Properties

Label 234.4.h.b.217.1
Level $234$
Weight $4$
Character 234.217
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 217.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 234.217
Dual form 234.4.h.b.55.1

$q$-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 \(\left(\mathbb{Z}/234\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(209\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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 0.925593 0.378521i \(-0.123567\pi\)
−0.790605 + 0.612326i \(0.790234\pi\)
\(8\) 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 −0.763087 0.646296i \(-0.776317\pi\)
0.941252 + 0.337704i \(0.109650\pi\)
\(12\) 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 0.946112 0.323840i \(-0.104974\pi\)
−0.753510 + 0.657437i \(0.771641\pi\)
\(18\) 0 0
\(19\) −37.5000 64.9519i −0.452794 0.784263i 0.545764 0.837939i \(-0.316239\pi\)
−0.998558 + 0.0536762i \(0.982906\pi\)
\(20\) 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 0.0356377 + 0.999365i \(0.488654\pi\)
−0.883294 + 0.468819i \(0.844680\pi\)
\(24\) 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 −0.886086 0.463522i \(-0.846586\pi\)
0.844464 + 0.535612i \(0.179919\pi\)
\(30\) 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 −0.173785 + 0.984784i \(0.555600\pi\)
−0.765955 + 0.642894i \(0.777734\pi\)
\(38\) 150.000 0.640348
\(39\) 0 0
\(40\) −16.0000 −0.0632456
\(41\) 97.5000 168.875i 0.371389 0.643264i −0.618391 0.785871i \(-0.712215\pi\)
0.989779 + 0.142607i \(0.0455484\pi\)
\(42\) 0 0
\(43\) −99.5000 172.339i −0.352875 0.611197i 0.633877 0.773434i \(-0.281462\pi\)
−0.986752 + 0.162237i \(0.948129\pi\)
\(44\) −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 0.998806 + 0.0488617i \(0.0155594\pi\)
−0.457087 + 0.889422i \(0.651107\pi\)
\(60\) 0 0
\(61\) −87.5000 151.554i −0.183659 0.318108i 0.759465 0.650549i \(-0.225461\pi\)
−0.943124 + 0.332441i \(0.892128\pi\)
\(62\) 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 0.205387 + 0.978681i \(0.434155\pi\)
−0.950256 + 0.311470i \(0.899179\pi\)
\(68\) 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 0.897148 0.441729i \(-0.145635\pi\)
−0.831123 + 0.556088i \(0.812302\pi\)
\(72\) 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 0.369580 + 0.929199i \(0.379502\pi\)
−0.989500 + 0.144534i \(0.953832\pi\)
\(90\) 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 0.890292 0.455389i \(-0.150500\pi\)
−0.839525 + 0.543321i \(0.817167\pi\)
\(98\) 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 −0.993542 0.113465i \(-0.963805\pi\)
0.595035 + 0.803700i \(0.297138\pi\)
\(102\) 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 −0.418955 0.908007i \(-0.637603\pi\)
0.995835 0.0911779i \(-0.0290632\pi\)
\(108\) 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 0.992997 0.118139i \(-0.0376929\pi\)
−0.598810 + 0.800891i \(0.704360\pi\)
\(114\) 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 −0.995020 0.0996756i \(-0.968220\pi\)
0.583832 + 0.811875i \(0.301553\pi\)
\(128\) −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 −0.947266 0.320447i \(-0.896167\pi\)
0.196118 0.980580i \(-0.437167\pi\)
\(138\) 0 0
\(139\) −1413.50 2448.25i −0.862529 1.49394i −0.869480 0.493968i \(-0.835546\pi\)
0.00695133 0.999976i \(-0.497787\pi\)
\(140\) −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 0.959287 0.282434i \(-0.0911419\pi\)
−0.724239 + 0.689549i \(0.757809\pi\)
\(150\) 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 0.959754 0.280843i \(-0.0906139\pi\)
−0.723094 + 0.690750i \(0.757281\pi\)
\(164\) −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 0.452953 + 0.891534i \(0.350371\pi\)
−0.998568 + 0.0534983i \(0.982963\pi\)
\(168\) 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 −0.877059 0.480382i \(-0.840498\pi\)
0.0225069 0.999747i \(-0.492835\pi\)
\(174\) 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 −0.533846 0.845582i \(-0.679254\pi\)
0.999218 + 0.0395333i \(0.0125871\pi\)
\(180\) 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 0.588842 0.808248i \(-0.299584\pi\)
−0.994384 + 0.105828i \(0.966251\pi\)
\(192\) 0 0
\(193\) −1313.50 + 2275.05i −0.489885 + 0.848506i −0.999932 0.0116407i \(-0.996295\pi\)
0.510047 + 0.860146i \(0.329628\pi\)
\(194\) −194.000 −0.0717958
\(195\) 0 0
\(196\) −1272.00 −0.463557
\(197\) 601.500 1041.83i 0.217539 0.376788i −0.736516 0.676420i \(-0.763531\pi\)
0.954055 + 0.299632i \(0.0968639\pi\)
\(198\) 0 0
\(199\) −371.500 643.457i −0.132336 0.229213i 0.792240 0.610209i \(-0.208915\pi\)
−0.924577 + 0.380996i \(0.875581\pi\)
\(200\) −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 −0.835615 0.549315i \(-0.814889\pi\)
0.893528 + 0.449007i \(0.148222\pi\)
\(212\) 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 −0.642166 0.766566i \(-0.721964\pi\)
0.984948 + 0.172849i \(0.0552973\pi\)
\(224\) 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 0.987681 0.156482i \(-0.0500154\pi\)
−0.629358 + 0.777116i \(0.716682\pi\)
\(228\) 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 −0.953347 0.301878i \(-0.902386\pi\)
0.215239 0.976561i \(-0.430947\pi\)
\(242\) −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 0.969749 0.244103i \(-0.0784934\pi\)
−0.696274 + 0.717776i \(0.745160\pi\)
\(252\) 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 0.281939 + 0.959432i \(0.409022\pi\)
−0.971862 + 0.235550i \(0.924311\pi\)
\(258\) 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 −0.245055 0.969509i \(-0.578806\pi\)
0.962147 0.272531i \(-0.0878606\pi\)
\(264\) 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 −0.995595 0.0937632i \(-0.970110\pi\)
0.416596 0.909092i \(-0.363223\pi\)
\(270\) 0 0
\(271\) −3774.50 + 6537.63i −0.846068 + 1.46543i 0.0386217 + 0.999254i \(0.487703\pi\)
−0.884690 + 0.466180i \(0.845630\pi\)
\(272\) −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 0.914307 0.405022i \(-0.132736\pi\)
−0.807913 + 0.589302i \(0.799403\pi\)
\(278\) 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 −0.995132 0.0985482i \(-0.968580\pi\)
0.582911 + 0.812536i \(0.301913\pi\)
\(284\) 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 0.938247 + 0.345967i \(0.112449\pi\)
−0.169507 + 0.985529i \(0.554218\pi\)
\(294\) 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 0.947671 0.319248i \(-0.103430\pi\)
−0.750312 + 0.661084i \(0.770097\pi\)
\(332\) −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 0.880165 0.474669i \(-0.157432\pi\)
−0.851157 + 0.524911i \(0.824099\pi\)
\(348\) 0 0
\(349\) −4863.50 + 8423.83i −0.745952 + 1.29203i 0.203797 + 0.979013i \(0.434672\pi\)
−0.949749 + 0.313013i \(0.898662\pi\)
\(350\) 1210.00 0.184792
\(351\) 0 0
\(352\) −416.000 −0.0629911
\(353\) 1131.50 1959.82i 0.170605 0.295497i −0.768026 0.640418i \(-0.778761\pi\)
0.938632 + 0.344921i \(0.112094\pi\)
\(354\) 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 −0.802355 0.596847i \(-0.796420\pi\)
0.918062 + 0.396437i \(0.129753\pi\)
\(368\) −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 0.743549 0.668681i \(-0.233141\pi\)
−0.950870 + 0.309592i \(0.899808\pi\)
\(374\) −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 −0.391808 0.920047i \(-0.628150\pi\)
0.992688 0.120708i \(-0.0385165\pi\)
\(380\) 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 0.942510 + 0.334177i \(0.108458\pi\)
−0.181850 + 0.983326i \(0.558208\pi\)
\(384\) 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 0.844446 0.535641i \(-0.179930\pi\)
−0.886101 + 0.463492i \(0.846596\pi\)
\(398\) 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 −0.106577 + 0.994304i \(0.533989\pi\)
−0.807804 + 0.589451i \(0.799344\pi\)
\(402\) 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 0.999531 0.0306167i \(-0.00974712\pi\)
−0.526280 + 0.850311i \(0.676414\pi\)
\(410\) −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 −0.938479 0.345336i \(-0.887765\pi\)
0.768309 + 0.640079i \(0.221098\pi\)
\(420\) 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 0.489465 + 0.872023i \(0.337192\pi\)
−0.999927 + 0.0121219i \(0.996141\pi\)
\(432\) 0 0
\(433\) 5834.50 + 10105.7i 0.647548 + 1.12159i 0.983707 + 0.179780i \(0.0575387\pi\)
−0.336159 + 0.941805i \(0.609128\pi\)
\(434\) 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 0.219110 + 0.975700i \(0.429685\pi\)
−0.954536 + 0.298095i \(0.903649\pi\)
\(440\) −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 0.690233 0.723587i \(-0.257508\pi\)
−0.971761 + 0.235966i \(0.924175\pi\)
\(450\) 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 −0.392897 + 0.919582i \(0.628527\pi\)
−0.599933 + 0.800050i \(0.704806\pi\)
\(458\) 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 −0.928727 0.370764i \(-0.879096\pi\)
0.143273 0.989683i \(-0.454237\pi\)
\(462\) 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 −0.999967 0.00815506i \(-0.997404\pi\)
0.507046 + 0.861919i \(0.330737\pi\)
\(480\) 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 0.675894 0.736998i \(-0.263757\pi\)
−0.976207 + 0.216843i \(0.930424\pi\)
\(488\) −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 −0.630122 0.776496i \(-0.716995\pi\)
0.987526 + 0.157454i \(0.0503285\pi\)
\(492\) 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 0.999994 + 0.00337525i \(0.00107438\pi\)
−0.497074 + 0.867708i \(0.665592\pi\)
\(504\) 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 −0.849764 0.527163i \(-0.823256\pi\)
0.881418 + 0.472336i \(0.156589\pi\)
\(510\) 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 −0.563167 0.826343i \(-0.690417\pi\)
0.997218 + 0.0745454i \(0.0237506\pi\)
\(524\) −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 −0.880207 0.474590i \(-0.842597\pi\)
0.851110 + 0.524987i \(0.175930\pi\)
\(558\) 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 0.955231 0.295861i \(-0.0956066\pi\)
−0.733839 + 0.679324i \(0.762273\pi\)
\(564\) 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 −0.887571 0.460671i \(-0.847609\pi\)
0.842738 + 0.538323i \(0.180942\pi\)
\(570\) 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 −0.394163 0.919040i \(-0.628966\pi\)
0.992994 0.118165i \(-0.0377011\pi\)
\(588\) 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 −0.744295 0.667851i \(-0.767214\pi\)
0.950523 + 0.310653i \(0.100548\pi\)
\(602\) 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 0.643189 0.765707i \(-0.277611\pi\)
−0.984717 + 0.174165i \(0.944277\pi\)
\(608\) −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 −0.803447 0.595377i \(-0.797003\pi\)
0.917335 + 0.398117i \(0.130336\pi\)
\(614\) −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 0.725064 0.688682i \(-0.241810\pi\)
−0.958948 + 0.283583i \(0.908477\pi\)
\(618\) 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 0.971918 0.235319i \(-0.0756134\pi\)
−0.689751 + 0.724046i \(0.742280\pi\)
\(632\) 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 0.861842 + 0.507177i \(0.169311\pi\)
0.00830761 + 0.999965i \(0.497356\pi\)
\(642\) 0 0
\(643\) −2615.50 4530.18i −0.160413 0.277843i 0.774604 0.632446i \(-0.217949\pi\)
−0.935017 + 0.354604i \(0.884616\pi\)
\(644\) 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 −0.930484 0.366332i \(-0.880614\pi\)
0.782495 + 0.622657i \(0.213947\pi\)
\(648\) 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 −0.621919 0.783082i \(-0.713647\pi\)
0.989128 + 0.147057i \(0.0469800\pi\)
\(654\) 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 0.832585 0.553898i \(-0.186860\pi\)
−0.895982 + 0.444091i \(0.853527\pi\)
\(660\) 0 0
\(661\) −1055.50 + 1828.18i −0.0621092 + 0.107576i −0.895408 0.445247i \(-0.853116\pi\)
0.833299 + 0.552823i \(0.186449\pi\)
\(662\) −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 −0.312377 0.949958i \(-0.601125\pi\)
0.978876 0.204453i \(-0.0655414\pi\)
\(674\) 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 0.999377 0.0353071i \(-0.0112409\pi\)
−0.530265 + 0.847832i \(0.677908\pi\)
\(684\) 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 −0.972311 0.233692i \(-0.924919\pi\)
0.688539 + 0.725200i \(0.258253\pi\)
\(692\) −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 0.648263 0.761416i \(-0.275496\pi\)
−0.983537 + 0.180704i \(0.942162\pi\)
\(710\) 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 0.984340 0.176279i \(-0.0564062\pi\)
−0.644833 + 0.764324i \(0.723073\pi\)
\(720\) 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 −0.899212 0.437513i \(-0.855859\pi\)
0.828503 + 0.559984i \(0.189193\pi\)
\(740\) −3384.00 −0.168106
\(741\) 0 0
\(742\) 6180.00 0.305761
\(743\) −4595.50 + 7959.64i −0.226908 + 0.393016i −0.956890 0.290450i \(-0.906195\pi\)
0.729982 + 0.683466i \(0.239528\pi\)
\(744\) 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 −0.845169 0.534499i \(-0.820500\pi\)
0.885474 + 0.464689i \(0.153834\pi\)
\(752\) 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 −0.648982 0.760804i \(-0.724805\pi\)
0.983366 + 0.181633i \(0.0581383\pi\)
\(758\) 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 0.915467 0.402394i \(-0.131822\pi\)
−0.806217 + 0.591620i \(0.798488\pi\)
\(762\) 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 −0.984423 0.175814i \(-0.943744\pi\)
0.644471 + 0.764629i \(0.277078\pi\)
\(770\) 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 0.899413 0.437100i \(-0.143994\pi\)
−0.828246 + 0.560365i \(0.810661\pi\)
\(774\) 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 0