Properties

Label 234.4.h.b.55.1
Level $234$
Weight $4$
Character 234.55
Analytic conductor $13.806$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [234,4,Mod(55,234)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(234, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("234.55");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 234 = 2 \cdot 3^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 234.h (of order \(3\), 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: \(13.8064469413\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 26)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 55.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 234.55
Dual form 234.4.h.b.217.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} -2.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +8.00000 q^{8} +O(q^{10})\) \(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} -2.00000 q^{5} +(2.50000 - 4.33013i) q^{7} +8.00000 q^{8} +(2.00000 + 3.46410i) q^{10} +(6.50000 + 11.2583i) q^{11} +(-13.0000 - 45.0333i) q^{13} -10.0000 q^{14} +(-8.00000 - 13.8564i) q^{16} +(13.5000 - 23.3827i) q^{17} +(-37.5000 + 64.9519i) q^{19} +(4.00000 - 6.92820i) q^{20} +(13.0000 - 22.5167i) q^{22} +(-93.5000 - 161.947i) q^{23} -121.000 q^{25} +(-65.0000 + 67.5500i) q^{26} +(10.0000 + 17.3205i) q^{28} +(-6.50000 - 11.2583i) q^{29} -104.000 q^{31} +(-16.0000 + 27.7128i) q^{32} -54.0000 q^{34} +(-5.00000 + 8.66025i) q^{35} +(-211.500 - 366.329i) q^{37} +150.000 q^{38} -16.0000 q^{40} +(97.5000 + 168.875i) q^{41} +(-99.5000 + 172.339i) q^{43} -52.0000 q^{44} +(-187.000 + 323.894i) q^{46} -388.000 q^{47} +(159.000 + 275.396i) q^{49} +(121.000 + 209.578i) q^{50} +(182.000 + 45.0333i) q^{52} -618.000 q^{53} +(-13.0000 - 22.5167i) q^{55} +(20.0000 - 34.6410i) q^{56} +(-13.0000 + 22.5167i) q^{58} +(245.500 - 425.218i) q^{59} +(-87.5000 + 151.554i) q^{61} +(104.000 + 180.133i) q^{62} +64.0000 q^{64} +(26.0000 + 90.0666i) q^{65} +(-408.500 - 707.543i) q^{67} +(54.0000 + 93.5307i) q^{68} +20.0000 q^{70} +(39.5000 - 68.4160i) q^{71} +230.000 q^{73} +(-423.000 + 732.657i) q^{74} +(-150.000 - 259.808i) q^{76} +65.0000 q^{77} +764.000 q^{79} +(16.0000 + 27.7128i) q^{80} +(195.000 - 337.750i) q^{82} +732.000 q^{83} +(-27.0000 + 46.7654i) q^{85} +398.000 q^{86} +(52.0000 + 90.0666i) q^{88} +(-520.500 - 901.532i) q^{89} +(-227.500 - 56.2917i) q^{91} +748.000 q^{92} +(388.000 + 672.036i) q^{94} +(75.0000 - 129.904i) q^{95} +(48.5000 - 84.0045i) q^{97} +(318.000 - 550.792i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{2} - 4 q^{4} - 4 q^{5} + 5 q^{7} + 16 q^{8} + 4 q^{10} + 13 q^{11} - 26 q^{13} - 20 q^{14} - 16 q^{16} + 27 q^{17} - 75 q^{19} + 8 q^{20} + 26 q^{22} - 187 q^{23} - 242 q^{25} - 130 q^{26} + 20 q^{28} - 13 q^{29} - 208 q^{31} - 32 q^{32} - 108 q^{34} - 10 q^{35} - 423 q^{37} + 300 q^{38} - 32 q^{40} + 195 q^{41} - 199 q^{43} - 104 q^{44} - 374 q^{46} - 776 q^{47} + 318 q^{49} + 242 q^{50} + 364 q^{52} - 1236 q^{53} - 26 q^{55} + 40 q^{56} - 26 q^{58} + 491 q^{59} - 175 q^{61} + 208 q^{62} + 128 q^{64} + 52 q^{65} - 817 q^{67} + 108 q^{68} + 40 q^{70} + 79 q^{71} + 460 q^{73} - 846 q^{74} - 300 q^{76} + 130 q^{77} + 1528 q^{79} + 32 q^{80} + 390 q^{82} + 1464 q^{83} - 54 q^{85} + 796 q^{86} + 104 q^{88} - 1041 q^{89} - 455 q^{91} + 1496 q^{92} + 776 q^{94} + 150 q^{95} + 97 q^{97} + 636 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/234\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.73205i −0.353553 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −2.00000 −0.178885 −0.0894427 0.995992i \(-0.528509\pi\)
−0.0894427 + 0.995992i \(0.528509\pi\)
\(6\) 0 0
\(7\) 2.50000 4.33013i 0.134987 0.233805i −0.790605 0.612326i \(-0.790234\pi\)
0.925593 + 0.378521i \(0.123567\pi\)
\(8\) 8.00000 0.353553
\(9\) 0 0
\(10\) 2.00000 + 3.46410i 0.0632456 + 0.109545i
\(11\) 6.50000 + 11.2583i 0.178166 + 0.308592i 0.941252 0.337704i \(-0.109650\pi\)
−0.763087 + 0.646296i \(0.776317\pi\)
\(12\) 0 0
\(13\) −13.0000 45.0333i −0.277350 0.960769i
\(14\) −10.0000 −0.190901
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 13.5000 23.3827i 0.192602 0.333596i −0.753510 0.657437i \(-0.771641\pi\)
0.946112 + 0.323840i \(0.104974\pi\)
\(18\) 0 0
\(19\) −37.5000 + 64.9519i −0.452794 + 0.784263i −0.998558 0.0536762i \(-0.982906\pi\)
0.545764 + 0.837939i \(0.316239\pi\)
\(20\) 4.00000 6.92820i 0.0447214 0.0774597i
\(21\) 0 0
\(22\) 13.0000 22.5167i 0.125982 0.218208i
\(23\) −93.5000 161.947i −0.847656 1.46818i −0.883294 0.468819i \(-0.844680\pi\)
0.0356377 0.999365i \(-0.488654\pi\)
\(24\) 0 0
\(25\) −121.000 −0.968000
\(26\) −65.0000 + 67.5500i −0.490290 + 0.509525i
\(27\) 0 0
\(28\) 10.0000 + 17.3205i 0.0674937 + 0.116902i
\(29\) −6.50000 11.2583i −0.0416214 0.0720903i 0.844464 0.535612i \(-0.179919\pi\)
−0.886086 + 0.463522i \(0.846586\pi\)
\(30\) 0 0
\(31\) −104.000 −0.602547 −0.301273 0.953538i \(-0.597412\pi\)
−0.301273 + 0.953538i \(0.597412\pi\)
\(32\) −16.0000 + 27.7128i −0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −54.0000 −0.272380
\(35\) −5.00000 + 8.66025i −0.0241473 + 0.0418243i
\(36\) 0 0
\(37\) −211.500 366.329i −0.939740 1.62768i −0.765955 0.642894i \(-0.777734\pi\)
−0.173785 0.984784i \(-0.555600\pi\)
\(38\) 150.000 0.640348
\(39\) 0 0
\(40\) −16.0000 −0.0632456
\(41\) 97.5000 + 168.875i 0.371389 + 0.643264i 0.989779 0.142607i \(-0.0455484\pi\)
−0.618391 + 0.785871i \(0.712215\pi\)
\(42\) 0 0
\(43\) −99.5000 + 172.339i −0.352875 + 0.611197i −0.986752 0.162237i \(-0.948129\pi\)
0.633877 + 0.773434i \(0.281462\pi\)
\(44\) −52.0000 −0.178166
\(45\) 0 0
\(46\) −187.000 + 323.894i −0.599384 + 1.03816i
\(47\) −388.000 −1.20416 −0.602081 0.798435i \(-0.705662\pi\)
−0.602081 + 0.798435i \(0.705662\pi\)
\(48\) 0 0
\(49\) 159.000 + 275.396i 0.463557 + 0.802904i
\(50\) 121.000 + 209.578i 0.342240 + 0.592777i
\(51\) 0 0
\(52\) 182.000 + 45.0333i 0.485363 + 0.120096i
\(53\) −618.000 −1.60168 −0.800838 0.598881i \(-0.795612\pi\)
−0.800838 + 0.598881i \(0.795612\pi\)
\(54\) 0 0
\(55\) −13.0000 22.5167i −0.0318713 0.0552027i
\(56\) 20.0000 34.6410i 0.0477252 0.0826625i
\(57\) 0 0
\(58\) −13.0000 + 22.5167i −0.0294308 + 0.0509756i
\(59\) 245.500 425.218i 0.541718 0.938284i −0.457087 0.889422i \(-0.651107\pi\)
0.998806 0.0488617i \(-0.0155594\pi\)
\(60\) 0 0
\(61\) −87.5000 + 151.554i −0.183659 + 0.318108i −0.943124 0.332441i \(-0.892128\pi\)
0.759465 + 0.650549i \(0.225461\pi\)
\(62\) 104.000 + 180.133i 0.213032 + 0.368983i
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 26.0000 + 90.0666i 0.0496139 + 0.171868i
\(66\) 0 0
\(67\) −408.500 707.543i −0.744869 1.29015i −0.950256 0.311470i \(-0.899179\pi\)
0.205387 0.978681i \(-0.434155\pi\)
\(68\) 54.0000 + 93.5307i 0.0963009 + 0.166798i
\(69\) 0 0
\(70\) 20.0000 0.0341494
\(71\) 39.5000 68.4160i 0.0660252 0.114359i −0.831123 0.556088i \(-0.812302\pi\)
0.897148 + 0.441729i \(0.145635\pi\)
\(72\) 0 0
\(73\) 230.000 0.368760 0.184380 0.982855i \(-0.440972\pi\)
0.184380 + 0.982855i \(0.440972\pi\)
\(74\) −423.000 + 732.657i −0.664497 + 1.15094i
\(75\) 0 0
\(76\) −150.000 259.808i −0.226397 0.392131i
\(77\) 65.0000 0.0962005
\(78\) 0 0
\(79\) 764.000 1.08806 0.544030 0.839066i \(-0.316898\pi\)
0.544030 + 0.839066i \(0.316898\pi\)
\(80\) 16.0000 + 27.7128i 0.0223607 + 0.0387298i
\(81\) 0 0
\(82\) 195.000 337.750i 0.262612 0.454857i
\(83\) 732.000 0.968041 0.484021 0.875057i \(-0.339176\pi\)
0.484021 + 0.875057i \(0.339176\pi\)
\(84\) 0 0
\(85\) −27.0000 + 46.7654i −0.0344537 + 0.0596755i
\(86\) 398.000 0.499040
\(87\) 0 0
\(88\) 52.0000 + 90.0666i 0.0629911 + 0.109104i
\(89\) −520.500 901.532i −0.619920 1.07373i −0.989500 0.144534i \(-0.953832\pi\)
0.369580 0.929199i \(-0.379502\pi\)
\(90\) 0 0
\(91\) −227.500 56.2917i −0.262071 0.0648458i
\(92\) 748.000 0.847656
\(93\) 0 0
\(94\) 388.000 + 672.036i 0.425736 + 0.737396i
\(95\) 75.0000 129.904i 0.0809983 0.140293i
\(96\) 0 0
\(97\) 48.5000 84.0045i 0.0507673 0.0879316i −0.839525 0.543321i \(-0.817167\pi\)
0.890292 + 0.455389i \(0.150500\pi\)
\(98\) 318.000 550.792i 0.327784 0.567739i
\(99\) 0 0
\(100\) 242.000 419.156i 0.242000 0.419156i
\(101\) −404.500 700.615i −0.398507 0.690235i 0.595035 0.803700i \(-0.297138\pi\)
−0.993542 + 0.113465i \(0.963805\pi\)
\(102\) 0 0
\(103\) 1288.00 1.23214 0.616070 0.787691i \(-0.288724\pi\)
0.616070 + 0.787691i \(0.288724\pi\)
\(104\) −104.000 360.267i −0.0980581 0.339683i
\(105\) 0 0
\(106\) 618.000 + 1070.41i 0.566278 + 0.980822i
\(107\) 638.500 + 1105.91i 0.576880 + 0.999185i 0.995835 + 0.0911779i \(0.0290632\pi\)
−0.418955 + 0.908007i \(0.637603\pi\)
\(108\) 0 0
\(109\) 826.000 0.725839 0.362920 0.931820i \(-0.381780\pi\)
0.362920 + 0.931820i \(0.381780\pi\)
\(110\) −26.0000 + 45.0333i −0.0225364 + 0.0390342i
\(111\) 0 0
\(112\) −80.0000 −0.0674937
\(113\) 473.500 820.126i 0.394187 0.682752i −0.598810 0.800891i \(-0.704360\pi\)
0.992997 + 0.118139i \(0.0376929\pi\)
\(114\) 0 0
\(115\) 187.000 + 323.894i 0.151633 + 0.262637i
\(116\) 52.0000 0.0416214
\(117\) 0 0
\(118\) −982.000 −0.766105
\(119\) −67.5000 116.913i −0.0519976 0.0900625i
\(120\) 0 0
\(121\) 581.000 1006.32i 0.436514 0.756064i
\(122\) 350.000 0.259734
\(123\) 0 0
\(124\) 208.000 360.267i 0.150637 0.260910i
\(125\) 492.000 0.352047
\(126\) 0 0
\(127\) −588.500 1019.31i −0.411188 0.712199i 0.583832 0.811875i \(-0.301553\pi\)
−0.995020 + 0.0996756i \(0.968220\pi\)
\(128\) −64.0000 110.851i −0.0441942 0.0765466i
\(129\) 0 0
\(130\) 130.000 135.100i 0.0877058 0.0911465i
\(131\) 1420.00 0.947069 0.473534 0.880775i \(-0.342978\pi\)
0.473534 + 0.880775i \(0.342978\pi\)
\(132\) 0 0
\(133\) 187.500 + 324.760i 0.122243 + 0.211731i
\(134\) −817.000 + 1415.09i −0.526702 + 0.912274i
\(135\) 0 0
\(136\) 108.000 187.061i 0.0680950 0.117944i
\(137\) −1204.50 + 2086.26i −0.751149 + 1.30103i 0.196118 + 0.980580i \(0.437167\pi\)
−0.947266 + 0.320447i \(0.896167\pi\)
\(138\) 0 0
\(139\) −1413.50 + 2448.25i −0.862529 + 1.49394i 0.00695133 + 0.999976i \(0.497787\pi\)
−0.869480 + 0.493968i \(0.835546\pi\)
\(140\) −20.0000 34.6410i −0.0120736 0.0209121i
\(141\) 0 0
\(142\) −158.000 −0.0933737
\(143\) 422.500 439.075i 0.247072 0.256764i
\(144\) 0 0
\(145\) 13.0000 + 22.5167i 0.00744546 + 0.0128959i
\(146\) −230.000 398.372i −0.130376 0.225818i
\(147\) 0 0
\(148\) 1692.00 0.939740
\(149\) 427.500 740.452i 0.235048 0.407115i −0.724239 0.689549i \(-0.757809\pi\)
0.959287 + 0.282434i \(0.0911419\pi\)
\(150\) 0 0
\(151\) 2064.00 1.11236 0.556179 0.831063i \(-0.312267\pi\)
0.556179 + 0.831063i \(0.312267\pi\)
\(152\) −300.000 + 519.615i −0.160087 + 0.277279i
\(153\) 0 0
\(154\) −65.0000 112.583i −0.0340120 0.0589105i
\(155\) 208.000 0.107787
\(156\) 0 0
\(157\) −1894.00 −0.962788 −0.481394 0.876504i \(-0.659869\pi\)
−0.481394 + 0.876504i \(0.659869\pi\)
\(158\) −764.000 1323.29i −0.384687 0.666298i
\(159\) 0 0
\(160\) 32.0000 55.4256i 0.0158114 0.0273861i
\(161\) −935.000 −0.457691
\(162\) 0 0
\(163\) 492.500 853.035i 0.236660 0.409907i −0.723094 0.690750i \(-0.757281\pi\)
0.959754 + 0.280843i \(0.0906139\pi\)
\(164\) −780.000 −0.371389
\(165\) 0 0
\(166\) −732.000 1267.86i −0.342254 0.592802i
\(167\) −1177.50 2039.49i −0.545615 0.945033i −0.998568 0.0534983i \(-0.982963\pi\)
0.452953 0.891534i \(-0.350371\pi\)
\(168\) 0 0
\(169\) −1859.00 + 1170.87i −0.846154 + 0.532939i
\(170\) 108.000 0.0487248
\(171\) 0 0
\(172\) −398.000 689.356i −0.176437 0.305598i
\(173\) −1944.50 + 3367.97i −0.854553 + 1.48013i 0.0225069 + 0.999747i \(0.492835\pi\)
−0.877059 + 0.480382i \(0.840498\pi\)
\(174\) 0 0
\(175\) −302.500 + 523.945i −0.130668 + 0.226323i
\(176\) 104.000 180.133i 0.0445414 0.0771481i
\(177\) 0 0
\(178\) −1041.00 + 1803.06i −0.438350 + 0.759244i
\(179\) 1114.50 + 1930.37i 0.465372 + 0.806048i 0.999218 0.0395333i \(-0.0125871\pi\)
−0.533846 + 0.845582i \(0.679254\pi\)
\(180\) 0 0
\(181\) −1038.00 −0.426265 −0.213132 0.977023i \(-0.568367\pi\)
−0.213132 + 0.977023i \(0.568367\pi\)
\(182\) 130.000 + 450.333i 0.0529464 + 0.183412i
\(183\) 0 0
\(184\) −748.000 1295.57i −0.299692 0.519081i
\(185\) 423.000 + 732.657i 0.168106 + 0.291168i
\(186\) 0 0
\(187\) 351.000 0.137260
\(188\) 776.000 1344.07i 0.301041 0.521417i
\(189\) 0 0
\(190\) −300.000 −0.114549
\(191\) −1070.50 + 1854.16i −0.405543 + 0.702421i −0.994384 0.105828i \(-0.966251\pi\)
0.588842 + 0.808248i \(0.299584\pi\)
\(192\) 0 0
\(193\) −1313.50 2275.05i −0.489885 0.848506i 0.510047 0.860146i \(-0.329628\pi\)
−0.999932 + 0.0116407i \(0.996295\pi\)
\(194\) −194.000 −0.0717958
\(195\) 0 0
\(196\) −1272.00 −0.463557
\(197\) 601.500 + 1041.83i 0.217539 + 0.376788i 0.954055 0.299632i \(-0.0968639\pi\)
−0.736516 + 0.676420i \(0.763531\pi\)
\(198\) 0 0
\(199\) −371.500 + 643.457i −0.132336 + 0.229213i −0.924577 0.380996i \(-0.875581\pi\)
0.792240 + 0.610209i \(0.208915\pi\)
\(200\) −968.000 −0.342240
\(201\) 0 0
\(202\) −809.000 + 1401.23i −0.281787 + 0.488070i
\(203\) −65.0000 −0.0224734
\(204\) 0 0
\(205\) −195.000 337.750i −0.0664361 0.115071i
\(206\) −1288.00 2230.88i −0.435627 0.754529i
\(207\) 0 0
\(208\) −520.000 + 540.400i −0.173344 + 0.180144i
\(209\) −975.000 −0.322690
\(210\) 0 0
\(211\) 177.500 + 307.439i 0.0579128 + 0.100308i 0.893528 0.449007i \(-0.148222\pi\)
−0.835615 + 0.549315i \(0.814889\pi\)
\(212\) 1236.00 2140.81i 0.400419 0.693546i
\(213\) 0 0
\(214\) 1277.00 2211.83i 0.407916 0.706530i
\(215\) 199.000 344.678i 0.0631241 0.109334i
\(216\) 0 0
\(217\) −260.000 + 450.333i −0.0813362 + 0.140878i
\(218\) −826.000 1430.67i −0.256623 0.444484i
\(219\) 0 0
\(220\) 104.000 0.0318713
\(221\) −1228.50 303.975i −0.373927 0.0925229i
\(222\) 0 0
\(223\) 1141.50 + 1977.14i 0.342782 + 0.593717i 0.984948 0.172849i \(-0.0552973\pi\)
−0.642166 + 0.766566i \(0.721964\pi\)
\(224\) 80.0000 + 138.564i 0.0238626 + 0.0413313i
\(225\) 0 0
\(226\) −1894.00 −0.557465
\(227\) 1225.50 2122.63i 0.358323 0.620633i −0.629358 0.777116i \(-0.716682\pi\)
0.987681 + 0.156482i \(0.0500154\pi\)
\(228\) 0 0
\(229\) −1878.00 −0.541929 −0.270964 0.962589i \(-0.587343\pi\)
−0.270964 + 0.962589i \(0.587343\pi\)
\(230\) 374.000 647.787i 0.107221 0.185712i
\(231\) 0 0
\(232\) −52.0000 90.0666i −0.0147154 0.0254878i
\(233\) −1630.00 −0.458304 −0.229152 0.973391i \(-0.573595\pi\)
−0.229152 + 0.973391i \(0.573595\pi\)
\(234\) 0 0
\(235\) 776.000 0.215407
\(236\) 982.000 + 1700.87i 0.270859 + 0.469142i
\(237\) 0 0
\(238\) −135.000 + 233.827i −0.0367679 + 0.0636838i
\(239\) 5544.00 1.50047 0.750233 0.661173i \(-0.229941\pi\)
0.750233 + 0.661173i \(0.229941\pi\)
\(240\) 0 0
\(241\) −2761.50 + 4783.06i −0.738107 + 1.27844i 0.215239 + 0.976561i \(0.430947\pi\)
−0.953347 + 0.301878i \(0.902386\pi\)
\(242\) −2324.00 −0.617324
\(243\) 0 0
\(244\) −350.000 606.218i −0.0918297 0.159054i
\(245\) −318.000 550.792i −0.0829236 0.143628i
\(246\) 0 0
\(247\) 3412.50 + 844.375i 0.879078 + 0.217515i
\(248\) −832.000 −0.213032
\(249\) 0 0
\(250\) −492.000 852.169i −0.124467 0.215584i
\(251\) 1087.50 1883.61i 0.273476 0.473674i −0.696274 0.717776i \(-0.745160\pi\)
0.969749 + 0.244103i \(0.0784934\pi\)
\(252\) 0 0
\(253\) 1215.50 2105.31i 0.302047 0.523160i
\(254\) −1177.00 + 2038.62i −0.290754 + 0.503601i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −2842.50 4923.35i −0.689923 1.19498i −0.971862 0.235550i \(-0.924311\pi\)
0.281939 0.959432i \(-0.409022\pi\)
\(258\) 0 0
\(259\) −2115.00 −0.507412
\(260\) −364.000 90.0666i −0.0868243 0.0214834i
\(261\) 0 0
\(262\) −1420.00 2459.51i −0.334839 0.579959i
\(263\) 3058.50 + 5297.48i 0.717092 + 1.24204i 0.962147 + 0.272531i \(0.0878606\pi\)
−0.245055 + 0.969509i \(0.578806\pi\)
\(264\) 0 0
\(265\) 1236.00 0.286517
\(266\) 375.000 649.519i 0.0864388 0.149716i
\(267\) 0 0
\(268\) 3268.00 0.744869
\(269\) −2554.50 + 4424.52i −0.578999 + 1.00285i 0.416596 + 0.909092i \(0.363223\pi\)
−0.995595 + 0.0937632i \(0.970110\pi\)
\(270\) 0 0
\(271\) −3774.50 6537.63i −0.846068 1.46543i −0.884690 0.466180i \(-0.845630\pi\)
0.0386217 0.999254i \(-0.487703\pi\)
\(272\) −432.000 −0.0963009
\(273\) 0 0
\(274\) 4818.00 1.06228
\(275\) −786.500 1362.26i −0.172464 0.298717i
\(276\) 0 0
\(277\) 490.500 849.571i 0.106395 0.184281i −0.807913 0.589302i \(-0.799403\pi\)
0.914307 + 0.405022i \(0.132736\pi\)
\(278\) 5654.00 1.21980
\(279\) 0 0
\(280\) −40.0000 + 69.2820i −0.00853735 + 0.0147871i
\(281\) 2762.00 0.586360 0.293180 0.956057i \(-0.405287\pi\)
0.293180 + 0.956057i \(0.405287\pi\)
\(282\) 0 0
\(283\) −1962.50 3399.15i −0.412221 0.713988i 0.582911 0.812536i \(-0.301913\pi\)
−0.995132 + 0.0985482i \(0.968580\pi\)
\(284\) 158.000 + 273.664i 0.0330126 + 0.0571795i
\(285\) 0 0
\(286\) −1183.00 292.717i −0.244588 0.0605199i
\(287\) 975.000 0.200531
\(288\) 0 0
\(289\) 2092.00 + 3623.45i 0.425809 + 0.737523i
\(290\) 26.0000 45.0333i 0.00526473 0.00911879i
\(291\) 0 0
\(292\) −460.000 + 796.743i −0.0921899 + 0.159678i
\(293\) 3855.50 6677.92i 0.768740 1.33150i −0.169507 0.985529i \(-0.554218\pi\)
0.938247 0.345967i \(-0.112449\pi\)
\(294\) 0 0
\(295\) −491.000 + 850.437i −0.0969055 + 0.167845i
\(296\) −1692.00 2930.63i −0.332248 0.575471i
\(297\) 0 0
\(298\) −1710.00 −0.332408
\(299\) −6077.50 + 6315.92i −1.17549 + 1.22160i
\(300\) 0 0
\(301\) 497.500 + 861.695i 0.0952672 + 0.165008i
\(302\) −2064.00 3574.95i −0.393278 0.681177i
\(303\) 0 0
\(304\) 1200.00 0.226397
\(305\) 175.000 303.109i 0.0328540 0.0569048i
\(306\) 0 0
\(307\) 10388.0 1.93119 0.965594 0.260056i \(-0.0837409\pi\)
0.965594 + 0.260056i \(0.0837409\pi\)
\(308\) −130.000 + 225.167i −0.0240501 + 0.0416560i
\(309\) 0 0
\(310\) −208.000 360.267i −0.0381084 0.0660057i
\(311\) 7272.00 1.32591 0.662954 0.748660i \(-0.269303\pi\)
0.662954 + 0.748660i \(0.269303\pi\)
\(312\) 0 0
\(313\) 7910.00 1.42843 0.714217 0.699925i \(-0.246783\pi\)
0.714217 + 0.699925i \(0.246783\pi\)
\(314\) 1894.00 + 3280.50i 0.340397 + 0.589585i
\(315\) 0 0
\(316\) −1528.00 + 2646.57i −0.272015 + 0.471144i
\(317\) −7398.00 −1.31077 −0.655383 0.755296i \(-0.727493\pi\)
−0.655383 + 0.755296i \(0.727493\pi\)
\(318\) 0 0
\(319\) 84.5000 146.358i 0.0148310 0.0256881i
\(320\) −128.000 −0.0223607
\(321\) 0 0
\(322\) 935.000 + 1619.47i 0.161818 + 0.280278i
\(323\) 1012.50 + 1753.70i 0.174418 + 0.302101i
\(324\) 0 0
\(325\) 1573.00 + 5449.03i 0.268475 + 0.930024i
\(326\) −1970.00 −0.334688
\(327\) 0 0
\(328\) 780.000 + 1351.00i 0.131306 + 0.227428i
\(329\) −970.000 + 1680.09i −0.162547 + 0.281539i
\(330\) 0 0
\(331\) 1188.50 2058.54i 0.197359 0.341836i −0.750312 0.661084i \(-0.770097\pi\)
0.947671 + 0.319248i \(0.103430\pi\)
\(332\) −1464.00 + 2535.72i −0.242010 + 0.419174i
\(333\) 0 0
\(334\) −2355.00 + 4078.98i −0.385808 + 0.668239i
\(335\) 817.000 + 1415.09i 0.133246 + 0.230789i
\(336\) 0 0
\(337\) −7618.00 −1.23139 −0.615696 0.787984i \(-0.711125\pi\)
−0.615696 + 0.787984i \(0.711125\pi\)
\(338\) 3887.00 + 2049.02i 0.625518 + 0.329739i
\(339\) 0 0
\(340\) −108.000 187.061i −0.0172268 0.0298377i
\(341\) −676.000 1170.87i −0.107353 0.185941i
\(342\) 0 0
\(343\) 3305.00 0.520272
\(344\) −796.000 + 1378.71i −0.124760 + 0.216091i
\(345\) 0 0
\(346\) 7778.00 1.20852
\(347\) 187.500 324.760i 0.0290073 0.0502421i −0.851157 0.524911i \(-0.824099\pi\)
0.880165 + 0.474669i \(0.157432\pi\)
\(348\) 0 0
\(349\) −4863.50 8423.83i −0.745952 1.29203i −0.949749 0.313013i \(-0.898662\pi\)
0.203797 0.979013i \(-0.434672\pi\)
\(350\) 1210.00 0.184792
\(351\) 0 0
\(352\) −416.000 −0.0629911
\(353\) 1131.50 + 1959.82i 0.170605 + 0.295497i 0.938632 0.344921i \(-0.112094\pi\)
−0.768026 + 0.640418i \(0.778761\pi\)
\(354\) 0 0
\(355\) −79.0000 + 136.832i −0.0118109 + 0.0204572i
\(356\) 4164.00 0.619920
\(357\) 0 0
\(358\) 2229.00 3860.74i 0.329068 0.569962i
\(359\) 4488.00 0.659798 0.329899 0.944016i \(-0.392985\pi\)
0.329899 + 0.944016i \(0.392985\pi\)
\(360\) 0 0
\(361\) 617.000 + 1068.68i 0.0899548 + 0.155806i
\(362\) 1038.00 + 1797.87i 0.150707 + 0.261033i
\(363\) 0 0
\(364\) 650.000 675.500i 0.0935969 0.0972687i
\(365\) −460.000 −0.0659658
\(366\) 0 0
\(367\) 813.500 + 1409.02i 0.115707 + 0.200410i 0.918062 0.396437i \(-0.129753\pi\)
−0.802355 + 0.596847i \(0.796420\pi\)
\(368\) −1496.00 + 2591.15i −0.211914 + 0.367046i
\(369\) 0 0
\(370\) 846.000 1465.31i 0.118869 0.205887i
\(371\) −1545.00 + 2676.02i −0.216206 + 0.374480i
\(372\) 0 0
\(373\) −1493.50 + 2586.82i −0.207320 + 0.359089i −0.950870 0.309592i \(-0.899808\pi\)
0.743549 + 0.668681i \(0.233141\pi\)
\(374\) −351.000 607.950i −0.0485288 0.0840544i
\(375\) 0 0
\(376\) −3104.00 −0.425736
\(377\) −422.500 + 439.075i −0.0577185 + 0.0599828i
\(378\) 0 0
\(379\) 4433.50 + 7679.05i 0.600880 + 1.04076i 0.992688 + 0.120708i \(0.0385165\pi\)
−0.391808 + 0.920047i \(0.628150\pi\)
\(380\) 300.000 + 519.615i 0.0404991 + 0.0701466i
\(381\) 0 0
\(382\) 4282.00 0.573524
\(383\) 5701.50 9875.29i 0.760661 1.31750i −0.181850 0.983326i \(-0.558208\pi\)
0.942510 0.334177i \(-0.108458\pi\)
\(384\) 0 0
\(385\) −130.000 −0.0172089
\(386\) −2627.00 + 4550.10i −0.346401 + 0.599984i
\(387\) 0 0
\(388\) 194.000 + 336.018i 0.0253837 + 0.0439658i
\(389\) −2622.00 −0.341750 −0.170875 0.985293i \(-0.554659\pi\)
−0.170875 + 0.985293i \(0.554659\pi\)
\(390\) 0 0
\(391\) −5049.00 −0.653041
\(392\) 1272.00 + 2203.17i 0.163892 + 0.283869i
\(393\) 0 0
\(394\) 1203.00 2083.66i 0.153823 0.266429i
\(395\) −1528.00 −0.194638
\(396\) 0 0
\(397\) −329.500 + 570.711i −0.0416552 + 0.0721490i −0.886101 0.463492i \(-0.846596\pi\)
0.844446 + 0.535641i \(0.179930\pi\)
\(398\) 1486.00 0.187152
\(399\) 0 0
\(400\) 968.000 + 1676.63i 0.121000 + 0.209578i
\(401\) −7342.50 12717.6i −0.914381 1.58376i −0.807804 0.589451i \(-0.799344\pi\)
−0.106577 0.994304i \(-0.533989\pi\)
\(402\) 0 0
\(403\) 1352.00 + 4683.47i 0.167116 + 0.578908i
\(404\) 3236.00 0.398507
\(405\) 0 0
\(406\) 65.0000 + 112.583i 0.00794556 + 0.0137621i
\(407\) 2749.50 4762.27i 0.334859 0.579993i
\(408\) 0 0
\(409\) 3914.50 6780.11i 0.473251 0.819694i −0.526280 0.850311i \(-0.676414\pi\)
0.999531 + 0.0306167i \(0.00974712\pi\)
\(410\) −390.000 + 675.500i −0.0469774 + 0.0813672i
\(411\) 0 0
\(412\) −2576.00 + 4461.76i −0.308035 + 0.533532i
\(413\) −1227.50 2126.09i −0.146250 0.253313i
\(414\) 0 0
\(415\) −1464.00 −0.173169
\(416\) 1456.00 + 360.267i 0.171602 + 0.0424604i
\(417\) 0 0
\(418\) 975.000 + 1688.75i 0.114088 + 0.197606i
\(419\) −1459.50 2527.93i −0.170170 0.294743i 0.768309 0.640079i \(-0.221098\pi\)
−0.938479 + 0.345336i \(0.887765\pi\)
\(420\) 0 0
\(421\) −3110.00 −0.360029 −0.180014 0.983664i \(-0.557614\pi\)
−0.180014 + 0.983664i \(0.557614\pi\)
\(422\) 355.000 614.878i 0.0409505 0.0709284i
\(423\) 0 0
\(424\) −4944.00 −0.566278
\(425\) −1633.50 + 2829.30i −0.186439 + 0.322921i
\(426\) 0 0
\(427\) 437.500 + 757.772i 0.0495834 + 0.0858810i
\(428\) −5108.00 −0.576880
\(429\) 0 0
\(430\) −796.000 −0.0892710
\(431\) −4567.50 7911.14i −0.510461 0.884145i −0.999927 0.0121219i \(-0.996141\pi\)
0.489465 0.872023i \(-0.337192\pi\)
\(432\) 0 0
\(433\) 5834.50 10105.7i 0.647548 1.12159i −0.336159 0.941805i \(-0.609128\pi\)
0.983707 0.179780i \(-0.0575387\pi\)
\(434\) 1040.00 0.115027
\(435\) 0 0
\(436\) −1652.00 + 2861.35i −0.181460 + 0.314298i
\(437\) 14025.0 1.53526
\(438\) 0 0
\(439\) −6764.50 11716.5i −0.735426 1.27380i −0.954536 0.298095i \(-0.903649\pi\)
0.219110 0.975700i \(-0.429685\pi\)
\(440\) −104.000 180.133i −0.0112682 0.0195171i
\(441\) 0 0
\(442\) 702.000 + 2431.80i 0.0755446 + 0.261694i
\(443\) 1932.00 0.207206 0.103603 0.994619i \(-0.466963\pi\)
0.103603 + 0.994619i \(0.466963\pi\)
\(444\) 0 0
\(445\) 1041.00 + 1803.06i 0.110895 + 0.192075i
\(446\) 2283.00 3954.27i 0.242384 0.419821i
\(447\) 0 0
\(448\) 160.000 277.128i 0.0168734 0.0292256i
\(449\) −2678.50 + 4639.30i −0.281528 + 0.487621i −0.971761 0.235966i \(-0.924175\pi\)
0.690233 + 0.723587i \(0.257508\pi\)
\(450\) 0 0
\(451\) −1267.50 + 2195.37i −0.132338 + 0.229215i
\(452\) 1894.00 + 3280.50i 0.197094 + 0.341376i
\(453\) 0 0
\(454\) −4902.00 −0.506745
\(455\) 455.000 + 112.583i 0.0468807 + 0.0116000i
\(456\) 0 0
\(457\) −9699.50 16800.0i −0.992830 1.71963i −0.599933 0.800050i \(-0.704806\pi\)
−0.392897 0.919582i \(-0.628527\pi\)
\(458\) 1878.00 + 3252.79i 0.191601 + 0.331862i
\(459\) 0 0
\(460\) −1496.00 −0.151633
\(461\) −7774.50 + 13465.8i −0.785455 + 1.36045i 0.143273 + 0.989683i \(0.454237\pi\)
−0.928727 + 0.370764i \(0.879096\pi\)
\(462\) 0 0
\(463\) 4072.00 0.408730 0.204365 0.978895i \(-0.434487\pi\)
0.204365 + 0.978895i \(0.434487\pi\)
\(464\) −104.000 + 180.133i −0.0104053 + 0.0180226i
\(465\) 0 0
\(466\) 1630.00 + 2823.24i 0.162035 + 0.280653i
\(467\) −15224.0 −1.50853 −0.754264 0.656571i \(-0.772006\pi\)
−0.754264 + 0.656571i \(0.772006\pi\)
\(468\) 0 0
\(469\) −4085.00 −0.402191
\(470\) −776.000 1344.07i −0.0761579 0.131909i
\(471\) 0 0
\(472\) 1964.00 3401.75i 0.191526 0.331733i
\(473\) −2587.00 −0.251481
\(474\) 0 0
\(475\) 4537.50 7859.18i 0.438305 0.759166i
\(476\) 540.000 0.0519976
\(477\) 0 0
\(478\) −5544.00 9602.49i −0.530495 0.918844i
\(479\) −5167.50 8950.37i −0.492921 0.853764i 0.507046 0.861919i \(-0.330737\pi\)
−0.999967 + 0.00815506i \(0.997404\pi\)
\(480\) 0 0
\(481\) −13747.5 + 14286.8i −1.30319 + 1.35431i
\(482\) 11046.0 1.04384
\(483\) 0 0
\(484\) 2324.00 + 4025.29i 0.218257 + 0.378032i
\(485\) −97.0000 + 168.009i −0.00908153 + 0.0157297i
\(486\) 0 0
\(487\) −3227.50 + 5590.19i −0.300312 + 0.520156i −0.976207 0.216843i \(-0.930424\pi\)
0.675894 + 0.736998i \(0.263757\pi\)
\(488\) −700.000 + 1212.44i −0.0649334 + 0.112468i
\(489\) 0 0
\(490\) −636.000 + 1101.58i −0.0586358 + 0.101560i
\(491\) 3888.50 + 6735.08i 0.357404 + 0.619043i 0.987526 0.157454i \(-0.0503285\pi\)
−0.630122 + 0.776496i \(0.716995\pi\)
\(492\) 0 0
\(493\) −351.000 −0.0320654
\(494\) −1950.00 6755.00i −0.177601 0.615226i
\(495\) 0 0
\(496\) 832.000 + 1441.07i 0.0753184 + 0.130455i
\(497\) −197.500 342.080i −0.0178251 0.0308740i
\(498\) 0 0
\(499\) −3044.00 −0.273082 −0.136541 0.990634i \(-0.543599\pi\)
−0.136541 + 0.990634i \(0.543599\pi\)
\(500\) −984.000 + 1704.34i −0.0880116 + 0.152441i
\(501\) 0 0
\(502\) −4350.00 −0.386753
\(503\) 5673.50 9826.79i 0.502920 0.871083i −0.497074 0.867708i \(-0.665592\pi\)
0.999994 0.00337525i \(-0.00107438\pi\)
\(504\) 0 0
\(505\) 809.000 + 1401.23i 0.0712872 + 0.123473i
\(506\) −4862.00 −0.427159
\(507\) 0 0
\(508\) 4708.00 0.411188
\(509\) 363.500 + 629.600i 0.0316539 + 0.0548262i 0.881418 0.472336i \(-0.156589\pi\)
−0.849764 + 0.527163i \(0.823256\pi\)
\(510\) 0 0
\(511\) 575.000 995.929i 0.0497779 0.0862178i
\(512\) 512.000 0.0441942
\(513\) 0 0
\(514\) −5685.00 + 9846.71i −0.487849 + 0.844980i
\(515\) −2576.00 −0.220412
\(516\) 0 0
\(517\) −2522.00 4368.23i −0.214540 0.371595i
\(518\) 2115.00 + 3663.29i 0.179397 + 0.310725i
\(519\) 0 0
\(520\) 208.000 + 720.533i 0.0175412 + 0.0607644i
\(521\) −9582.00 −0.805749 −0.402874 0.915255i \(-0.631989\pi\)
−0.402874 + 0.915255i \(0.631989\pi\)
\(522\) 0 0
\(523\) 5191.50 + 8991.94i 0.434051 + 0.751798i 0.997218 0.0745454i \(-0.0237506\pi\)
−0.563167 + 0.826343i \(0.690417\pi\)
\(524\) −2840.00 + 4919.02i −0.236767 + 0.410093i
\(525\) 0 0
\(526\) 6117.00 10595.0i 0.507061 0.878255i
\(527\) −1404.00 + 2431.80i −0.116052 + 0.201007i
\(528\) 0 0
\(529\) −11401.0 + 19747.1i −0.937043 + 1.62301i
\(530\) −1236.00 2140.81i −0.101299 0.175455i
\(531\) 0 0
\(532\) −1500.00 −0.122243
\(533\) 6337.50 6586.12i 0.515024 0.535228i
\(534\) 0 0
\(535\) −1277.00 2211.83i −0.103195 0.178740i
\(536\) −3268.00 5660.34i −0.263351 0.456137i
\(537\) 0 0
\(538\) 10218.0 0.818828
\(539\) −2067.00 + 3580.15i −0.165180 + 0.286100i
\(540\) 0 0
\(541\) 12230.0 0.971920 0.485960 0.873981i \(-0.338470\pi\)
0.485960 + 0.873981i \(0.338470\pi\)
\(542\) −7549.00 + 13075.3i −0.598261 + 1.03622i
\(543\) 0 0
\(544\) 432.000 + 748.246i 0.0340475 + 0.0589720i
\(545\) −1652.00 −0.129842
\(546\) 0 0
\(547\) −14636.0 −1.14404 −0.572020 0.820239i \(-0.693840\pi\)
−0.572020 + 0.820239i \(0.693840\pi\)
\(548\) −4818.00 8345.02i −0.375574 0.650514i
\(549\) 0 0
\(550\) −1573.00 + 2724.52i −0.121951 + 0.211225i
\(551\) 975.000 0.0753837
\(552\) 0 0
\(553\) 1910.00 3308.22i 0.146874 0.254394i
\(554\) −1962.00 −0.150465
\(555\) 0 0
\(556\) −5654.00 9793.02i −0.431264 0.746972i
\(557\) −382.500 662.509i −0.0290970 0.0503975i 0.851110 0.524987i \(-0.175930\pi\)
−0.880207 + 0.474590i \(0.842597\pi\)
\(558\) 0 0
\(559\) 9054.50 + 2240.41i 0.685089 + 0.169515i
\(560\) 160.000 0.0120736
\(561\) 0 0
\(562\) −2762.00 4783.92i −0.207309 0.359071i
\(563\) 2957.50 5122.54i 0.221392 0.383462i −0.733839 0.679324i \(-0.762273\pi\)
0.955231 + 0.295861i \(0.0956066\pi\)
\(564\) 0 0
\(565\) −947.000 + 1640.25i −0.0705143 + 0.122134i
\(566\) −3925.00 + 6798.30i −0.291484 + 0.504865i
\(567\) 0 0
\(568\) 316.000 547.328i 0.0233434 0.0404320i
\(569\) −608.500 1053.95i −0.0448324 0.0776520i 0.842738 0.538323i \(-0.180942\pi\)
−0.887571 + 0.460671i \(0.847609\pi\)
\(570\) 0 0
\(571\) −23436.0 −1.71763 −0.858814 0.512287i \(-0.828798\pi\)
−0.858814 + 0.512287i \(0.828798\pi\)
\(572\) 676.000 + 2341.73i 0.0494143 + 0.171176i
\(573\) 0 0
\(574\) −975.000 1688.75i −0.0708985 0.122800i
\(575\) 11313.5 + 19595.6i 0.820531 + 1.42120i
\(576\) 0 0
\(577\) 7854.00 0.566666 0.283333 0.959022i \(-0.408560\pi\)
0.283333 + 0.959022i \(0.408560\pi\)
\(578\) 4184.00 7246.90i 0.301092 0.521507i
\(579\) 0 0
\(580\) −104.000 −0.00744546
\(581\) 1830.00 3169.65i 0.130673 0.226333i
\(582\) 0 0
\(583\) −4017.00 6957.65i −0.285364 0.494265i
\(584\) 1840.00 0.130376
\(585\) 0 0
\(586\) −15422.0 −1.08716
\(587\) 8516.50 + 14751.0i 0.598831 + 1.03721i 0.992994 + 0.118165i \(0.0377011\pi\)
−0.394163 + 0.919040i \(0.628966\pi\)
\(588\) 0 0
\(589\) 3900.00 6755.00i 0.272830 0.472555i
\(590\) 1964.00 0.137045
\(591\) 0 0
\(592\) −3384.00 + 5861.26i −0.234935 + 0.406919i
\(593\) 14506.0 1.00454 0.502268 0.864712i \(-0.332499\pi\)
0.502268 + 0.864712i \(0.332499\pi\)
\(594\) 0 0
\(595\) 135.000 + 233.827i 0.00930161 + 0.0161109i
\(596\) 1710.00 + 2961.81i 0.117524 + 0.203558i
\(597\) 0 0
\(598\) 17017.0 + 4210.62i 1.16367 + 0.287935i
\(599\) −15388.0 −1.04964 −0.524822 0.851212i \(-0.675868\pi\)
−0.524822 + 0.851212i \(0.675868\pi\)
\(600\) 0 0
\(601\) 3038.50 + 5262.84i 0.206228 + 0.357197i 0.950523 0.310653i \(-0.100548\pi\)
−0.744295 + 0.667851i \(0.767214\pi\)
\(602\) 995.000 1723.39i 0.0673641 0.116678i
\(603\) 0 0
\(604\) −4128.00 + 7149.91i −0.278089 + 0.481665i
\(605\) −1162.00 + 2012.64i −0.0780860 + 0.135249i
\(606\) 0 0
\(607\) −5107.50 + 8846.45i −0.341527 + 0.591543i −0.984717 0.174165i \(-0.944277\pi\)
0.643189 + 0.765707i \(0.277611\pi\)
\(608\) −1200.00 2078.46i −0.0800435 0.138639i
\(609\) 0 0
\(610\) −700.000 −0.0464626
\(611\) 5044.00 + 17472.9i 0.333974 + 1.15692i
\(612\) 0 0
\(613\) 1728.50 + 2993.85i 0.113888 + 0.197260i 0.917335 0.398117i \(-0.130336\pi\)
−0.803447 + 0.595377i \(0.797003\pi\)
\(614\) −10388.0 17992.5i −0.682778 1.18261i
\(615\) 0 0
\(616\) 520.000 0.0340120
\(617\) −3584.50 + 6208.54i −0.233884 + 0.405099i −0.958948 0.283583i \(-0.908477\pi\)
0.725064 + 0.688682i \(0.241810\pi\)
\(618\) 0 0
\(619\) 20212.0 1.31242 0.656211 0.754578i \(-0.272158\pi\)
0.656211 + 0.754578i \(0.272158\pi\)
\(620\) −416.000 + 720.533i −0.0269467 + 0.0466731i
\(621\) 0 0
\(622\) −7272.00 12595.5i −0.468779 0.811949i
\(623\) −5205.00 −0.334725
\(624\) 0 0
\(625\) 14141.0 0.905024
\(626\) −7910.00 13700.5i −0.505027 0.874733i
\(627\) 0 0
\(628\) 3788.00 6561.01i 0.240697 0.416899i
\(629\) −11421.0 −0.723983
\(630\) 0 0
\(631\) 4472.50 7746.60i 0.282167 0.488728i −0.689751 0.724046i \(-0.742280\pi\)
0.971918 + 0.235319i \(0.0756134\pi\)
\(632\) 6112.00 0.384687
\(633\) 0 0
\(634\) 7398.00 + 12813.7i 0.463426 + 0.802677i
\(635\) 1177.00 + 2038.62i 0.0735556 + 0.127402i
\(636\) 0 0
\(637\) 10335.0 10740.4i 0.642838 0.668057i
\(638\) −338.000 −0.0209742
\(639\) 0 0
\(640\) 128.000 + 221.703i 0.00790569 + 0.0136931i
\(641\) 14121.5 24459.2i 0.870149 1.50714i 0.00830761 0.999965i \(-0.497356\pi\)
0.861842 0.507177i \(-0.169311\pi\)
\(642\) 0 0
\(643\) −2615.50 + 4530.18i −0.160413 + 0.277843i −0.935017 0.354604i \(-0.884616\pi\)
0.774604 + 0.632446i \(0.217949\pi\)
\(644\) 1870.00 3238.94i 0.114423 0.198186i
\(645\) 0 0
\(646\) 2025.00 3507.40i 0.123332 0.213618i
\(647\) −2435.50 4218.41i −0.147990 0.256326i 0.782495 0.622657i \(-0.213947\pi\)
−0.930484 + 0.366332i \(0.880614\pi\)
\(648\) 0 0
\(649\) 6383.00 0.386063
\(650\) 7865.00 8173.55i 0.474601 0.493220i
\(651\) 0 0
\(652\) 1970.00 + 3412.14i 0.118330 + 0.204954i
\(653\) 6127.50 + 10613.1i 0.367209 + 0.636025i 0.989128 0.147057i \(-0.0469800\pi\)
−0.621919 + 0.783082i \(0.713647\pi\)
\(654\) 0 0
\(655\) −2840.00 −0.169417
\(656\) 1560.00 2702.00i 0.0928472 0.160816i
\(657\) 0 0
\(658\) 3880.00 0.229876
\(659\) −1072.50 + 1857.62i −0.0633971 + 0.109807i −0.895982 0.444091i \(-0.853527\pi\)
0.832585 + 0.553898i \(0.186860\pi\)
\(660\) 0 0
\(661\) −1055.50 1828.18i −0.0621092 0.107576i 0.833299 0.552823i \(-0.186449\pi\)
−0.895408 + 0.445247i \(0.853116\pi\)
\(662\) −4754.00 −0.279108
\(663\) 0 0
\(664\) 5856.00 0.342254
\(665\) −375.000 649.519i −0.0218675 0.0378756i
\(666\) 0 0
\(667\) −1215.50 + 2105.31i −0.0705612 + 0.122216i
\(668\) 9420.00 0.545615
\(669\) 0 0
\(670\) 1634.00 2830.17i 0.0942193 0.163193i
\(671\) −2275.00 −0.130887
\(672\) 0 0
\(673\) 11636.5 + 20155.0i 0.666499 + 1.15441i 0.978876 + 0.204453i \(0.0655414\pi\)
−0.312377 + 0.949958i \(0.601125\pi\)
\(674\) 7618.00 + 13194.8i 0.435363 + 0.754070i
\(675\) 0 0
\(676\) −338.000 8781.50i −0.0192308 0.499630i
\(677\) 5910.00 0.335509 0.167755 0.985829i \(-0.446348\pi\)
0.167755 + 0.985829i \(0.446348\pi\)
\(678\) 0 0
\(679\) −242.500 420.022i −0.0137059 0.0237393i
\(680\) −216.000 + 374.123i −0.0121812 + 0.0210985i
\(681\) 0 0
\(682\) −1352.00 + 2341.73i −0.0759102 + 0.131480i
\(683\) 8373.50 14503.3i 0.469111 0.812525i −0.530265 0.847832i \(-0.677908\pi\)
0.999377 + 0.0353071i \(0.0112409\pi\)
\(684\) 0 0
\(685\) 2409.00 4172.51i 0.134370 0.232735i
\(686\) −3305.00 5724.43i −0.183944 0.318600i
\(687\) 0 0
\(688\) 3184.00 0.176437
\(689\) 8034.00 + 27830.6i 0.444225 + 1.53884i
\(690\) 0 0
\(691\) −5154.50 8927.86i −0.283772 0.491507i 0.688539 0.725200i \(-0.258253\pi\)
−0.972311 + 0.233692i \(0.924919\pi\)
\(692\) −7778.00 13471.9i −0.427276 0.740064i
\(693\) 0 0
\(694\) −750.000 −0.0410225
\(695\) 2827.00 4896.51i 0.154294 0.267245i
\(696\) 0 0
\(697\) 5265.00 0.286121
\(698\) −9727.00 + 16847.7i −0.527468 + 0.913601i
\(699\) 0 0
\(700\) −1210.00 2095.78i −0.0653339 0.113162i
\(701\) 24294.0 1.30895 0.654473 0.756085i \(-0.272890\pi\)
0.654473 + 0.756085i \(0.272890\pi\)
\(702\) 0 0
\(703\) 31725.0 1.70204
\(704\) 416.000 + 720.533i 0.0222707 + 0.0385740i
\(705\) 0 0
\(706\) 2263.00 3919.63i 0.120636 0.208948i
\(707\) −4045.00 −0.215174
\(708\) 0 0
\(709\) −6329.50 + 10963.0i −0.335274 + 0.580712i −0.983537 0.180704i \(-0.942162\pi\)
0.648263 + 0.761416i \(0.275496\pi\)
\(710\) 316.000 0.0167032
\(711\) 0 0
\(712\) −4164.00 7212.26i −0.219175 0.379622i
\(713\) 9724.00 + 16842.5i 0.510753 + 0.884650i
\(714\) 0 0
\(715\) −845.000 + 878.150i −0.0441975 + 0.0459314i
\(716\) −8916.00 −0.465372
\(717\) 0 0
\(718\) −4488.00 7773.44i −0.233274 0.404042i
\(719\) 6545.50 11337.1i 0.339508 0.588044i −0.644833 0.764324i \(-0.723073\pi\)
0.984340 + 0.176279i \(0.0564062\pi\)
\(720\) 0 0
\(721\) 3220.00 5577.20i 0.166323 0.288080i
\(722\) 1234.00 2137.35i 0.0636077 0.110172i
\(723\) 0 0
\(724\) 2076.00 3595.74i 0.106566 0.184578i
\(725\) 786.500 + 1362.26i 0.0402895 + 0.0697834i
\(726\) 0 0
\(727\) 10792.0 0.550555 0.275277 0.961365i \(-0.411230\pi\)
0.275277 + 0.961365i \(0.411230\pi\)
\(728\) −1820.00 450.333i −0.0926562 0.0229265i
\(729\) 0 0
\(730\) 460.000 + 796.743i 0.0233224 + 0.0403956i
\(731\) 2686.50 + 4653.15i 0.135929 + 0.235435i
\(732\) 0 0
\(733\) −2698.00 −0.135952 −0.0679761 0.997687i \(-0.521654\pi\)
−0.0679761 + 0.997687i \(0.521654\pi\)
\(734\) 1627.00 2818.05i 0.0818170 0.141711i
\(735\) 0 0
\(736\) 5984.00 0.299692
\(737\) 5310.50 9198.06i 0.265420 0.459721i
\(738\) 0 0
\(739\) −1420.50 2460.38i −0.0707090 0.122472i 0.828503 0.559984i \(-0.189193\pi\)
−0.899212 + 0.437513i \(0.855859\pi\)
\(740\) −3384.00 −0.168106
\(741\) 0 0
\(742\) 6180.00 0.305761
\(743\) −4595.50 7959.64i −0.226908 0.393016i 0.729982 0.683466i \(-0.239528\pi\)
−0.956890 + 0.290450i \(0.906195\pi\)
\(744\) 0 0
\(745\) −855.000 + 1480.90i −0.0420467 + 0.0728270i
\(746\) 5974.00 0.293195
\(747\) 0 0
\(748\) −702.000 + 1215.90i −0.0343151 + 0.0594354i
\(749\) 6385.00 0.311486
\(750\) 0 0
\(751\) 829.500 + 1436.74i 0.0403048 + 0.0698099i 0.885474 0.464689i \(-0.153834\pi\)
−0.845169 + 0.534499i \(0.820500\pi\)
\(752\) 3104.00 + 5376.29i 0.150520 + 0.260709i
\(753\) 0 0
\(754\) 1183.00 + 292.717i 0.0571384 + 0.0141381i
\(755\) −4128.00 −0.198985
\(756\) 0 0
\(757\) 6964.50 + 12062.9i 0.334384 + 0.579171i 0.983366 0.181633i \(-0.0581383\pi\)
−0.648982 + 0.760804i \(0.724805\pi\)
\(758\) 8867.00 15358.1i 0.424886 0.735925i
\(759\) 0 0
\(760\) 600.000 1039.23i 0.0286372 0.0496011i
\(761\) 2293.50 3972.46i 0.109250 0.189227i −0.806217 0.591620i \(-0.798488\pi\)
0.915467 + 0.402394i \(0.131822\pi\)
\(762\) 0 0
\(763\) 2065.00 3576.68i 0.0979791 0.169705i
\(764\) −4282.00 7416.64i −0.202771 0.351210i
\(765\) 0 0
\(766\) −22806.0 −1.07574
\(767\) −22340.5 5527.84i −1.05172 0.260233i
\(768\) 0 0
\(769\) −7249.50 12556.5i −0.339953 0.588815i 0.644471 0.764629i \(-0.277078\pi\)
−0.984423 + 0.175814i \(0.943744\pi\)
\(770\) 130.000 + 225.167i 0.00608425 + 0.0105382i
\(771\) 0 0
\(772\) 10508.0 0.489885
\(773\) 1529.50 2649.17i 0.0711673 0.123265i −0.828246 0.560365i \(-0.810661\pi\)
0.899413 + 0.437100i \(0.143994\pi\)
\(774\) 0 0
\(775\) 12584.0 0.583265
\(776\) 388.000 672.036i 0.0179490 0.0310885i
\(777\) 0 0
\(778\) 2622.00 + 4541.44i 0.120827 + 0.209278i
\(779\) −14625.0 −0.672651
\(780\) 0