 0 0
\(211\) 927.754 + 674.053i 0.302698 + 0.219923i 0.728757 0.684773i \(-0.240098\pi\)
−0.426059 + 0.904695i \(0.640098\pi\)
\(212\) −8346.14 + 6063.83i −2.70385 + 1.96446i
\(213\) 0 0
\(214\) −5426.98 3942.93i −1.73355 1.25950i
\(215\) −80.3531 + 1725.02i −0.0254886 + 0.547189i
\(216\) 0 0
\(217\) 1385.69 4264.70i 0.433486 1.33413i
\(218\) 5897.87 1.83236
\(219\) 0 0
\(220\) 2718.79 + 1025.55i 0.833185 + 0.314286i
\(221\) −162.347 499.653i −0.0494147 0.152083i
\(222\) 0 0
\(223\) −2818.81 2047.98i −0.846463 0.614991i 0.0777058 0.996976i \(-0.475241\pi\)
−0.924168 + 0.381985i \(0.875241\pi\)
\(224\) −3583.50 −1.06890
\(225\) 0 0
\(226\) 7508.02 2.20985
\(227\) −3201.97 2326.37i −0.936221 0.680205i 0.0112867 0.999936i \(-0.496407\pi\)
−0.947508 + 0.319732i \(0.896407\pi\)
\(228\) 0 0
\(229\) 362.469 + 1115.57i 0.104597 + 0.321915i 0.989636 0.143602i \(-0.0458684\pi\)
−0.885039 + 0.465517i \(0.845868\pi\)
\(230\) 89.5991 24.5671i 0.0256869 0.00704307i
\(231\) 0 0
\(232\) −2603.39 −0.736727
\(233\) 247.309 761.138i 0.0695354 0.214008i −0.910250 0.414059i \(-0.864111\pi\)
0.979785 + 0.200051i \(0.0641108\pi\)
\(234\) 0 0
\(235\) −5194.53 + 1424.28i −1.44193 + 0.395362i
\(236\) −7608.71 5528.05i −2.09867 1.52477i
\(237\) 0 0
\(238\) 5947.51 4321.12i 1.61983 1.17688i
\(239\) −543.446 394.837i −0.147082 0.106861i 0.511811 0.859098i \(-0.328975\pi\)
−0.658893 + 0.752237i \(0.728975\pi\)
\(240\) 0 0
\(241\) 3825.36 2779.28i 1.02246 0.742860i 0.0556741 0.998449i \(-0.482269\pi\)
0.966786 + 0.255589i \(0.0822692\pi\)
\(242\) −1452.12 + 4469.16i −0.385726 + 1.18714i
\(243\) 0 0
\(244\) 2176.71 6699.22i 0.571105 1.75768i
\(245\) −290.483 + 6236.09i −0.0757479 + 1.62616i
\(246\) 0 0
\(247\) −387.205 1191.69i −0.0997460 0.306987i
\(248\) −3542.30 2573.63i −0.907001 0.658975i
\(249\) 0 0
\(250\) −4576.23 + 4738.67i −1.15770 + 1.19880i
\(251\) −6948.68 −1.74740 −0.873699 0.486467i \(-0.838285\pi\)
−0.873699 + 0.486467i \(0.838285\pi\)
\(252\) 0 0
\(253\) −9.95728 30.6453i −0.00247434 0.00761524i
\(254\) 609.108 + 1874.64i 0.150468 + 0.463093i
\(255\) 0 0
\(256\) −1940.10 + 5971.03i −0.473658 + 1.45777i
\(257\) −7689.52 −1.86638 −0.933189 0.359387i \(-0.882986\pi\)
−0.933189 + 0.359387i \(0.882986\pi\)
\(258\) 0 0
\(259\) −9781.80 + 7106.89i −2.34676 + 1.70502i
\(260\) 1004.54 1255.36i 0.239612 0.299438i
\(261\) 0 0
\(262\) 5214.17 3788.32i 1.22951 0.893294i
\(263\) 382.580 277.961i 0.0896993 0.0651704i −0.542032 0.840358i \(-0.682345\pi\)
0.631731 + 0.775188i \(0.282345\pi\)
\(264\) 0 0
\(265\) −7822.89 + 2144.95i −1.81342 + 0.497220i
\(266\) 14185.1 10306.1i 3.26971 2.37558i
\(267\) 0 0
\(268\) −6959.01 −1.58615
\(269\) 2123.30 6534.83i 0.481263 1.48117i −0.356059 0.934464i \(-0.615880\pi\)
0.837322 0.546711i \(-0.184120\pi\)
\(270\) 0 0
\(271\) −1165.02 3585.58i −0.261145 0.803721i −0.992557 0.121785i \(-0.961138\pi\)
0.731412 0.681936i \(-0.238862\pi\)
\(272\) −392.195 1207.05i −0.0874277 0.269075i
\(273\) 0 0
\(274\) −9276.30 −2.04526
\(275\) 1715.58 + 1508.97i 0.376193 + 0.330888i
\(276\) 0 0
\(277\) 6318.28 + 4590.50i 1.37050 + 0.995727i 0.997698 + 0.0678157i \(0.0216030\pi\)
0.372802 + 0.927911i \(0.378397\pi\)
\(278\) 3401.17 + 10467.7i 0.733771 + 2.25832i
\(279\) 0 0
\(280\) 9207.03 + 3472.98i 1.96509 + 0.741251i
\(281\) −312.625 + 962.162i −0.0663689 + 0.204262i −0.978741 0.205099i \(-0.934248\pi\)
0.912372 + 0.409361i \(0.134248\pi\)
\(282\) 0 0
\(283\) −312.162 + 960.736i −0.0655693 + 0.201802i −0.978474 0.206372i \(-0.933834\pi\)
0.912904 + 0.408174i \(0.133834\pi\)
\(284\) −268.281 + 194.918i −0.0560548 + 0.0407262i
\(285\) 0 0
\(286\) −704.948 512.175i −0.145750 0.105893i
\(287\) 8793.47 6388.83i 1.80858 1.31401i
\(288\) 0 0
\(289\) 1791.58 + 1301.66i 0.364661 + 0.264941i
\(290\) −4378.96 1651.79i −0.886695 0.334470i
\(291\) 0 0
\(292\) 1520.74 4680.34i 0.304775 0.938001i
\(293\) 875.947 0.174653 0.0873266 0.996180i \(-0.472168\pi\)
0.0873266 + 0.996180i \(0.472168\pi\)
\(294\) 0 0
\(295\) −4063.54 6178.38i −0.801995 1.21939i
\(296\) 3648.28 + 11228.3i 0.716393 + 2.20483i
\(297\) 0 0
\(298\) −8183.71 5945.81i −1.59084 1.15581i
\(299\) −17.8290 −0.00344842
\(300\) 0 0
\(301\) 4637.29 0.888003
\(302\) 7571.33 + 5500.89i 1.44265 + 1.04815i
\(303\) 0 0
\(304\) −935.403 2878.87i −0.176477 0.543140i
\(305\) 3460.46 4324.47i 0.649657 0.811863i
\(306\) 0 0
\(307\) 4913.38 0.913424 0.456712 0.889615i \(-0.349027\pi\)
0.456712 + 0.889615i \(0.349027\pi\)
\(308\) 2411.26 7421.09i 0.446085 1.37291i
\(309\) 0 0
\(310\) −4325.33 6576.42i −0.792459 1.20489i
\(311\) 5935.48 + 4312.38i 1.08222 + 0.786279i 0.978069 0.208283i \(-0.0667874\pi\)
0.104151 + 0.994561i \(0.466787\pi\)
\(312\) 0 0
\(313\) 4500.18 3269.57i 0.812669 0.590439i −0.101934 0.994791i \(-0.532503\pi\)
0.914603 + 0.404352i \(0.132503\pi\)
\(314\) −7804.50 5670.30i −1.40265 1.01909i
\(315\) 0 0
\(316\) −8224.50 + 5975.45i −1.46413 + 1.06375i
\(317\) −1905.62 + 5864.88i −0.337634 + 1.03913i 0.627776 + 0.778394i \(0.283966\pi\)
−0.965410 + 0.260737i \(0.916034\pi\)
\(318\) 0 0
\(319\) −501.597 + 1543.76i −0.0880378 + 0.270953i
\(320\) −5295.49 + 6617.67i −0.925085 + 1.15606i
\(321\) 0 0
\(322\) −77.0948 237.273i −0.0133426 0.0410644i
\(323\) −5206.84 3782.99i −0.896955 0.651676i
\(324\) 0 0
\(325\) 1087.40 644.779i 0.185594 0.110049i
\(326\) −7972.39 −1.35445
\(327\) 0 0
\(328\) −3279.67 10093.8i −0.552103 1.69920i
\(329\) 4469.59 + 13756.0i 0.748986 + 2.30514i
\(330\) 0 0
\(331\) 2614.40 8046.28i 0.434139 1.33614i −0.459826 0.888009i \(-0.652088\pi\)
0.893966 0.448135i \(-0.147912\pi\)
\(332\) 4326.81 0.715254
\(333\) 0 0
\(334\) 3115.10 2263.26i 0.510332 0.370778i
\(335\) −5119.64 1931.18i −0.834973 0.314960i
\(336\) 0 0
\(337\) 1948.65 1415.78i 0.314985 0.228850i −0.419047 0.907964i \(-0.637636\pi\)
0.734033 + 0.679114i \(0.237636\pi\)
\(338\) 7988.17 5803.74i 1.28550 0.933971i
\(339\) 0 0
\(340\) 384.262 8249.35i 0.0612928 1.31583i
\(341\) −2208.61 + 1604.65i −0.350742 + 0.254829i
\(342\) 0 0
\(343\) 6466.27 1.01792
\(344\) 1399.24 4306.42i 0.219308 0.674960i
\(345\) 0 0
\(346\) 457.090 + 1406.78i 0.0710211 + 0.218581i
\(347\) −1523.44 4688.67i −0.235685 0.725363i −0.997030 0.0770164i \(-0.975461\pi\)
0.761345 0.648347i \(-0.224539\pi\)
\(348\) 0 0
\(349\) 1386.26 0.212622 0.106311 0.994333i \(-0.466096\pi\)
0.106311 + 0.994333i \(0.466096\pi\)
\(350\) 13282.9 + 11683.3i 2.02858 + 1.78428i
\(351\) 0 0
\(352\) 1765.00 + 1282.35i 0.267258 + 0.194175i
\(353\) 2634.19 + 8107.19i 0.397177 + 1.22239i 0.927253 + 0.374436i \(0.122164\pi\)
−0.530075 + 0.847950i \(0.677836\pi\)
\(354\) 0 0
\(355\) −251.462 + 68.9480i −0.0375949 + 0.0103081i
\(356\) −1315.92 + 4049.99i −0.195909 + 0.602947i
\(357\) 0 0
\(358\) −3513.56 + 10813.6i −0.518707 + 1.59642i
\(359\) 2112.51 1534.83i 0.310568 0.225641i −0.421572 0.906795i \(-0.638521\pi\)
0.732140 + 0.681154i \(0.238521\pi\)
\(360\) 0 0
\(361\) −6869.49 4990.97i −1.00153 0.727653i
\(362\) 3698.30 2686.97i 0.536957 0.390122i
\(363\) 0 0
\(364\) −3492.92 2537.75i −0.502963 0.365424i
\(365\) 2417.61 3021.25i 0.346695 0.433258i
\(366\) 0 0
\(367\) 2633.51 8105.10i 0.374572 1.15281i −0.569195 0.822203i \(-0.692745\pi\)
0.943767 0.330612i \(-0.107255\pi\)
\(368\) −43.0710 −0.00610117
\(369\) 0 0
\(370\) −987.561 + 21201.0i −0.138759 + 2.97888i
\(371\) 6731.14 + 20716.3i 0.941950 + 2.89902i
\(372\) 0 0
\(373\) 7030.32 + 5107.83i 0.975915 + 0.709044i 0.956792 0.290774i \(-0.0939126\pi\)
0.0191228 + 0.999817i \(0.493913\pi\)
\(374\) −4475.66 −0.618800
\(375\) 0 0
\(376\) 14123.1 1.93709
\(377\) 726.607 + 527.911i 0.0992630 + 0.0721188i
\(378\) 0 0
\(379\) −580.539 1786.71i −0.0786815 0.242157i 0.903977 0.427581i \(-0.140634\pi\)
−0.982659 + 0.185424i \(0.940634\pi\)
\(380\) 916.481 19675.1i 0.123722 2.65608i
\(381\) 0 0
\(382\) −23773.5 −3.18418
\(383\) 1069.50 3291.59i 0.142687 0.439145i −0.854019 0.520241i \(-0.825842\pi\)
0.996706 + 0.0810962i \(0.0258421\pi\)
\(384\) 0 0
\(385\) 3833.34 4790.45i 0.507442 0.634140i
\(386\) −13690.0 9946.35i −1.80519 1.31154i
\(387\) 0 0
\(388\) 2968.11 2156.46i 0.388359 0.282159i
\(389\) 3790.30 + 2753.81i 0.494025 + 0.358930i 0.806730 0.590920i \(-0.201235\pi\)
−0.312705 + 0.949850i \(0.601235\pi\)
\(390\) 0 0
\(391\) −74.0872 + 53.8275i −0.00958248 + 0.00696208i
\(392\) 5058.35 15568.0i 0.651748 2.00588i
\(393\) 0 0
\(394\) 1026.27 3158.53i 0.131225 0.403870i
\(395\) −7708.88 + 2113.69i −0.981964 + 0.269244i
\(396\) 0 0
\(397\) 1300.05 + 4001.14i 0.164352 + 0.505822i 0.998988 0.0449791i \(-0.0143221\pi\)
−0.834636 + 0.550802i \(0.814322\pi\)
\(398\) −9544.99 6934.84i −1.20213 0.873398i
\(399\) 0 0
\(400\) 2626.92 1557.65i 0.328365 0.194706i
\(401\) −5195.34 −0.646990 −0.323495 0.946230i \(-0.604858\pi\)
−0.323495 + 0.946230i \(0.604858\pi\)
\(402\) 0 0
\(403\) 466.781 + 1436.60i 0.0576973 + 0.177574i
\(404\) −1428.28 4395.80i −0.175890 0.541334i
\(405\) 0 0
\(406\) −3883.65 + 11952.6i −0.474734 + 1.46108i
\(407\) 7361.07 0.896498
\(408\) 0 0
\(409\) 3935.79 2859.52i 0.475825 0.345707i −0.323882 0.946097i \(-0.604988\pi\)
0.799707 + 0.600390i \(0.204988\pi\)
\(410\) 887.781 19058.9i 0.106937 2.29574i
\(411\) 0 0
\(412\) −19053.8 + 13843.4i −2.27843 + 1.65538i
\(413\) −16065.3 + 11672.1i −1.91410 + 1.39067i
\(414\) 0 0
\(415\) 3183.17 + 1200.72i 0.376520 + 0.142027i
\(416\) 976.594 709.537i 0.115100 0.0836248i
\(417\) 0 0
\(418\) −10674.6 −1.24908
\(419\) −867.455 + 2669.75i −0.101141 + 0.311279i −0.988805 0.149211i \(-0.952326\pi\)
0.887665 + 0.460491i \(0.152326\pi\)
\(420\) 0 0
\(421\) −1080.79 3326.34i −0.125118 0.385073i 0.868805 0.495155i \(-0.164889\pi\)
−0.993923 + 0.110082i \(0.964889\pi\)
\(422\) −1670.41 5140.98i −0.192687 0.593031i
\(423\) 0 0
\(424\) 21269.2 2.43614
\(425\) 2571.95 5962.29i 0.293548 0.680503i
\(426\) 0 0
\(427\) −12032.4 8742.08i −1.36368 0.990771i
\(428\) 6253.08 + 19245.0i 0.706201 + 2.17346i
\(429\) 0 0
\(430\) 5085.88 6355.72i 0.570379 0.712791i
\(431\) −3618.89 + 11137.8i −0.404445 + 1.24475i 0.516912 + 0.856038i \(0.327081\pi\)
−0.921358 + 0.388716i \(0.872919\pi\)
\(432\) 0 0
\(433\) −1199.16 + 3690.63i −0.133090 + 0.409608i −0.995288 0.0969629i \(-0.969087\pi\)
0.862198 + 0.506571i \(0.169087\pi\)
\(434\) −17100.3 + 12424.1i −1.89134 + 1.37414i
\(435\) 0 0
\(436\) −14393.4 10457.4i −1.58101 1.14867i
\(437\) −176.701 + 128.381i −0.0193427 + 0.0140533i
\(438\) 0 0
\(439\) −2160.59 1569.76i −0.234897 0.170662i 0.464110 0.885778i \(-0.346374\pi\)
−0.699007 + 0.715115i \(0.746374\pi\)
\(440\) −3291.99 5005.28i −0.356680 0.542312i
\(441\) 0 0
\(442\) −765.260 + 2355.23i −0.0823522 + 0.253454i
\(443\) −3909.49 −0.419290 −0.209645 0.977778i \(-0.567231\pi\)
−0.209645 + 0.977778i \(0.567231\pi\)
\(444\) 0 0
\(445\) −2092.01 + 2614.34i −0.222855 + 0.278498i
\(446\) 5075.21 + 15619.9i 0.538830 + 1.65835i
\(447\) 0 0
\(448\) 18413.1 + 13377.9i 1.94182 + 1.41082i
\(449\) 4920.17 0.517142 0.258571 0.965992i \(-0.416748\pi\)
0.258571 + 0.965992i \(0.416748\pi\)
\(450\) 0 0
\(451\) −6617.33 −0.690904
\(452\) −18322.9 13312.4i −1.90672 1.38531i
\(453\) 0 0
\(454\) 5765.09 + 17743.1i 0.595967 + 1.83420i
\(455\) −1865.44 2836.30i −0.192205 0.292237i
\(456\) 0 0
\(457\) 14959.5 1.53124 0.765621 0.643292i \(-0.222432\pi\)
0.765621 + 0.643292i \(0.222432\pi\)
\(458\) 1708.58 5258.47i 0.174316 0.536489i
\(459\) 0 0
\(460\) −262.221 98.9123i −0.0265785 0.0100257i
\(461\) −12555.3 9121.95i −1.26846 0.921587i −0.269316 0.963052i \(-0.586798\pi\)
−0.999140 + 0.0414644i \(0.986798\pi\)
\(462\) 0 0
\(463\) −11214.2 + 8147.57i −1.12563 + 0.817818i −0.985053 0.172251i \(-0.944896\pi\)
−0.140577 + 0.990070i \(0.544896\pi\)
\(464\) 1755.32 + 1275.32i 0.175623 + 0.127597i
\(465\) 0 0
\(466\) −3051.96 + 2217.38i −0.303389 + 0.220425i
\(467\) 3917.68 12057.4i 0.388199 1.19475i −0.545935 0.837828i \(-0.683825\pi\)
0.934133 0.356925i \(-0.116175\pi\)
\(468\) 0 0
\(469\) −4540.55 + 13974.4i −0.447042 + 1.37586i
\(470\) 23755.5 + 8960.79i 2.33140 + 0.879426i
\(471\) 0 0
\(472\) 5991.83 + 18441.0i 0.584314 + 1.79833i
\(473\) −2284.03 1659.44i −0.222029 0.161314i
\(474\) 0 0
\(475\) 6134.22 14220.3i 0.592542 1.37363i
\(476\) −22176.3 −2.13540
\(477\) 0 0
\(478\) 978.465 + 3011.41i 0.0936275 + 0.288156i
\(479\) 609.873 + 1876.99i 0.0581749 + 0.179044i 0.975921 0.218123i \(-0.0699934\pi\)
−0.917746 + 0.397167i \(0.869993\pi\)
\(480\) 0 0
\(481\) 1258.61 3873.61i 0.119309 0.367196i
\(482\) −22288.4 −2.10624
\(483\) 0 0
\(484\) 11468.0 8331.99i 1.07701 0.782494i
\(485\) 2782.03 762.803i 0.260465 0.0714167i
\(486\) 0 0
\(487\) 3127.00 2271.90i 0.290960 0.211395i −0.432724 0.901527i \(-0.642447\pi\)
0.723684 + 0.690132i \(0.242447\pi\)
\(488\) −11749.0 + 8536.12i −1.08986 + 0.791827i
\(489\) 0 0
\(490\) 18385.8 22976.4i 1.69507 2.11830i
\(491\) 13861.6 10071.1i 1.27407 0.925663i 0.274709 0.961527i \(-0.411418\pi\)
0.999357 + 0.0358642i \(0.0114184\pi\)
\(492\) 0 0
\(493\) 4613.18 0.421434
\(494\) −1825.18 + 5617.32i −0.166232 + 0.511609i
\(495\) 0 0
\(496\) 1127.64 + 3470.52i 0.102082 + 0.314176i
\(497\) 216.368 + 665.912i 0.0195280 + 0.0601011i
\(498\) 0 0
\(499\) 7564.31 0.678607 0.339303 0.940677i \(-0.389809\pi\)
0.339303 + 0.940677i \(0.389809\pi\)
\(500\) 19570.1 3450.42i 1.75040 0.308615i
\(501\) 0 0
\(502\) 26498.7 + 19252.4i 2.35596 + 1.71171i
\(503\) 1784.15 + 5491.04i 0.158153 + 0.486746i 0.998467 0.0553549i \(-0.0176290\pi\)
−0.840313 + 0.542101i \(0.817629\pi\)
\(504\) 0 0
\(505\) 169.102 3630.28i 0.0149009 0.319892i
\(506\) −46.9359 + 144.454i −0.00412362 + 0.0126912i
\(507\) 0 0
\(508\) 1837.41 5654.96i 0.160476 0.493894i
\(509\) 12222.1 8879.87i 1.06431 0.773268i 0.0894303 0.995993i \(-0.471495\pi\)
0.974881 + 0.222726i \(0.0714954\pi\)
\(510\) 0 0
\(511\) −8406.35 6107.57i −0.727739 0.528734i
\(512\) 6994.84 5082.05i 0.603772 0.438666i
\(513\) 0 0
\(514\) 29323.8 + 21305.0i 2.51638 + 1.82826i
\(515\) −17859.3 + 4896.81i −1.52810 + 0.418989i
\(516\) 0 0
\(517\) 2721.12 8374.74i 0.231479 0.712419i
\(518\) 56993.5 4.83427
\(519\) 0 0
\(520\) −3196.80 + 876.527i −0.269594 + 0.0739197i
\(521\) 805.776 + 2479.92i 0.0677576 + 0.208536i 0.979202 0.202886i \(-0.0650321\pi\)
−0.911445 + 0.411422i \(0.865032\pi\)
\(522\) 0 0
\(523\) 16751.5 + 12170.7i 1.40056 + 1.01756i 0.994612 + 0.103665i \(0.0330571\pi\)
0.405944 + 0.913898i \(0.366943\pi\)
\(524\) −19441.9 −1.62085
\(525\) 0 0
\(526\) −2229.10 −0.184778
\(527\) 6276.92 + 4560.45i 0.518837 + 0.376957i
\(528\) 0 0
\(529\) −3758.85 11568.5i −0.308938 0.950814i
\(530\) 35775.4 + 13494.8i 2.93205 + 1.10600i
\(531\) 0 0
\(532\) −52891.4 −4.31040
\(533\) −1131.45 + 3482.23i −0.0919482 + 0.282987i
\(534\) 0 0
\(535\) −740.335 + 15893.5i −0.0598271 + 1.28437i
\(536\) 11607.2 + 8433.15i 0.935366 + 0.679583i
\(537\) 0 0
\(538\) −26202.9 + 19037.6i −2.09979 + 1.52559i
\(539\) −8256.93 5999.01i −0.659835 0.479398i
\(540\) 0 0
\(541\) −3227.92 + 2345.22i −0.256523 + 0.186375i −0.708613 0.705597i \(-0.750679\pi\)
0.452090 + 0.891972i \(0.350679\pi\)
\(542\) −5491.61 + 16901.4i −0.435212 + 1.33944i
\(543\) 0 0
\(544\) 1916.01 5896.86i 0.151008 0.464754i
\(545\) −7687.01 11687.7i −0.604175 0.918613i
\(546\) 0 0
\(547\) 5000.73 + 15390.7i 0.390888 + 1.20303i 0.932118 + 0.362156i \(0.117959\pi\)
−0.541229 + 0.840875i \(0.682041\pi\)
\(548\) 22638.3 + 16447.7i 1.76471 + 1.28213i
\(549\) 0 0
\(550\) −2361.48 10507.7i −0.183080 0.814636i
\(551\) 11002.6 0.850685
\(552\) 0 0
\(553\) 6633.04 + 20414.4i 0.510064 + 1.56982i
\(554\) −11375.9 35011.6i −0.872415 2.68502i
\(555\) 0 0
\(556\) 10259.8 31576.4i 0.782576 2.40852i
\(557\) 7509.23 0.571232 0.285616 0.958344i \(-0.407802\pi\)
0.285616 + 0.958344i \(0.407802\pi\)
\(558\) 0 0
\(559\) −1263.78 + 918.188i −0.0956209 + 0.0694726i
\(560\) −4506.50 6851.88i −0.340062 0.517044i
\(561\) 0 0
\(562\) 3858.01 2803.01i 0.289574 0.210388i
\(563\) −8574.50 + 6229.74i −0.641869 + 0.466345i −0.860492 0.509464i \(-0.829844\pi\)
0.218623 + 0.975809i \(0.429844\pi\)
\(564\) 0 0
\(565\) −9785.61 14878.5i −0.728644 1.10786i
\(566\) 3852.30 2798.86i 0.286085 0.207853i
\(567\) 0 0
\(568\) 683.685 0.0505049
\(569\) −5959.06 + 18340.1i −0.439045 + 1.35124i 0.449838 + 0.893110i \(0.351482\pi\)
−0.888884 + 0.458133i \(0.848518\pi\)
\(570\) 0 0
\(571\) −3864.92 11895.0i −0.283261 0.871786i −0.986915 0.161244i \(-0.948449\pi\)
0.703654 0.710543i \(-0.251551\pi\)
\(572\) 812.255 + 2499.87i 0.0593743 + 0.182735i
\(573\) 0 0
\(574\) −51235.0 −3.72563
\(575\) −165.463 145.537i −0.0120005 0.0105553i
\(576\) 0 0
\(577\) −9726.10 7066.43i −0.701738 0.509843i 0.178760 0.983893i \(-0.442792\pi\)
−0.880498 + 0.474050i \(0.842792\pi\)
\(578\) −3225.70 9927.70i −0.232131 0.714425i
\(579\) 0 0
\(580\) 7757.85 + 11795.4i 0.555392 + 0.844442i
\(581\) 2823.11 8688.64i 0.201588 0.620423i
\(582\) 0 0
\(583\) 4097.97 12612.2i 0.291116 0.895962i
\(584\) −8208.29 + 5963.67i −0.581612 + 0.422566i
\(585\) 0 0
\(586\) −3340.41 2426.95i −0.235480 0.171086i
\(587\) −3939.75 + 2862.40i −0.277020 + 0.201267i −0.717617 0.696438i \(-0.754767\pi\)
0.440596 + 0.897705i \(0.354767\pi\)
\(588\) 0 0
\(589\) 14970.7 + 10876.9i 1.04730 + 0.760906i
\(590\) −1621.94 + 34819.9i −0.113177 + 2.42968i
\(591\) 0 0
\(592\) 3040.53 9357.80i 0.211090 0.649668i
\(593\) 17446.6 1.20817 0.604087 0.796918i \(-0.293538\pi\)
0.604087 + 0.796918i \(0.293538\pi\)
\(594\) 0 0
\(595\) −16314.8 6154.09i −1.12410 0.424022i
\(596\) 9429.44 + 29020.8i 0.648062 + 1.99453i
\(597\) 0 0
\(598\) 67.9906 + 49.3981i 0.00464940 + 0.00337799i
\(599\) −3313.42 −0.226014 −0.113007 0.993594i \(-0.536048\pi\)
−0.113007 + 0.993594i \(0.536048\pi\)
\(600\) 0 0
\(601\) 14375.6 0.975698 0.487849 0.872928i \(-0.337782\pi\)
0.487849 + 0.872928i \(0.337782\pi\)
\(602\) −17684.2 12848.3i −1.19727 0.869866i
\(603\) 0 0
\(604\) −8723.84 26849.2i −0.587695 1.80874i
\(605\) 10749.0 2947.27i 0.722331 0.198055i
\(606\) 0 0
\(607\) −18139.8 −1.21297 −0.606485 0.795095i \(-0.707421\pi\)
−0.606485 + 0.795095i \(0.707421\pi\)
\(608\) 4569.76 14064.3i 0.304816 0.938127i
\(609\) 0 0
\(610\) −25178.0 + 6903.54i −1.67119 + 0.458223i
\(611\) −3941.77 2863.87i −0.260994 0.189623i
\(612\) 0 0
\(613\) 7938.14 5767.40i 0.523032 0.380005i −0.294713 0.955586i \(-0.595224\pi\)
0.817745 + 0.575581i \(0.195224\pi\)
\(614\) −18737.1 13613.3i −1.23154 0.894768i
\(615\) 0 0
\(616\) −13015.0 + 9455.92i −0.851279 + 0.618490i
\(617\) 6604.87 20327.7i 0.430960 1.32636i −0.466211 0.884674i \(-0.654381\pi\)
0.897171 0.441684i \(-0.145619\pi\)
\(618\) 0 0
\(619\) −1887.91 + 5810.38i −0.122587 + 0.377284i −0.993454 0.114235i \(-0.963558\pi\)
0.870867 + 0.491519i \(0.163558\pi\)
\(620\) −1104.83 + 23718.6i −0.0715663 + 1.53639i
\(621\) 0 0
\(622\) −10686.7 32890.4i −0.688905 2.12023i
\(623\) 7274.17 + 5284.99i 0.467790 + 0.339870i
\(624\) 0 0
\(625\) 15355.0 + 2892.42i 0.982717 + 0.185115i
\(626\) −26220.2 −1.67408
\(627\) 0 0
\(628\) 8992.51 + 27676.1i 0.571401 + 1.75859i
\(629\) −6464.73 19896.4i −0.409802 1.26124i
\(630\) 0 0
\(631\) 1660.22 5109.62i 0.104742 0.322362i −0.884928 0.465728i \(-0.845792\pi\)
0.989670 + 0.143366i \(0.0457925\pi\)
\(632\) 20959.2 1.31917
\(633\) 0 0
\(634\) 23516.6 17085.8i 1.47313 1.07029i
\(635\) 2921.05 3650.38i 0.182548 0.228127i
\(636\) 0 0
\(637\) −4568.65 + 3319.32i −0.284170 + 0.206462i
\(638\) 6190.06 4497.34i 0.384117 0.279078i
\(639\) 0 0
\(640\) 28233.8 7741.40i 1.74381 0.478134i
\(641\) 3931.14 2856.14i 0.242232 0.175992i −0.460045 0.887896i \(-0.652167\pi\)
0.702277 + 0.711904i \(0.252167\pi\)
\(642\) 0 0
\(643\) −28678.3 −1.75889 −0.879443 0.476004i \(-0.842085\pi\)
−0.879443 + 0.476004i \(0.842085\pi\)
\(644\) −232.561 + 715.748i −0.0142301 + 0.0437957i
\(645\) 0 0
\(646\) 9374.83 + 28852.7i 0.570971 + 1.75727i
\(647\) −7092.34 21828.0i −0.430956 1.32635i −0.897174 0.441677i \(-0.854384\pi\)
0.466218 0.884670i \(-0.345616\pi\)
\(648\) 0 0
\(649\) 12089.6 0.731214
\(650\) −5933.24 553.953i −0.358032 0.0334274i
\(651\) 0 0
\(652\) 19456.2 + 14135.7i 1.16865 + 0.849077i
\(653\) 223.006 + 686.342i 0.0133643 + 0.0411311i 0.957516 0.288379i \(-0.0931164\pi\)
−0.944152 + 0.329510i \(0.893116\pi\)
\(654\) 0 0
\(655\) −14303.1 5395.27i −0.853235 0.321849i
\(656\) −2733.33 + 8412.32i −0.162681 + 0.500680i
\(657\) 0 0
\(658\) 21068.4 64841.9i 1.24823 3.84164i
\(659\) 4089.82 2971.43i 0.241755 0.175645i −0.460310 0.887758i \(-0.652262\pi\)
0.702065 + 0.712113i \(0.252262\pi\)
\(660\) 0 0
\(661\) 8085.92 + 5874.76i 0.475803 + 0.345691i 0.799699 0.600402i \(-0.204993\pi\)
−0.323896 + 0.946093i \(0.604993\pi\)
\(662\) −32263.4 + 23440.8i −1.89419 + 1.37621i
\(663\) 0 0
\(664\) −7216.87 5243.36i −0.421790 0.306449i
\(665\) −38911.4 14677.8i −2.26905 0.855909i
\(666\) 0 0
\(667\) 48.3779 148.892i 0.00280840 0.00864336i
\(668\) −11615.2 −0.672761
\(669\) 0 0
\(670\) 14173.0 + 21549.3i 0.817242 + 1.24257i
\(671\) 2798.07 + 8611.57i 0.160981 + 0.495448i
\(672\) 0 0
\(673\) −9263.26 6730.15i −0.530568 0.385480i 0.290002 0.957026i \(-0.406344\pi\)
−0.820570 + 0.571546i \(0.806344\pi\)
\(674\) −11353.8 −0.648861
\(675\) 0 0
\(676\) −29785.2 −1.69465
\(677\) 5591.20 + 4062.25i 0.317411 + 0.230613i 0.735070 0.677991i \(-0.237149\pi\)
−0.417659 + 0.908604i \(0.637149\pi\)
\(678\) 0 0
\(679\) −2393.78 7367.28i −0.135294 0.416392i
\(680\) −10637.8 + 13293.8i −0.599910 + 0.749696i
\(681\) 0 0
\(682\) 12868.4 0.722520
\(683\) 281.809 867.320i 0.0157879 0.0485902i −0.942852 0.333211i \(-0.891868\pi\)
0.958640 + 0.284621i \(0.0918678\pi\)
\(684\) 0 0
\(685\) 12090.3 + 18382.6i 0.674374 + 1.02535i
\(686\) −24659.0 17915.8i −1.37243 0.997127i
\(687\) 0 0
\(688\) −3053.01 + 2218.14i −0.169179 + 0.122916i
\(689\) −5936.26 4312.94i −0.328234 0.238476i
\(690\) 0 0
\(691\) −9916.86 + 7205.02i −0.545955 + 0.396660i −0.826292 0.563242i \(-0.809554\pi\)
0.280337 + 0.959902i \(0.409554\pi\)
\(692\) 1378.84 4243.62i 0.0757449 0.233119i
\(693\) 0 0
\(694\) −7181.09 + 22101.1i −0.392781 + 1.20886i
\(695\) 16310.7 20383.1i 0.890215 1.11248i
\(696\) 0 0
\(697\) 5811.55 + 17886.1i 0.315822 + 0.972001i
\(698\) −5286.50 3840.86i −0.286672 0.208279i
\(699\) 0 0
\(700\) −11700.8 52064.2i −0.631783 2.81120i
\(701\) 3564.19 0.192037 0.0960184 0.995380i \(-0.469389\pi\)
0.0960184 + 0.995380i \(0.469389\pi\)
\(702\) 0 0
\(703\) −15418.7 47453.7i −0.827205 2.54588i
\(704\) −4281.85 13178.2i −0.229230 0.705498i
\(705\) 0 0
\(706\) 12416.8 38215.1i 0.661917 2.03717i
\(707\) −9759.10 −0.519135
\(708\) 0 0
\(709\) −244.783 + 177.845i −0.0129662 + 0.00942046i −0.594249 0.804281i \(-0.702551\pi\)
0.581283 + 0.813701i \(0.302551\pi\)
\(710\) 1149.98 + 433.782i 0.0607857 + 0.0229289i
\(711\) 0 0
\(712\) 7102.79 5160.48i 0.373860 0.271625i
\(713\) 213.016 154.765i 0.0111886 0.00812903i
\(714\) 0 0
\(715\) −96.1672 + 2064.52i −0.00503000 + 0.107984i
\(716\) 27748.1 20160.2i 1.44832 1.05226i
\(717\) 0 0
\(718\) −12308.5 −0.639763
\(719\) −1252.88 + 3855.98i −0.0649857 + 0.200005i −0.978277 0.207301i \(-0.933532\pi\)
0.913291 + 0.407307i \(0.133532\pi\)
\(720\) 0 0
\(721\) 15366.8 + 47294.3i 0.793746 + 2.44290i
\(722\) 12368.4 + 38066.0i 0.637540 + 1.96215i
\(723\) 0 0
\(724\) −13789.7 −0.707860
\(725\) 2434.03 + 10830.5i 0.124686 + 0.554809i
\(726\) 0 0
\(727\) 7113.44 + 5168.22i 0.362893 + 0.263657i 0.754258 0.656579i \(-0.227997\pi\)
−0.391365 + 0.920236i \(0.627997\pi\)
\(728\) 2750.66 + 8465.65i 0.140036 + 0.430986i
\(729\) 0 0
\(730\) −17590.4 + 4823.09i −0.891848 + 0.244535i
\(731\) −2479.44 + 7630.93i −0.125452 + 0.386101i
\(732\) 0 0
\(733\) 6934.01 21340.7i 0.349405 1.07536i −0.609779 0.792572i \(-0.708742\pi\)
0.959183 0.282785i \(-0.0912583\pi\)
\(734\) −32499.3 + 23612.1i −1.63429 + 1.18738i
\(735\) 0 0
\(736\) −170.230 123.680i −0.00852551 0.00619415i
\(737\) 7237.07 5258.04i 0.361711 0.262798i
\(738\) 0 0
\(739\) −13666.6 9929.34i −0.680288 0.494258i 0.193165 0.981166i \(-0.438125\pi\)
−0.873453 + 0.486908i \(0.838125\pi\)
\(740\) 40001.3 49988.8i 1.98713 2.48328i
\(741\) 0 0
\(742\) 31728.7 97651.0i 1.56981 4.83138i
\(743\) −26236.6 −1.29546 −0.647730 0.761870i \(-0.724281\pi\)
−0.647730 + 0.761870i \(0.724281\pi\)
\(744\) 0 0
\(745\) −1116.40 + 23966.9i −0.0549017 + 1.17863i
\(746\) −12658.0 38957.2i −0.621235 1.91196i
\(747\) 0 0
\(748\) 10922.6 + 7935.74i 0.533917 + 0.387913i
\(749\) 42725.7 2.08433
\(750\) 0 0
\(751\) −562.279 −0.0273207 −0.0136604 0.999907i \(-0.504348\pi\)
−0.0136604 + 0.999907i \(0.504348\pi\)
\(752\) −9522.46 6918.48i −0.461767 0.335493i
\(753\) 0 0
\(754\) −1308.24 4026.36i −0.0631875 0.194471i
\(755\) 1032.86 22173.5i 0.0497877 1.06884i
\(756\) 0 0
\(757\) −6641.56 −0.318879 −0.159440 0.987208i \(-0.550969\pi\)
−0.159440 + 0.987208i \(0.550969\pi\)
\(758\) −2736.50 + 8422.08i −0.131127 + 0.403567i
\(759\) 0 0
\(760\) −25371.5 + 31706.2i −1.21095 + 1.51330i
\(761\) 16269.3 + 11820.3i 0.774981 + 0.563056i 0.903468 0.428655i \(-0.141012\pi\)
−0.128488 + 0.991711i \(0.541012\pi\)
\(762\) 0 0
\(763\) −30390.8 + 22080.2i −1.44197 + 1.04765i
\(764\) 58017.8 + 42152.4i 2.74740 + 1.99610i
\(765\) 0 0
\(766\) −13198.4 + 9589.20i −0.622556 + 0.452313i
\(767\) 2067.11 6361.90i 0.0973127 0.299498i
\(768\) 0 0
\(769\) −4878.26 + 15013.7i −0.228757 + 0.704043i 0.769131 + 0.639091i \(0.220689\pi\)
−0.997888 + 0.0649518i \(0.979311\pi\)
\(770\) −27891.1 + 7647.42i −1.30536 + 0.357914i
\(771\) 0 0
\(772\) 15773.9 + 48547.0i 0.735381 + 2.26327i
\(773\) −32460.8 23584.1i −1.51039 1.09736i −0.966003 0.258533i \(-0.916761\pi\)
−0.544390 0.838832i \(-0.683239\pi\)
\(774\) 0 0
\(775\) −7394.89 + 17142.8i −0.342751 + 0.794565i
\(776\) −7563.91 −0.349908
\(777\) 0 0
\(778\) −6824.37 21003.2i −0.314480 0.967870i
\(779\) 13860.8 + 42659.1i 0.637503 + 1.96203i
\(780\) 0 0
\(781\) 131.726 405.412i 0.00603526 0.0185746i
\(782\) 431.668 0.0197397