Properties

Label 36.4.e.a.13.1
Level $36$
Weight $4$
Character 36.13
Analytic conductor $2.124$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [36,4,Mod(13,36)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(36, 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("36.13");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 36 = 2^{2} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 36.e (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: \(2.12406876021\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.6831243.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} + 13x^{4} + 49x^{2} + 48 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{2}\cdot 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 13.1
Root \(1.23396i\) of defining polynomial
Character \(\chi\) \(=\) 36.13
Dual form 36.4.e.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.14739 - 3.13036i) q^{3} +(6.92194 - 11.9892i) q^{5} +(-15.3540 - 26.5939i) q^{7} +(7.40171 + 25.9656i) q^{9} +O(q^{10})\) \(q+(-4.14739 - 3.13036i) q^{3} +(6.92194 - 11.9892i) q^{5} +(-15.3540 - 26.5939i) q^{7} +(7.40171 + 25.9656i) q^{9} +(21.9523 + 38.0225i) q^{11} +(6.11853 - 10.5976i) q^{13} +(-66.2383 + 28.0555i) q^{15} +76.0286 q^{17} -44.1789 q^{19} +(-19.5694 + 158.359i) q^{21} +(39.3135 - 68.0930i) q^{23} +(-33.3265 - 57.7232i) q^{25} +(50.5840 - 130.860i) q^{27} +(46.3903 + 80.3504i) q^{29} +(71.5329 - 123.899i) q^{31} +(27.9793 - 226.413i) q^{33} -425.118 q^{35} -32.4741 q^{37} +(-58.5502 + 24.7992i) q^{39} +(167.778 - 290.599i) q^{41} +(249.166 + 431.567i) q^{43} +(362.540 + 90.9925i) q^{45} +(140.882 + 244.016i) q^{47} +(-299.990 + 519.599i) q^{49} +(-315.320 - 237.997i) q^{51} -628.565 q^{53} +607.810 q^{55} +(183.227 + 138.296i) q^{57} +(-252.327 + 437.043i) q^{59} +(-185.951 - 322.076i) q^{61} +(576.882 - 595.517i) q^{63} +(-84.7041 - 146.712i) q^{65} +(81.3304 - 140.868i) q^{67} +(-376.204 + 159.343i) q^{69} +433.512 q^{71} -629.645 q^{73} +(-42.4763 + 343.725i) q^{75} +(674.111 - 1167.59i) q^{77} +(-86.3649 - 149.588i) q^{79} +(-619.429 + 384.380i) q^{81} +(87.4288 + 151.431i) q^{83} +(526.265 - 911.518i) q^{85} +(59.1267 - 478.463i) q^{87} +336.716 q^{89} -375.775 q^{91} +(-684.522 + 289.933i) q^{93} +(-305.804 + 529.668i) q^{95} +(-42.1594 - 73.0222i) q^{97} +(-824.794 + 851.437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 3 q^{3} + 6 q^{5} - 6 q^{7} + 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 3 q^{3} + 6 q^{5} - 6 q^{7} + 39 q^{9} + 51 q^{11} + 12 q^{13} - 180 q^{15} - 222 q^{17} + 30 q^{19} - 120 q^{21} + 210 q^{23} - 3 q^{25} + 648 q^{27} + 456 q^{29} + 48 q^{31} - 603 q^{33} - 1104 q^{35} - 96 q^{37} - 36 q^{39} + 897 q^{41} + 129 q^{43} + 1494 q^{45} + 522 q^{47} - 225 q^{49} - 1647 q^{51} - 2208 q^{53} - 216 q^{55} - 645 q^{57} + 453 q^{59} - 402 q^{61} + 1896 q^{63} + 1110 q^{65} - 213 q^{67} - 198 q^{69} + 120 q^{71} + 750 q^{73} + 921 q^{75} + 1128 q^{77} + 552 q^{79} - 549 q^{81} - 612 q^{83} + 1188 q^{85} - 1386 q^{87} - 924 q^{89} - 264 q^{91} - 1998 q^{93} - 2184 q^{95} + 93 q^{97} - 1854 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/36\mathbb{Z}\right)^\times\).

\(n\) \(19\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −4.14739 3.13036i −0.798166 0.602438i
\(4\) 0 0
\(5\) 6.92194 11.9892i 0.619117 1.07234i −0.370530 0.928821i \(-0.620824\pi\)
0.989647 0.143522i \(-0.0458427\pi\)
\(6\) 0 0
\(7\) −15.3540 26.5939i −0.829038 1.43594i −0.898794 0.438372i \(-0.855555\pi\)
0.0697558 0.997564i \(-0.477778\pi\)
\(8\) 0 0
\(9\) 7.40171 + 25.9656i 0.274137 + 0.961691i
\(10\) 0 0
\(11\) 21.9523 + 38.0225i 0.601715 + 1.04220i 0.992561 + 0.121745i \(0.0388490\pi\)
−0.390846 + 0.920456i \(0.627818\pi\)
\(12\) 0 0
\(13\) 6.11853 10.5976i 0.130536 0.226096i −0.793347 0.608770i \(-0.791663\pi\)
0.923883 + 0.382674i \(0.124997\pi\)
\(14\) 0 0
\(15\) −66.2383 + 28.0555i −1.14018 + 0.482927i
\(16\) 0 0
\(17\) 76.0286 1.08468 0.542342 0.840158i \(-0.317538\pi\)
0.542342 + 0.840158i \(0.317538\pi\)
\(18\) 0 0
\(19\) −44.1789 −0.533439 −0.266720 0.963774i \(-0.585940\pi\)
−0.266720 + 0.963774i \(0.585940\pi\)
\(20\) 0 0
\(21\) −19.5694 + 158.359i −0.203352 + 1.64556i
\(22\) 0 0
\(23\) 39.3135 68.0930i 0.356410 0.617321i −0.630948 0.775825i \(-0.717334\pi\)
0.987358 + 0.158504i \(0.0506672\pi\)
\(24\) 0 0
\(25\) −33.3265 57.7232i −0.266612 0.461786i
\(26\) 0 0
\(27\) 50.5840 130.860i 0.360552 0.932739i
\(28\) 0 0
\(29\) 46.3903 + 80.3504i 0.297050 + 0.514506i 0.975460 0.220178i \(-0.0706637\pi\)
−0.678409 + 0.734684i \(0.737330\pi\)
\(30\) 0 0
\(31\) 71.5329 123.899i 0.414442 0.717834i −0.580928 0.813955i \(-0.697310\pi\)
0.995370 + 0.0961208i \(0.0306435\pi\)
\(32\) 0 0
\(33\) 27.9793 226.413i 0.147593 1.19434i
\(34\) 0 0
\(35\) −425.118 −2.05309
\(36\) 0 0
\(37\) −32.4741 −0.144289 −0.0721447 0.997394i \(-0.522984\pi\)
−0.0721447 + 0.997394i \(0.522984\pi\)
\(38\) 0 0
\(39\) −58.5502 + 24.7992i −0.240398 + 0.101822i
\(40\) 0 0
\(41\) 167.778 290.599i 0.639084 1.10693i −0.346550 0.938031i \(-0.612647\pi\)
0.985634 0.168895i \(-0.0540197\pi\)
\(42\) 0 0
\(43\) 249.166 + 431.567i 0.883660 + 1.53054i 0.847242 + 0.531208i \(0.178262\pi\)
0.0364186 + 0.999337i \(0.488405\pi\)
\(44\) 0 0
\(45\) 362.540 + 90.9925i 1.20098 + 0.301430i
\(46\) 0 0
\(47\) 140.882 + 244.016i 0.437230 + 0.757305i 0.997475 0.0710223i \(-0.0226261\pi\)
−0.560244 + 0.828327i \(0.689293\pi\)
\(48\) 0 0
\(49\) −299.990 + 519.599i −0.874608 + 1.51487i
\(50\) 0 0
\(51\) −315.320 237.997i −0.865758 0.653455i
\(52\) 0 0
\(53\) −628.565 −1.62906 −0.814529 0.580123i \(-0.803005\pi\)
−0.814529 + 0.580123i \(0.803005\pi\)
\(54\) 0 0
\(55\) 607.810 1.49013
\(56\) 0 0
\(57\) 183.227 + 138.296i 0.425773 + 0.321364i
\(58\) 0 0
\(59\) −252.327 + 437.043i −0.556782 + 0.964375i 0.440980 + 0.897517i \(0.354631\pi\)
−0.997762 + 0.0668584i \(0.978702\pi\)
\(60\) 0 0
\(61\) −185.951 322.076i −0.390304 0.676026i 0.602186 0.798356i \(-0.294297\pi\)
−0.992489 + 0.122330i \(0.960963\pi\)
\(62\) 0 0
\(63\) 576.882 595.517i 1.15366 1.19092i
\(64\) 0 0
\(65\) −84.7041 146.712i −0.161635 0.279960i
\(66\) 0 0
\(67\) 81.3304 140.868i 0.148300 0.256863i −0.782299 0.622903i \(-0.785953\pi\)
0.930599 + 0.366040i \(0.119287\pi\)
\(68\) 0 0
\(69\) −376.204 + 159.343i −0.656372 + 0.278009i
\(70\) 0 0
\(71\) 433.512 0.724626 0.362313 0.932056i \(-0.381987\pi\)
0.362313 + 0.932056i \(0.381987\pi\)
\(72\) 0 0
\(73\) −629.645 −1.00951 −0.504756 0.863262i \(-0.668418\pi\)
−0.504756 + 0.863262i \(0.668418\pi\)
\(74\) 0 0
\(75\) −42.4763 + 343.725i −0.0653965 + 0.529199i
\(76\) 0 0
\(77\) 674.111 1167.59i 0.997689 1.72805i
\(78\) 0 0
\(79\) −86.3649 149.588i −0.122998 0.213038i 0.797951 0.602723i \(-0.205917\pi\)
−0.920948 + 0.389684i \(0.872584\pi\)
\(80\) 0 0
\(81\) −619.429 + 384.380i −0.849697 + 0.527271i
\(82\) 0 0
\(83\) 87.4288 + 151.431i 0.115621 + 0.200262i 0.918028 0.396516i \(-0.129781\pi\)
−0.802407 + 0.596778i \(0.796447\pi\)
\(84\) 0 0
\(85\) 526.265 911.518i 0.671547 1.16315i
\(86\) 0 0
\(87\) 59.1267 478.463i 0.0728626 0.589616i
\(88\) 0 0
\(89\) 336.716 0.401032 0.200516 0.979690i \(-0.435738\pi\)
0.200516 + 0.979690i \(0.435738\pi\)
\(90\) 0 0
\(91\) −375.775 −0.432879
\(92\) 0 0
\(93\) −684.522 + 289.933i −0.763244 + 0.323275i
\(94\) 0 0
\(95\) −305.804 + 529.668i −0.330261 + 0.572029i
\(96\) 0 0
\(97\) −42.1594 73.0222i −0.0441303 0.0764358i 0.843117 0.537731i \(-0.180718\pi\)
−0.887247 + 0.461295i \(0.847385\pi\)
\(98\) 0 0
\(99\) −824.794 + 851.437i −0.837322 + 0.864370i
\(100\) 0 0
\(101\) 874.902 + 1515.38i 0.861941 + 1.49293i 0.870053 + 0.492959i \(0.164085\pi\)
−0.00811161 + 0.999967i \(0.502582\pi\)
\(102\) 0 0
\(103\) −55.6978 + 96.4714i −0.0532822 + 0.0922875i −0.891436 0.453146i \(-0.850302\pi\)
0.838154 + 0.545433i \(0.183635\pi\)
\(104\) 0 0
\(105\) 1763.13 + 1330.77i 1.63870 + 1.23686i
\(106\) 0 0
\(107\) 895.520 0.809095 0.404548 0.914517i \(-0.367429\pi\)
0.404548 + 0.914517i \(0.367429\pi\)
\(108\) 0 0
\(109\) −716.957 −0.630019 −0.315009 0.949089i \(-0.602008\pi\)
−0.315009 + 0.949089i \(0.602008\pi\)
\(110\) 0 0
\(111\) 134.683 + 101.656i 0.115167 + 0.0869254i
\(112\) 0 0
\(113\) −115.526 + 200.096i −0.0961746 + 0.166579i −0.910098 0.414393i \(-0.863994\pi\)
0.813924 + 0.580972i \(0.197327\pi\)
\(114\) 0 0
\(115\) −544.252 942.672i −0.441320 0.764388i
\(116\) 0 0
\(117\) 320.461 + 80.4312i 0.253219 + 0.0635544i
\(118\) 0 0
\(119\) −1167.34 2021.90i −0.899245 1.55754i
\(120\) 0 0
\(121\) −298.306 + 516.681i −0.224122 + 0.388190i
\(122\) 0 0
\(123\) −1605.52 + 680.025i −1.17695 + 0.498502i
\(124\) 0 0
\(125\) 807.748 0.577978
\(126\) 0 0
\(127\) 1715.22 1.19843 0.599217 0.800586i \(-0.295478\pi\)
0.599217 + 0.800586i \(0.295478\pi\)
\(128\) 0 0
\(129\) 317.574 2569.86i 0.216750 1.75398i
\(130\) 0 0
\(131\) −666.435 + 1154.30i −0.444479 + 0.769859i −0.998016 0.0629650i \(-0.979944\pi\)
0.553537 + 0.832824i \(0.313278\pi\)
\(132\) 0 0
\(133\) 678.323 + 1174.89i 0.442241 + 0.765984i
\(134\) 0 0
\(135\) −1218.76 1512.26i −0.776992 0.964110i
\(136\) 0 0
\(137\) −1259.49 2181.50i −0.785443 1.36043i −0.928734 0.370746i \(-0.879102\pi\)
0.143292 0.989680i \(-0.454231\pi\)
\(138\) 0 0
\(139\) −311.442 + 539.433i −0.190044 + 0.329166i −0.945265 0.326305i \(-0.894196\pi\)
0.755220 + 0.655471i \(0.227530\pi\)
\(140\) 0 0
\(141\) 179.562 1453.04i 0.107247 0.867859i
\(142\) 0 0
\(143\) 537.263 0.314183
\(144\) 0 0
\(145\) 1284.44 0.735636
\(146\) 0 0
\(147\) 2870.71 1215.90i 1.61069 0.682217i
\(148\) 0 0
\(149\) −1204.47 + 2086.21i −0.662243 + 1.14704i 0.317781 + 0.948164i \(0.397062\pi\)
−0.980025 + 0.198875i \(0.936271\pi\)
\(150\) 0 0
\(151\) −33.8218 58.5810i −0.0182277 0.0315712i 0.856768 0.515703i \(-0.172469\pi\)
−0.874995 + 0.484131i \(0.839136\pi\)
\(152\) 0 0
\(153\) 562.741 + 1974.13i 0.297352 + 1.04313i
\(154\) 0 0
\(155\) −990.293 1715.24i −0.513176 0.888847i
\(156\) 0 0
\(157\) 2.19676 3.80490i 0.00111669 0.00193417i −0.865467 0.500967i \(-0.832978\pi\)
0.866583 + 0.499033i \(0.166311\pi\)
\(158\) 0 0
\(159\) 2606.91 + 1967.64i 1.30026 + 0.981406i
\(160\) 0 0
\(161\) −2414.48 −1.18191
\(162\) 0 0
\(163\) −2863.88 −1.37617 −0.688087 0.725628i \(-0.741549\pi\)
−0.688087 + 0.725628i \(0.741549\pi\)
\(164\) 0 0
\(165\) −2520.82 1902.66i −1.18937 0.897710i
\(166\) 0 0
\(167\) −214.757 + 371.970i −0.0995114 + 0.172359i −0.911483 0.411339i \(-0.865061\pi\)
0.811971 + 0.583698i \(0.198395\pi\)
\(168\) 0 0
\(169\) 1023.63 + 1772.97i 0.465920 + 0.806998i
\(170\) 0 0
\(171\) −327.000 1147.13i −0.146236 0.513003i
\(172\) 0 0
\(173\) 1287.14 + 2229.40i 0.565663 + 0.979756i 0.996988 + 0.0775599i \(0.0247129\pi\)
−0.431325 + 0.902197i \(0.641954\pi\)
\(174\) 0 0
\(175\) −1023.39 + 1772.56i −0.442063 + 0.765676i
\(176\) 0 0
\(177\) 2414.60 1022.71i 1.02538 0.434305i
\(178\) 0 0
\(179\) 807.448 0.337159 0.168580 0.985688i \(-0.446082\pi\)
0.168580 + 0.985688i \(0.446082\pi\)
\(180\) 0 0
\(181\) 4296.57 1.76443 0.882215 0.470847i \(-0.156052\pi\)
0.882215 + 0.470847i \(0.156052\pi\)
\(182\) 0 0
\(183\) −237.003 + 1917.87i −0.0957365 + 0.774714i
\(184\) 0 0
\(185\) −224.784 + 389.337i −0.0893321 + 0.154728i
\(186\) 0 0
\(187\) 1669.00 + 2890.79i 0.652671 + 1.13046i
\(188\) 0 0
\(189\) −4256.74 + 663.993i −1.63826 + 0.255547i
\(190\) 0 0
\(191\) 153.147 + 265.259i 0.0580176 + 0.100489i 0.893575 0.448913i \(-0.148189\pi\)
−0.835558 + 0.549402i \(0.814855\pi\)
\(192\) 0 0
\(193\) 856.177 1482.94i 0.319321 0.553080i −0.661026 0.750363i \(-0.729879\pi\)
0.980347 + 0.197283i \(0.0632119\pi\)
\(194\) 0 0
\(195\) −107.960 + 873.626i −0.0396469 + 0.320829i
\(196\) 0 0
\(197\) −263.636 −0.0953466 −0.0476733 0.998863i \(-0.515181\pi\)
−0.0476733 + 0.998863i \(0.515181\pi\)
\(198\) 0 0
\(199\) −3835.87 −1.36642 −0.683211 0.730221i \(-0.739417\pi\)
−0.683211 + 0.730221i \(0.739417\pi\)
\(200\) 0 0
\(201\) −778.278 + 329.643i −0.273112 + 0.115678i
\(202\) 0 0
\(203\) 1424.55 2467.40i 0.492532 0.853091i
\(204\) 0 0
\(205\) −2322.69 4023.02i −0.791336 1.37063i
\(206\) 0 0
\(207\) 2059.07 + 516.796i 0.691377 + 0.173526i
\(208\) 0 0
\(209\) −969.829 1679.79i −0.320978 0.555951i
\(210\) 0 0
\(211\) 2034.66 3524.14i 0.663848 1.14982i −0.315748 0.948843i \(-0.602255\pi\)
0.979596 0.200976i \(-0.0644112\pi\)
\(212\) 0 0
\(213\) −1797.95 1357.05i −0.578372 0.436542i
\(214\) 0 0
\(215\) 6898.84 2.18836
\(216\) 0 0
\(217\) −4393.27 −1.37435
\(218\) 0 0
\(219\) 2611.38 + 1971.01i 0.805758 + 0.608168i
\(220\) 0 0
\(221\) 465.183 805.720i 0.141591 0.245243i
\(222\) 0 0
\(223\) −3078.07 5331.38i −0.924318 1.60097i −0.792654 0.609672i \(-0.791301\pi\)
−0.131664 0.991294i \(-0.542032\pi\)
\(224\) 0 0
\(225\) 1252.15 1292.60i 0.371007 0.382991i
\(226\) 0 0
\(227\) −12.1307 21.0110i −0.00354689 0.00614339i 0.864247 0.503069i \(-0.167796\pi\)
−0.867793 + 0.496925i \(0.834462\pi\)
\(228\) 0 0
\(229\) 316.209 547.691i 0.0912476 0.158045i −0.816789 0.576937i \(-0.804248\pi\)
0.908036 + 0.418891i \(0.137581\pi\)
\(230\) 0 0
\(231\) −6450.79 + 2732.26i −1.83736 + 0.778223i
\(232\) 0 0
\(233\) −3163.59 −0.889502 −0.444751 0.895654i \(-0.646708\pi\)
−0.444751 + 0.895654i \(0.646708\pi\)
\(234\) 0 0
\(235\) 3900.72 1.08279
\(236\) 0 0
\(237\) −110.076 + 890.755i −0.0301697 + 0.244138i
\(238\) 0 0
\(239\) −1110.57 + 1923.57i −0.300573 + 0.520608i −0.976266 0.216575i \(-0.930511\pi\)
0.675693 + 0.737183i \(0.263845\pi\)
\(240\) 0 0
\(241\) 300.730 + 520.879i 0.0803805 + 0.139223i 0.903413 0.428771i \(-0.141053\pi\)
−0.823033 + 0.567994i \(0.807720\pi\)
\(242\) 0 0
\(243\) 3772.26 + 344.861i 0.995847 + 0.0910406i
\(244\) 0 0
\(245\) 4153.03 + 7193.26i 1.08297 + 1.87576i
\(246\) 0 0
\(247\) −270.310 + 468.191i −0.0696332 + 0.120608i
\(248\) 0 0
\(249\) 111.432 901.727i 0.0283604 0.229497i
\(250\) 0 0
\(251\) 1350.71 0.339665 0.169833 0.985473i \(-0.445677\pi\)
0.169833 + 0.985473i \(0.445677\pi\)
\(252\) 0 0
\(253\) 3452.09 0.857830
\(254\) 0 0
\(255\) −5036.01 + 2133.02i −1.23673 + 0.523824i
\(256\) 0 0
\(257\) 3521.95 6100.20i 0.854838 1.48062i −0.0219564 0.999759i \(-0.506990\pi\)
0.876795 0.480865i \(-0.159677\pi\)
\(258\) 0 0
\(259\) 498.607 + 863.613i 0.119621 + 0.207190i
\(260\) 0 0
\(261\) −1742.98 + 1799.28i −0.413363 + 0.426716i
\(262\) 0 0
\(263\) −1162.13 2012.87i −0.272472 0.471935i 0.697022 0.717050i \(-0.254508\pi\)
−0.969494 + 0.245114i \(0.921175\pi\)
\(264\) 0 0
\(265\) −4350.89 + 7535.97i −1.00858 + 1.74691i
\(266\) 0 0
\(267\) −1396.49 1054.04i −0.320090 0.241597i
\(268\) 0 0
\(269\) −3675.87 −0.833167 −0.416584 0.909097i \(-0.636773\pi\)
−0.416584 + 0.909097i \(0.636773\pi\)
\(270\) 0 0
\(271\) −1881.48 −0.421741 −0.210871 0.977514i \(-0.567630\pi\)
−0.210871 + 0.977514i \(0.567630\pi\)
\(272\) 0 0
\(273\) 1558.49 + 1176.31i 0.345509 + 0.260782i
\(274\) 0 0
\(275\) 1463.19 2534.31i 0.320849 0.555727i
\(276\) 0 0
\(277\) −732.008 1267.87i −0.158780 0.275015i 0.775649 0.631165i \(-0.217423\pi\)
−0.934429 + 0.356149i \(0.884089\pi\)
\(278\) 0 0
\(279\) 3746.58 + 940.337i 0.803948 + 0.201780i
\(280\) 0 0
\(281\) 4116.28 + 7129.61i 0.873867 + 1.51358i 0.857965 + 0.513709i \(0.171729\pi\)
0.0159023 + 0.999874i \(0.494938\pi\)
\(282\) 0 0
\(283\) −844.364 + 1462.48i −0.177358 + 0.307192i −0.940975 0.338477i \(-0.890088\pi\)
0.763617 + 0.645669i \(0.223422\pi\)
\(284\) 0 0
\(285\) 2926.34 1239.46i 0.608215 0.257612i
\(286\) 0 0
\(287\) −10304.2 −2.11930
\(288\) 0 0
\(289\) 867.343 0.176540
\(290\) 0 0
\(291\) −53.7342 + 434.825i −0.0108246 + 0.0875942i
\(292\) 0 0
\(293\) −255.866 + 443.173i −0.0510166 + 0.0883633i −0.890406 0.455167i \(-0.849579\pi\)
0.839389 + 0.543531i \(0.182913\pi\)
\(294\) 0 0
\(295\) 3493.18 + 6050.37i 0.689427 + 1.19412i
\(296\) 0 0
\(297\) 6086.04 949.340i 1.18905 0.185476i
\(298\) 0 0
\(299\) −481.082 833.258i −0.0930491 0.161166i
\(300\) 0 0
\(301\) 7651.37 13252.6i 1.46518 2.53776i
\(302\) 0 0
\(303\) 1115.11 9023.61i 0.211423 1.71087i
\(304\) 0 0
\(305\) −5148.55 −0.966575
\(306\) 0 0
\(307\) −3171.98 −0.589690 −0.294845 0.955545i \(-0.595268\pi\)
−0.294845 + 0.955545i \(0.595268\pi\)
\(308\) 0 0
\(309\) 532.991 225.751i 0.0981255 0.0415615i
\(310\) 0 0
\(311\) −2530.39 + 4382.76i −0.461367 + 0.799112i −0.999029 0.0440487i \(-0.985974\pi\)
0.537662 + 0.843160i \(0.319308\pi\)
\(312\) 0 0
\(313\) 4732.92 + 8197.66i 0.854698 + 1.48038i 0.876925 + 0.480628i \(0.159591\pi\)
−0.0222263 + 0.999753i \(0.507075\pi\)
\(314\) 0 0
\(315\) −3146.60 11038.5i −0.562828 1.97443i
\(316\) 0 0
\(317\) −3208.57 5557.40i −0.568489 0.984652i −0.996716 0.0809808i \(-0.974195\pi\)
0.428226 0.903671i \(-0.359139\pi\)
\(318\) 0 0
\(319\) −2036.75 + 3527.75i −0.357479 + 0.619172i
\(320\) 0 0
\(321\) −3714.07 2803.30i −0.645792 0.487430i
\(322\) 0 0
\(323\) −3358.86 −0.578613
\(324\) 0 0
\(325\) −815.637 −0.139210
\(326\) 0 0
\(327\) 2973.50 + 2244.33i 0.502860 + 0.379547i
\(328\) 0 0
\(329\) 4326.22 7493.23i 0.724961 1.25567i
\(330\) 0 0
\(331\) −3332.37 5771.83i −0.553364 0.958455i −0.998029 0.0627575i \(-0.980011\pi\)
0.444665 0.895697i \(-0.353323\pi\)
\(332\) 0 0
\(333\) −240.364 843.211i −0.0395551 0.138762i
\(334\) 0 0
\(335\) −1125.93 1950.17i −0.183630 0.318056i
\(336\) 0 0
\(337\) −5244.05 + 9082.95i −0.847660 + 1.46819i 0.0356314 + 0.999365i \(0.488656\pi\)
−0.883291 + 0.468825i \(0.844678\pi\)
\(338\) 0 0
\(339\) 1105.50 468.241i 0.177117 0.0750187i
\(340\) 0 0
\(341\) 6281.25 0.997503
\(342\) 0 0
\(343\) 7891.37 1.24226
\(344\) 0 0
\(345\) −693.676 + 5613.33i −0.108250 + 0.875976i
\(346\) 0 0
\(347\) −1074.48 + 1861.05i −0.166228 + 0.287915i −0.937091 0.349086i \(-0.886492\pi\)
0.770863 + 0.637001i \(0.219825\pi\)
\(348\) 0 0
\(349\) 1388.53 + 2405.00i 0.212969 + 0.368874i 0.952642 0.304093i \(-0.0983532\pi\)
−0.739673 + 0.672966i \(0.765020\pi\)
\(350\) 0 0
\(351\) −1077.30 1336.74i −0.163823 0.203276i
\(352\) 0 0
\(353\) −3898.72 6752.78i −0.587841 1.01817i −0.994515 0.104597i \(-0.966645\pi\)
0.406673 0.913574i \(-0.366689\pi\)
\(354\) 0 0
\(355\) 3000.75 5197.45i 0.448629 0.777047i
\(356\) 0 0
\(357\) −1487.84 + 12039.8i −0.220573 + 1.78491i
\(358\) 0 0
\(359\) 2309.31 0.339500 0.169750 0.985487i \(-0.445704\pi\)
0.169750 + 0.985487i \(0.445704\pi\)
\(360\) 0 0
\(361\) −4907.22 −0.715443
\(362\) 0 0
\(363\) 2854.59 1209.07i 0.412747 0.174821i
\(364\) 0 0
\(365\) −4358.36 + 7548.91i −0.625006 + 1.08254i
\(366\) 0 0
\(367\) 3105.66 + 5379.16i 0.441728 + 0.765095i 0.997818 0.0660271i \(-0.0210324\pi\)
−0.556090 + 0.831122i \(0.687699\pi\)
\(368\) 0 0
\(369\) 8787.44 + 2205.52i 1.23972 + 0.311151i
\(370\) 0 0
\(371\) 9650.99 + 16716.0i 1.35055 + 2.33922i
\(372\) 0 0
\(373\) −4349.61 + 7533.75i −0.603792 + 1.04580i 0.388450 + 0.921470i \(0.373011\pi\)
−0.992241 + 0.124328i \(0.960323\pi\)
\(374\) 0 0
\(375\) −3350.05 2528.54i −0.461322 0.348196i
\(376\) 0 0
\(377\) 1135.36 0.155104
\(378\) 0 0
\(379\) 5954.77 0.807061 0.403531 0.914966i \(-0.367783\pi\)
0.403531 + 0.914966i \(0.367783\pi\)
\(380\) 0 0
\(381\) −7113.69 5369.26i −0.956550 0.721983i
\(382\) 0 0
\(383\) −2128.35 + 3686.41i −0.283952 + 0.491819i −0.972354 0.233510i \(-0.924979\pi\)
0.688403 + 0.725329i \(0.258312\pi\)
\(384\) 0 0
\(385\) −9332.31 16164.0i −1.23537 2.13973i
\(386\) 0 0
\(387\) −9361.67 + 9664.08i −1.22967 + 1.26939i
\(388\) 0 0
\(389\) −801.019 1387.41i −0.104404 0.180834i 0.809090 0.587684i \(-0.199960\pi\)
−0.913495 + 0.406851i \(0.866627\pi\)
\(390\) 0 0
\(391\) 2988.95 5177.02i 0.386593 0.669598i
\(392\) 0 0
\(393\) 6377.34 2701.15i 0.818560 0.346705i
\(394\) 0 0
\(395\) −2391.25 −0.304600
\(396\) 0 0
\(397\) −7987.87 −1.00982 −0.504912 0.863171i \(-0.668475\pi\)
−0.504912 + 0.863171i \(0.668475\pi\)
\(398\) 0 0
\(399\) 864.557 6996.13i 0.108476 0.877805i
\(400\) 0 0
\(401\) 3534.75 6122.36i 0.440191 0.762434i −0.557512 0.830169i \(-0.688244\pi\)
0.997703 + 0.0677350i \(0.0215772\pi\)
\(402\) 0 0
\(403\) −875.352 1516.15i −0.108200 0.187407i
\(404\) 0 0
\(405\) 320.739 + 10087.1i 0.0393523 + 1.23761i
\(406\) 0 0
\(407\) −712.881 1234.75i −0.0868211 0.150379i
\(408\) 0 0
\(409\) 5932.38 10275.2i 0.717207 1.24224i −0.244896 0.969549i \(-0.578754\pi\)
0.962102 0.272689i \(-0.0879129\pi\)
\(410\) 0 0
\(411\) −1605.28 + 12990.2i −0.192659 + 1.55903i
\(412\) 0 0
\(413\) 15496.9 1.84637
\(414\) 0 0
\(415\) 2420.71 0.286332
\(416\) 0 0
\(417\) 2980.29 1262.31i 0.349989 0.148239i
\(418\) 0 0
\(419\) 6171.30 10689.0i 0.719541 1.24628i −0.241641 0.970366i \(-0.577686\pi\)
0.961182 0.275916i \(-0.0889810\pi\)
\(420\) 0 0
\(421\) −2732.93 4733.58i −0.316377 0.547982i 0.663352 0.748308i \(-0.269133\pi\)
−0.979729 + 0.200326i \(0.935800\pi\)
\(422\) 0 0
\(423\) −5293.25 + 5464.24i −0.608432 + 0.628086i
\(424\) 0 0
\(425\) −2533.77 4388.61i −0.289190 0.500892i
\(426\) 0 0
\(427\) −5710.17 + 9890.30i −0.647153 + 1.12090i
\(428\) 0 0
\(429\) −2228.24 1681.82i −0.250770 0.189276i
\(430\) 0 0
\(431\) 8997.67 1.00557 0.502787 0.864410i \(-0.332308\pi\)
0.502787 + 0.864410i \(0.332308\pi\)
\(432\) 0 0
\(433\) −10967.4 −1.21723 −0.608615 0.793466i \(-0.708275\pi\)
−0.608615 + 0.793466i \(0.708275\pi\)
\(434\) 0 0
\(435\) −5327.09 4020.77i −0.587160 0.443175i
\(436\) 0 0
\(437\) −1736.83 + 3008.28i −0.190123 + 0.329303i
\(438\) 0 0
\(439\) −3563.51 6172.18i −0.387419 0.671029i 0.604683 0.796467i \(-0.293300\pi\)
−0.992102 + 0.125437i \(0.959967\pi\)
\(440\) 0 0
\(441\) −15712.2 3943.53i −1.69659 0.425821i
\(442\) 0 0
\(443\) −4434.28 7680.39i −0.475573 0.823716i 0.524036 0.851696i \(-0.324426\pi\)
−0.999608 + 0.0279799i \(0.991093\pi\)
\(444\) 0 0
\(445\) 2330.73 4036.94i 0.248286 0.430043i
\(446\) 0 0
\(447\) 11526.0 4881.89i 1.21960 0.516567i
\(448\) 0 0
\(449\) 9835.05 1.03373 0.516865 0.856067i \(-0.327099\pi\)
0.516865 + 0.856067i \(0.327099\pi\)
\(450\) 0 0
\(451\) 14732.4 1.53819
\(452\) 0 0
\(453\) −43.1075 + 348.833i −0.00447101 + 0.0361801i
\(454\) 0 0
\(455\) −2601.09 + 4505.23i −0.268003 + 0.464194i
\(456\) 0 0
\(457\) 4443.25 + 7695.93i 0.454806 + 0.787747i 0.998677 0.0514218i \(-0.0163753\pi\)
−0.543871 + 0.839169i \(0.683042\pi\)
\(458\) 0 0
\(459\) 3845.83 9949.07i 0.391085 1.01173i
\(460\) 0 0
\(461\) −932.894 1615.82i −0.0942499 0.163246i 0.815045 0.579397i \(-0.196712\pi\)
−0.909295 + 0.416151i \(0.863379\pi\)
\(462\) 0 0
\(463\) 6811.70 11798.2i 0.683729 1.18425i −0.290105 0.956995i \(-0.593690\pi\)
0.973834 0.227259i \(-0.0729763\pi\)
\(464\) 0 0
\(465\) −1262.18 + 10213.7i −0.125875 + 1.01860i
\(466\) 0 0
\(467\) −9328.97 −0.924397 −0.462199 0.886776i \(-0.652939\pi\)
−0.462199 + 0.886776i \(0.652939\pi\)
\(468\) 0 0
\(469\) −4994.99 −0.491785
\(470\) 0 0
\(471\) −21.0215 + 8.90377i −0.00205652 + 0.000871048i
\(472\) 0 0
\(473\) −10939.5 + 18947.8i −1.06342 + 1.84190i
\(474\) 0 0
\(475\) 1472.33 + 2550.15i 0.142221 + 0.246335i
\(476\) 0 0
\(477\) −4652.46 16321.1i −0.446586 1.56665i
\(478\) 0 0
\(479\) −1330.15 2303.89i −0.126881 0.219765i 0.795586 0.605841i \(-0.207163\pi\)
−0.922467 + 0.386077i \(0.873830\pi\)
\(480\) 0 0
\(481\) −198.694 + 344.147i −0.0188350 + 0.0326232i
\(482\) 0 0
\(483\) 10013.8 + 7558.19i 0.943361 + 0.712028i
\(484\) 0 0
\(485\) −1167.30 −0.109287
\(486\) 0 0
\(487\) −20450.7 −1.90289 −0.951447 0.307813i \(-0.900403\pi\)
−0.951447 + 0.307813i \(0.900403\pi\)
\(488\) 0 0
\(489\) 11877.6 + 8964.97i 1.09842 + 0.829059i
\(490\) 0 0
\(491\) −10327.4 + 17887.7i −0.949228 + 1.64411i −0.202173 + 0.979350i \(0.564800\pi\)
−0.747055 + 0.664762i \(0.768533\pi\)
\(492\) 0 0
\(493\) 3526.99 + 6108.92i 0.322206 + 0.558077i
\(494\) 0 0
\(495\) 4498.83 + 15782.2i 0.408500 + 1.43304i
\(496\) 0 0
\(497\) −6656.15 11528.8i −0.600743 1.04052i
\(498\) 0 0
\(499\) −8733.31 + 15126.5i −0.783480 + 1.35703i 0.146423 + 0.989222i \(0.453224\pi\)
−0.929903 + 0.367805i \(0.880109\pi\)
\(500\) 0 0
\(501\) 2055.08 870.439i 0.183262 0.0776215i
\(502\) 0 0
\(503\) 19951.2 1.76855 0.884275 0.466966i \(-0.154653\pi\)
0.884275 + 0.466966i \(0.154653\pi\)
\(504\) 0 0
\(505\) 24224.1 2.13457
\(506\) 0 0
\(507\) 1304.66 10557.5i 0.114284 0.924806i
\(508\) 0 0
\(509\) 3638.88 6302.73i 0.316878 0.548848i −0.662957 0.748657i \(-0.730699\pi\)
0.979835 + 0.199809i \(0.0640322\pi\)
\(510\) 0 0
\(511\) 9667.57 + 16744.7i 0.836924 + 1.44959i
\(512\) 0 0
\(513\) −2234.75 + 5781.24i −0.192332 + 0.497560i
\(514\) 0 0
\(515\) 771.074 + 1335.54i 0.0659759 + 0.114274i
\(516\) 0 0
\(517\) −6185.39 + 10713.4i −0.526176 + 0.911364i
\(518\) 0 0
\(519\) 1640.53 13275.4i 0.138750 1.12278i
\(520\) 0 0
\(521\) −11664.5 −0.980866 −0.490433 0.871479i \(-0.663161\pi\)
−0.490433 + 0.871479i \(0.663161\pi\)
\(522\) 0 0
\(523\) −8925.51 −0.746243 −0.373122 0.927782i \(-0.621713\pi\)
−0.373122 + 0.927782i \(0.621713\pi\)
\(524\) 0 0
\(525\) 9793.16 4147.94i 0.814112 0.344821i
\(526\) 0 0
\(527\) 5438.55 9419.84i 0.449539 0.778624i
\(528\) 0 0
\(529\) 2992.39 + 5182.98i 0.245943 + 0.425986i
\(530\) 0 0
\(531\) −13215.8 3316.97i −1.08007 0.271081i
\(532\) 0 0
\(533\) −2053.10 3556.08i −0.166848 0.288988i
\(534\) 0 0
\(535\) 6198.74 10736.5i 0.500925 0.867627i
\(536\) 0 0
\(537\) −3348.80 2527.60i −0.269109 0.203118i
\(538\) 0 0
\(539\) −26341.9 −2.10506
\(540\) 0 0
\(541\) 12334.1 0.980193 0.490097 0.871668i \(-0.336962\pi\)
0.490097 + 0.871668i \(0.336962\pi\)
\(542\) 0 0
\(543\) −17819.6 13449.8i −1.40831 1.06296i
\(544\) 0 0
\(545\) −4962.74 + 8595.71i −0.390056 + 0.675596i
\(546\) 0 0
\(547\) −2284.81 3957.41i −0.178595 0.309336i 0.762804 0.646629i \(-0.223822\pi\)
−0.941400 + 0.337293i \(0.890489\pi\)
\(548\) 0 0
\(549\) 6986.55 7212.24i 0.543131 0.560675i
\(550\) 0 0
\(551\) −2049.47 3549.79i −0.158458 0.274458i
\(552\) 0 0
\(553\) −2652.09 + 4593.56i −0.203939 + 0.353233i
\(554\) 0 0
\(555\) 2151.03 911.079i 0.164516 0.0696813i
\(556\) 0 0
\(557\) −8154.40 −0.620310 −0.310155 0.950686i \(-0.600381\pi\)
−0.310155 + 0.950686i \(0.600381\pi\)
\(558\) 0 0
\(559\) 6098.10 0.461399
\(560\) 0 0
\(561\) 2127.22 17213.8i 0.160092 1.29549i
\(562\) 0 0
\(563\) 8086.82 14006.8i 0.605362 1.04852i −0.386632 0.922234i \(-0.626362\pi\)
0.991994 0.126284i \(-0.0403050\pi\)
\(564\) 0 0
\(565\) 1599.32 + 2770.11i 0.119087 + 0.206264i
\(566\) 0 0
\(567\) 19732.9 + 10571.3i 1.46156 + 0.782984i
\(568\) 0 0
\(569\) 4548.76 + 7878.69i 0.335139 + 0.580478i 0.983512 0.180845i \(-0.0578834\pi\)
−0.648372 + 0.761323i \(0.724550\pi\)
\(570\) 0 0
\(571\) 1647.54 2853.63i 0.120749 0.209143i −0.799314 0.600913i \(-0.794804\pi\)
0.920063 + 0.391770i \(0.128137\pi\)
\(572\) 0 0
\(573\) 195.194 1579.54i 0.0142310 0.115159i
\(574\) 0 0
\(575\) −5240.73 −0.380093
\(576\) 0 0
\(577\) 15544.7 1.12155 0.560775 0.827968i \(-0.310503\pi\)
0.560775 + 0.827968i \(0.310503\pi\)
\(578\) 0 0
\(579\) −8193.04 + 3470.20i −0.588067 + 0.249079i
\(580\) 0 0
\(581\) 2684.76 4650.14i 0.191709 0.332049i
\(582\) 0 0
\(583\) −13798.4 23899.6i −0.980229 1.69781i
\(584\) 0 0
\(585\) 3182.51 3285.32i 0.224924 0.232190i
\(586\) 0 0
\(587\) 2344.33 + 4060.50i 0.164840 + 0.285511i 0.936598 0.350405i \(-0.113956\pi\)
−0.771759 + 0.635916i \(0.780623\pi\)
\(588\) 0 0
\(589\) −3160.25 + 5473.71i −0.221079 + 0.382921i
\(590\) 0 0
\(591\) 1093.40 + 825.275i 0.0761024 + 0.0574404i
\(592\) 0 0
\(593\) 16637.6 1.15215 0.576075 0.817397i \(-0.304584\pi\)
0.576075 + 0.817397i \(0.304584\pi\)
\(594\) 0 0
\(595\) −32321.1 −2.22695
\(596\) 0 0
\(597\) 15908.9 + 12007.7i 1.09063 + 0.823184i
\(598\) 0 0
\(599\) 2933.73 5081.37i 0.200115 0.346610i −0.748450 0.663191i \(-0.769202\pi\)
0.948565 + 0.316581i \(0.102535\pi\)
\(600\) 0 0
\(601\) −10337.9 17905.8i −0.701649 1.21529i −0.967887 0.251385i \(-0.919114\pi\)
0.266238 0.963907i \(-0.414219\pi\)
\(602\) 0 0
\(603\) 4259.72 + 1069.13i 0.287677 + 0.0722029i
\(604\) 0 0
\(605\) 4129.71 + 7152.87i 0.277515 + 0.480671i
\(606\) 0 0
\(607\) −6303.86 + 10918.6i −0.421525 + 0.730103i −0.996089 0.0883567i \(-0.971838\pi\)
0.574564 + 0.818460i \(0.305172\pi\)
\(608\) 0 0
\(609\) −13632.0 + 5773.90i −0.907056 + 0.384188i
\(610\) 0 0
\(611\) 3447.97 0.228298
\(612\) 0 0
\(613\) 12469.7 0.821608 0.410804 0.911724i \(-0.365248\pi\)
0.410804 + 0.911724i \(0.365248\pi\)
\(614\) 0 0
\(615\) −2960.39 + 23955.9i −0.194104 + 1.57072i
\(616\) 0 0
\(617\) −9293.48 + 16096.8i −0.606388 + 1.05030i 0.385442 + 0.922732i \(0.374049\pi\)
−0.991830 + 0.127563i \(0.959284\pi\)
\(618\) 0 0
\(619\) 5972.96 + 10345.5i 0.387841 + 0.671761i 0.992159 0.124983i \(-0.0398876\pi\)
−0.604318 + 0.796743i \(0.706554\pi\)
\(620\) 0 0
\(621\) −6922.00 8588.98i −0.447295 0.555014i
\(622\) 0 0
\(623\) −5169.94 8954.60i −0.332471 0.575856i
\(624\) 0 0
\(625\) 9757.00 16899.6i 0.624448 1.08158i
\(626\) 0 0
\(627\) −1236.09 + 10002.7i −0.0787318 + 0.637110i
\(628\) 0 0
\(629\) −2468.96 −0.156509
\(630\) 0 0
\(631\) 4285.35 0.270360 0.135180 0.990821i \(-0.456839\pi\)
0.135180 + 0.990821i \(0.456839\pi\)
\(632\) 0 0
\(633\) −19470.4 + 8246.76i −1.22256 + 0.517819i
\(634\) 0 0
\(635\) 11872.7 20564.0i 0.741972 1.28513i
\(636\) 0 0
\(637\) 3671.00 + 6358.36i 0.228336 + 0.395490i
\(638\) 0 0
\(639\) 3208.73 + 11256.4i 0.198647 + 0.696866i
\(640\) 0 0
\(641\) 10879.1 + 18843.2i 0.670357 + 1.16109i 0.977803 + 0.209527i \(0.0671925\pi\)
−0.307446 + 0.951566i \(0.599474\pi\)
\(642\) 0 0
\(643\) 3671.54 6359.30i 0.225181 0.390025i −0.731193 0.682171i \(-0.761036\pi\)
0.956374 + 0.292146i \(0.0943692\pi\)
\(644\) 0 0
\(645\) −28612.2 21595.8i −1.74667 1.31835i
\(646\) 0 0
\(647\) 9483.24 0.576236 0.288118 0.957595i \(-0.406970\pi\)
0.288118 + 0.957595i \(0.406970\pi\)
\(648\) 0 0
\(649\) −22156.6 −1.34010
\(650\) 0 0
\(651\) 18220.6 + 13752.5i 1.09696 + 0.827962i
\(652\) 0 0
\(653\) −2392.09 + 4143.23i −0.143353 + 0.248295i −0.928757 0.370688i \(-0.879122\pi\)
0.785404 + 0.618984i \(0.212455\pi\)
\(654\) 0 0
\(655\) 9226.05 + 15980.0i 0.550369 + 0.953266i
\(656\) 0 0
\(657\) −4660.45 16349.1i −0.276745 0.970838i
\(658\) 0 0
\(659\) 16034.0 + 27771.6i 0.947791 + 1.64162i 0.750064 + 0.661365i \(0.230023\pi\)
0.197727 + 0.980257i \(0.436644\pi\)
\(660\) 0 0
\(661\) 3762.64 6517.09i 0.221407 0.383488i −0.733829 0.679335i \(-0.762269\pi\)
0.955235 + 0.295847i \(0.0956019\pi\)
\(662\) 0 0
\(663\) −4451.49 + 1885.45i −0.260756 + 0.110445i
\(664\) 0 0
\(665\) 18781.3 1.09520
\(666\) 0 0
\(667\) 7295.07 0.423487
\(668\) 0 0
\(669\) −3923.16 + 31746.8i −0.226723 + 1.83468i
\(670\) 0 0
\(671\) 8164.08 14140.6i 0.469703 0.813550i
\(672\) 0 0
\(673\) 3670.98 + 6358.32i 0.210261 + 0.364183i 0.951796 0.306731i \(-0.0992352\pi\)
−0.741535 + 0.670914i \(0.765902\pi\)
\(674\) 0 0
\(675\) −9239.43 + 1441.23i −0.526853 + 0.0821819i
\(676\) 0 0
\(677\) −4760.52 8245.45i −0.270253 0.468092i 0.698673 0.715441i \(-0.253774\pi\)
−0.968927 + 0.247348i \(0.920441\pi\)
\(678\) 0 0
\(679\) −1294.63 + 2242.36i −0.0731713 + 0.126736i
\(680\) 0 0
\(681\) −15.4612 + 125.114i −0.000870006 + 0.00704022i
\(682\) 0 0
\(683\) −1475.06 −0.0826377 −0.0413188 0.999146i \(-0.513156\pi\)
−0.0413188 + 0.999146i \(0.513156\pi\)
\(684\) 0 0
\(685\) −34872.5 −1.94512
\(686\) 0 0
\(687\) −3025.91 + 1281.64i −0.168043 + 0.0711755i
\(688\) 0 0
\(689\) −3845.89 + 6661.28i −0.212651 + 0.368323i
\(690\) 0 0
\(691\) −17080.4 29584.0i −0.940329 1.62870i −0.764844 0.644215i \(-0.777184\pi\)
−0.175484 0.984482i \(-0.556149\pi\)
\(692\) 0 0
\(693\) 35306.9 + 8861.53i 1.93535 + 0.485746i
\(694\) 0 0
\(695\) 4311.56 + 7467.84i 0.235319 + 0.407585i
\(696\) 0 0
\(697\) 12755.9 22093.8i 0.693205 1.20067i
\(698\) 0 0
\(699\) 13120.7 + 9903.19i 0.709970 + 0.535870i
\(700\) 0 0
\(701\) −29427.2 −1.58552 −0.792759 0.609535i \(-0.791356\pi\)
−0.792759 + 0.609535i \(0.791356\pi\)
\(702\) 0 0
\(703\) 1434.67 0.0769696
\(704\) 0 0
\(705\) −16177.8 12210.7i −0.864244 0.652312i
\(706\) 0 0
\(707\) 26866.5 46534.1i 1.42916 2.47538i
\(708\) 0 0
\(709\) −9846.43 17054.5i −0.521566 0.903379i −0.999685 0.0250840i \(-0.992015\pi\)
0.478119 0.878295i \(-0.341319\pi\)
\(710\) 0 0
\(711\) 3244.91 3349.73i 0.171159 0.176687i
\(712\) 0 0
\(713\) −5624.42 9741.79i −0.295423 0.511687i
\(714\) 0 0
\(715\) 3718.90 6441.32i 0.194516 0.336912i
\(716\) 0 0
\(717\) 10627.4 4501.30i 0.553541 0.234455i
\(718\) 0 0
\(719\) −33746.9 −1.75041 −0.875206 0.483751i \(-0.839274\pi\)
−0.875206 + 0.483751i \(0.839274\pi\)
\(720\) 0 0
\(721\) 3420.74 0.176692
\(722\) 0 0
\(723\) 383.295 3101.68i 0.0197163 0.159547i
\(724\) 0 0
\(725\) 3092.05 5355.60i 0.158395 0.274347i
\(726\) 0 0
\(727\) −10380.4 17979.4i −0.529558 0.917221i −0.999406 0.0344737i \(-0.989025\pi\)
0.469848 0.882748i \(-0.344309\pi\)
\(728\) 0 0
\(729\) −14565.5 13238.8i −0.740005 0.672602i
\(730\) 0 0
\(731\) 18943.7 + 32811.4i 0.958492 + 1.66016i
\(732\) 0 0
\(733\) −7122.02 + 12335.7i −0.358878 + 0.621596i −0.987774 0.155894i \(-0.950174\pi\)
0.628895 + 0.777490i \(0.283507\pi\)
\(734\) 0 0
\(735\) 5293.24 42833.8i 0.265638 2.14959i
\(736\) 0 0
\(737\) 7141.55 0.356937
\(738\) 0 0
\(739\) 27490.2 1.36839 0.684196 0.729298i \(-0.260153\pi\)
0.684196 + 0.729298i \(0.260153\pi\)
\(740\) 0 0
\(741\) 2586.69 1095.60i 0.128238 0.0543157i
\(742\) 0 0
\(743\) −18234.0 + 31582.3i −0.900326 + 1.55941i −0.0732537 + 0.997313i \(0.523338\pi\)
−0.827072 + 0.562096i \(0.809995\pi\)
\(744\) 0 0
\(745\) 16674.6 + 28881.2i 0.820013 + 1.42030i
\(746\) 0 0
\(747\) −3284.88 + 3390.99i −0.160894 + 0.166091i
\(748\) 0 0
\(749\) −13749.8 23815.4i −0.670771 1.16181i
\(750\) 0 0
\(751\) −19341.5 + 33500.5i −0.939791 + 1.62777i −0.173931 + 0.984758i \(0.555647\pi\)
−0.765860 + 0.643007i \(0.777686\pi\)
\(752\) 0 0
\(753\) −5601.92 4228.20i −0.271109 0.204627i
\(754\) 0 0
\(755\) −936.449 −0.0451402
\(756\) 0 0
\(757\) 37768.4 1.81337 0.906683 0.421813i \(-0.138606\pi\)
0.906683 + 0.421813i \(0.138606\pi\)
\(758\) 0 0
\(759\) −14317.2 10806.3i −0.684690 0.516789i
\(760\) 0 0
\(761\) 10406.6 18024.7i 0.495714 0.858603i −0.504273 0.863544i \(-0.668240\pi\)
0.999988 + 0.00494154i \(0.00157295\pi\)
\(762\) 0 0
\(763\) 11008.2 + 19066.7i 0.522310 + 0.904667i
\(764\) 0 0
\(765\) 27563.4 + 6918.03i 1.30269 + 0.326957i
\(766\) 0 0
\(767\) 3087.74 + 5348.12i 0.145361 + 0.251772i
\(768\) 0 0
\(769\) −3060.85 + 5301.55i −0.143533 + 0.248607i −0.928825 0.370519i \(-0.879180\pi\)
0.785291 + 0.619126i \(0.212513\pi\)
\(770\) 0 0
\(771\) −33702.7 + 14275.0i −1.57429 + 0.666796i
\(772\) 0 0
\(773\) −34251.2 −1.59370 −0.796850 0.604177i \(-0.793502\pi\)
−0.796850 + 0.604177i \(0.793502\pi\)
\(774\) 0 0
\(775\) −9535.78 −0.441981
\(776\) 0 0
\(777\) 635.500 5142.56i 0.0293416 0.237437i
\(778\) 0 0
\(779\) −7412.23 + 12838.4i −0.340912 + 0.590478i
\(780\) 0 0
\(781\) 9516.59 + 16483.2i 0.436018 + 0.755206i
\(782\) 0 0
\(783\) 12861.2 2006.18i 0.587002 0.0915644i
\(784\) 0 0
\(785\) −30.4117 52.6746i −0.00138273 0.00239495i
\(786\) 0